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Slide 1 70
Electric Currents amp DC Circuits
Slide 2 70
1 The length of an aluminum wire is quadrupled and the radius is doubled By which factor does the resistance change
A 2B 4C 12D 14E 1
Slide 3 70
2 A copper wire has a length L and cross-sectional area A What happens to the resistivity of the wire if the length is doubled and cross-sectional area halved
A Four times as largeB Two times as largeC Stays the sameD Half as largeE Quarter as large
Slide 4 70
3 Which circuit has greater resistance between the terminals
A AB BC CD DE C and D
Slide 5 70
4 Which circuits have the same resistance between the terminals
A A and BB B and CC C and DD D and AE C and A
Slide 6 70
5 In the circuit shown above what is the value of the net resistance
A 1 ΩB 2 ΩC 3 ΩD 4 ΩE 6 Ω
Slide 7 70
6 What is the current in 4 - Ω resistor
A 1AB 2AC 3AD 4AE 5A
Slide 8 70
7 What is the voltage between points L and M
A 2 VB 3 VC 4 VD 3 VE 5 V
Slide 9 70
8 A lamp L1 a voltmeter V an ammeter A and a battery with zero internal resistance are connected as shown above Connecting another lamp L2 in series with the first lamp as shown by the dashed lines would
A Increase the ammeter reading
B Decrease the ammeter reading
C Increase the voltmeter reading
D Decrease the voltmeter reading
E Produce no change in either meter reading
Slide 10 70
9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation
ABCDE
Slide 11 70
10 Which circuit will retain stored energy if the battery is connected to it and then disconnected
A AB BC CD DE E
Slide 12 70
A AB BC CD DE E
11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance
Slide 13 70
12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2
A 49B 23C 31D 32E 94
Slide 14 70
13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery
A 5 VB 8 VC 10 VD 20 VE 40 V
Slide 15 70
14 The total equivalent resistance of the circuit shown on the diagram is
A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω
Slide 16 70
15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is
A VrtB V2RtC VR2tD VRt2
E V2tR
Slide 17 70
16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A
A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω
Slide 18 70
17 The equivalent capacitance for this network is
A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF
Slide 19 70
18 The charge stored in the circuit is
A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 2 70
1 The length of an aluminum wire is quadrupled and the radius is doubled By which factor does the resistance change
A 2B 4C 12D 14E 1
Slide 3 70
2 A copper wire has a length L and cross-sectional area A What happens to the resistivity of the wire if the length is doubled and cross-sectional area halved
A Four times as largeB Two times as largeC Stays the sameD Half as largeE Quarter as large
Slide 4 70
3 Which circuit has greater resistance between the terminals
A AB BC CD DE C and D
Slide 5 70
4 Which circuits have the same resistance between the terminals
A A and BB B and CC C and DD D and AE C and A
Slide 6 70
5 In the circuit shown above what is the value of the net resistance
A 1 ΩB 2 ΩC 3 ΩD 4 ΩE 6 Ω
Slide 7 70
6 What is the current in 4 - Ω resistor
A 1AB 2AC 3AD 4AE 5A
Slide 8 70
7 What is the voltage between points L and M
A 2 VB 3 VC 4 VD 3 VE 5 V
Slide 9 70
8 A lamp L1 a voltmeter V an ammeter A and a battery with zero internal resistance are connected as shown above Connecting another lamp L2 in series with the first lamp as shown by the dashed lines would
A Increase the ammeter reading
B Decrease the ammeter reading
C Increase the voltmeter reading
D Decrease the voltmeter reading
E Produce no change in either meter reading
Slide 10 70
9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation
ABCDE
Slide 11 70
10 Which circuit will retain stored energy if the battery is connected to it and then disconnected
A AB BC CD DE E
Slide 12 70
A AB BC CD DE E
11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance
Slide 13 70
12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2
A 49B 23C 31D 32E 94
Slide 14 70
13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery
A 5 VB 8 VC 10 VD 20 VE 40 V
Slide 15 70
14 The total equivalent resistance of the circuit shown on the diagram is
A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω
Slide 16 70
15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is
A VrtB V2RtC VR2tD VRt2
E V2tR
Slide 17 70
16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A
A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω
Slide 18 70
17 The equivalent capacitance for this network is
A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF
Slide 19 70
18 The charge stored in the circuit is
A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 3 70
2 A copper wire has a length L and cross-sectional area A What happens to the resistivity of the wire if the length is doubled and cross-sectional area halved
A Four times as largeB Two times as largeC Stays the sameD Half as largeE Quarter as large
Slide 4 70
3 Which circuit has greater resistance between the terminals
A AB BC CD DE C and D
Slide 5 70
4 Which circuits have the same resistance between the terminals
A A and BB B and CC C and DD D and AE C and A
Slide 6 70
5 In the circuit shown above what is the value of the net resistance
A 1 ΩB 2 ΩC 3 ΩD 4 ΩE 6 Ω
Slide 7 70
6 What is the current in 4 - Ω resistor
A 1AB 2AC 3AD 4AE 5A
Slide 8 70
7 What is the voltage between points L and M
A 2 VB 3 VC 4 VD 3 VE 5 V
Slide 9 70
8 A lamp L1 a voltmeter V an ammeter A and a battery with zero internal resistance are connected as shown above Connecting another lamp L2 in series with the first lamp as shown by the dashed lines would
A Increase the ammeter reading
B Decrease the ammeter reading
C Increase the voltmeter reading
D Decrease the voltmeter reading
E Produce no change in either meter reading
Slide 10 70
9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation
ABCDE
Slide 11 70
10 Which circuit will retain stored energy if the battery is connected to it and then disconnected
A AB BC CD DE E
Slide 12 70
A AB BC CD DE E
11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance
Slide 13 70
12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2
A 49B 23C 31D 32E 94
Slide 14 70
13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery
A 5 VB 8 VC 10 VD 20 VE 40 V
Slide 15 70
14 The total equivalent resistance of the circuit shown on the diagram is
A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω
Slide 16 70
15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is
A VrtB V2RtC VR2tD VRt2
E V2tR
Slide 17 70
16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A
A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω
Slide 18 70
17 The equivalent capacitance for this network is
A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF
Slide 19 70
18 The charge stored in the circuit is
A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 4 70
3 Which circuit has greater resistance between the terminals
A AB BC CD DE C and D
Slide 5 70
4 Which circuits have the same resistance between the terminals
A A and BB B and CC C and DD D and AE C and A
Slide 6 70
5 In the circuit shown above what is the value of the net resistance
A 1 ΩB 2 ΩC 3 ΩD 4 ΩE 6 Ω
Slide 7 70
6 What is the current in 4 - Ω resistor
A 1AB 2AC 3AD 4AE 5A
Slide 8 70
7 What is the voltage between points L and M
A 2 VB 3 VC 4 VD 3 VE 5 V
Slide 9 70
8 A lamp L1 a voltmeter V an ammeter A and a battery with zero internal resistance are connected as shown above Connecting another lamp L2 in series with the first lamp as shown by the dashed lines would
A Increase the ammeter reading
B Decrease the ammeter reading
C Increase the voltmeter reading
D Decrease the voltmeter reading
E Produce no change in either meter reading
Slide 10 70
9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation
ABCDE
Slide 11 70
10 Which circuit will retain stored energy if the battery is connected to it and then disconnected
A AB BC CD DE E
Slide 12 70
A AB BC CD DE E
11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance
Slide 13 70
12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2
A 49B 23C 31D 32E 94
Slide 14 70
13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery
A 5 VB 8 VC 10 VD 20 VE 40 V
Slide 15 70
14 The total equivalent resistance of the circuit shown on the diagram is
A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω
Slide 16 70
15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is
A VrtB V2RtC VR2tD VRt2
E V2tR
Slide 17 70
16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A
A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω
Slide 18 70
17 The equivalent capacitance for this network is
A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF
Slide 19 70
18 The charge stored in the circuit is
A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 5 70
4 Which circuits have the same resistance between the terminals
A A and BB B and CC C and DD D and AE C and A
Slide 6 70
5 In the circuit shown above what is the value of the net resistance
A 1 ΩB 2 ΩC 3 ΩD 4 ΩE 6 Ω
Slide 7 70
6 What is the current in 4 - Ω resistor
A 1AB 2AC 3AD 4AE 5A
Slide 8 70
7 What is the voltage between points L and M
A 2 VB 3 VC 4 VD 3 VE 5 V
Slide 9 70
8 A lamp L1 a voltmeter V an ammeter A and a battery with zero internal resistance are connected as shown above Connecting another lamp L2 in series with the first lamp as shown by the dashed lines would
A Increase the ammeter reading
B Decrease the ammeter reading
C Increase the voltmeter reading
D Decrease the voltmeter reading
E Produce no change in either meter reading
Slide 10 70
9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation
ABCDE
Slide 11 70
10 Which circuit will retain stored energy if the battery is connected to it and then disconnected
A AB BC CD DE E
Slide 12 70
A AB BC CD DE E
11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance
Slide 13 70
12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2
A 49B 23C 31D 32E 94
Slide 14 70
13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery
A 5 VB 8 VC 10 VD 20 VE 40 V
Slide 15 70
14 The total equivalent resistance of the circuit shown on the diagram is
A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω
Slide 16 70
15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is
A VrtB V2RtC VR2tD VRt2
E V2tR
Slide 17 70
16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A
A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω
Slide 18 70
17 The equivalent capacitance for this network is
A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF
Slide 19 70
18 The charge stored in the circuit is
A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 6 70
5 In the circuit shown above what is the value of the net resistance
A 1 ΩB 2 ΩC 3 ΩD 4 ΩE 6 Ω
Slide 7 70
6 What is the current in 4 - Ω resistor
A 1AB 2AC 3AD 4AE 5A
Slide 8 70
7 What is the voltage between points L and M
A 2 VB 3 VC 4 VD 3 VE 5 V
Slide 9 70
8 A lamp L1 a voltmeter V an ammeter A and a battery with zero internal resistance are connected as shown above Connecting another lamp L2 in series with the first lamp as shown by the dashed lines would
A Increase the ammeter reading
B Decrease the ammeter reading
C Increase the voltmeter reading
D Decrease the voltmeter reading
E Produce no change in either meter reading
Slide 10 70
9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation
ABCDE
Slide 11 70
10 Which circuit will retain stored energy if the battery is connected to it and then disconnected
A AB BC CD DE E
Slide 12 70
A AB BC CD DE E
11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance
Slide 13 70
12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2
A 49B 23C 31D 32E 94
Slide 14 70
13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery
A 5 VB 8 VC 10 VD 20 VE 40 V
Slide 15 70
14 The total equivalent resistance of the circuit shown on the diagram is
A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω
Slide 16 70
15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is
A VrtB V2RtC VR2tD VRt2
E V2tR
Slide 17 70
16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A
A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω
Slide 18 70
17 The equivalent capacitance for this network is
A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF
Slide 19 70
18 The charge stored in the circuit is
A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 7 70
6 What is the current in 4 - Ω resistor
A 1AB 2AC 3AD 4AE 5A
Slide 8 70
7 What is the voltage between points L and M
A 2 VB 3 VC 4 VD 3 VE 5 V
Slide 9 70
8 A lamp L1 a voltmeter V an ammeter A and a battery with zero internal resistance are connected as shown above Connecting another lamp L2 in series with the first lamp as shown by the dashed lines would
A Increase the ammeter reading
B Decrease the ammeter reading
C Increase the voltmeter reading
D Decrease the voltmeter reading
E Produce no change in either meter reading
Slide 10 70
9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation
ABCDE
Slide 11 70
10 Which circuit will retain stored energy if the battery is connected to it and then disconnected
A AB BC CD DE E
Slide 12 70
A AB BC CD DE E
11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance
Slide 13 70
12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2
A 49B 23C 31D 32E 94
Slide 14 70
13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery
A 5 VB 8 VC 10 VD 20 VE 40 V
Slide 15 70
14 The total equivalent resistance of the circuit shown on the diagram is
A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω
Slide 16 70
15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is
A VrtB V2RtC VR2tD VRt2
E V2tR
Slide 17 70
16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A
A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω
Slide 18 70
17 The equivalent capacitance for this network is
A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF
Slide 19 70
18 The charge stored in the circuit is
A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 8 70
7 What is the voltage between points L and M
A 2 VB 3 VC 4 VD 3 VE 5 V
Slide 9 70
8 A lamp L1 a voltmeter V an ammeter A and a battery with zero internal resistance are connected as shown above Connecting another lamp L2 in series with the first lamp as shown by the dashed lines would
A Increase the ammeter reading
B Decrease the ammeter reading
C Increase the voltmeter reading
D Decrease the voltmeter reading
E Produce no change in either meter reading
Slide 10 70
9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation
ABCDE
Slide 11 70
10 Which circuit will retain stored energy if the battery is connected to it and then disconnected
A AB BC CD DE E
Slide 12 70
A AB BC CD DE E
11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance
Slide 13 70
12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2
A 49B 23C 31D 32E 94
Slide 14 70
13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery
A 5 VB 8 VC 10 VD 20 VE 40 V
Slide 15 70
14 The total equivalent resistance of the circuit shown on the diagram is
A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω
Slide 16 70
15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is
A VrtB V2RtC VR2tD VRt2
E V2tR
Slide 17 70
16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A
A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω
Slide 18 70
17 The equivalent capacitance for this network is
A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF
Slide 19 70
18 The charge stored in the circuit is
A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 9 70
8 A lamp L1 a voltmeter V an ammeter A and a battery with zero internal resistance are connected as shown above Connecting another lamp L2 in series with the first lamp as shown by the dashed lines would
A Increase the ammeter reading
B Decrease the ammeter reading
C Increase the voltmeter reading
D Decrease the voltmeter reading
E Produce no change in either meter reading
Slide 10 70
9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation
ABCDE
Slide 11 70
10 Which circuit will retain stored energy if the battery is connected to it and then disconnected
A AB BC CD DE E
Slide 12 70
A AB BC CD DE E
11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance
Slide 13 70
12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2
A 49B 23C 31D 32E 94
Slide 14 70
13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery
A 5 VB 8 VC 10 VD 20 VE 40 V
Slide 15 70
14 The total equivalent resistance of the circuit shown on the diagram is
A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω
Slide 16 70
15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is
A VrtB V2RtC VR2tD VRt2
E V2tR
Slide 17 70
16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A
A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω
Slide 18 70
17 The equivalent capacitance for this network is
A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF
Slide 19 70
18 The charge stored in the circuit is
A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 10 70
9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation
ABCDE
Slide 11 70
10 Which circuit will retain stored energy if the battery is connected to it and then disconnected
A AB BC CD DE E
Slide 12 70
A AB BC CD DE E
11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance
Slide 13 70
12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2
A 49B 23C 31D 32E 94
Slide 14 70
13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery
A 5 VB 8 VC 10 VD 20 VE 40 V
Slide 15 70
14 The total equivalent resistance of the circuit shown on the diagram is
A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω
Slide 16 70
15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is
A VrtB V2RtC VR2tD VRt2
E V2tR
Slide 17 70
16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A
A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω
Slide 18 70
17 The equivalent capacitance for this network is
A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF
Slide 19 70
18 The charge stored in the circuit is
A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 11 70
10 Which circuit will retain stored energy if the battery is connected to it and then disconnected
A AB BC CD DE E
Slide 12 70
A AB BC CD DE E
11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance
Slide 13 70
12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2
A 49B 23C 31D 32E 94
Slide 14 70
13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery
A 5 VB 8 VC 10 VD 20 VE 40 V
Slide 15 70
14 The total equivalent resistance of the circuit shown on the diagram is
A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω
Slide 16 70
15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is
A VrtB V2RtC VR2tD VRt2
E V2tR
Slide 17 70
16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A
A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω
Slide 18 70
17 The equivalent capacitance for this network is
A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF
Slide 19 70
18 The charge stored in the circuit is
A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 12 70
A AB BC CD DE E
11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance
Slide 13 70
12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2
A 49B 23C 31D 32E 94
Slide 14 70
13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery
A 5 VB 8 VC 10 VD 20 VE 40 V
Slide 15 70
14 The total equivalent resistance of the circuit shown on the diagram is
A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω
Slide 16 70
15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is
A VrtB V2RtC VR2tD VRt2
E V2tR
Slide 17 70
16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A
A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω
Slide 18 70
17 The equivalent capacitance for this network is
A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF
Slide 19 70
18 The charge stored in the circuit is
A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 13 70
12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2
A 49B 23C 31D 32E 94
Slide 14 70
13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery
A 5 VB 8 VC 10 VD 20 VE 40 V
Slide 15 70
14 The total equivalent resistance of the circuit shown on the diagram is
A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω
Slide 16 70
15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is
A VrtB V2RtC VR2tD VRt2
E V2tR
Slide 17 70
16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A
A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω
Slide 18 70
17 The equivalent capacitance for this network is
A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF
Slide 19 70
18 The charge stored in the circuit is
A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 14 70
13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery
A 5 VB 8 VC 10 VD 20 VE 40 V
Slide 15 70
14 The total equivalent resistance of the circuit shown on the diagram is
A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω
Slide 16 70
15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is
A VrtB V2RtC VR2tD VRt2
E V2tR
Slide 17 70
16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A
A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω
Slide 18 70
17 The equivalent capacitance for this network is
A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF
Slide 19 70
18 The charge stored in the circuit is
A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 15 70
14 The total equivalent resistance of the circuit shown on the diagram is
A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω
Slide 16 70
15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is
A VrtB V2RtC VR2tD VRt2
E V2tR
Slide 17 70
16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A
A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω
Slide 18 70
17 The equivalent capacitance for this network is
A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF
Slide 19 70
18 The charge stored in the circuit is
A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 16 70
15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is
A VrtB V2RtC VR2tD VRt2
E V2tR
Slide 17 70
16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A
A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω
Slide 18 70
17 The equivalent capacitance for this network is
A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF
Slide 19 70
18 The charge stored in the circuit is
A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 17 70
16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A
A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω
Slide 18 70
17 The equivalent capacitance for this network is
A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF
Slide 19 70
18 The charge stored in the circuit is
A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 18 70
17 The equivalent capacitance for this network is
A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF
Slide 19 70
18 The charge stored in the circuit is
A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 19 70
18 The charge stored in the circuit is
A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 20 70
19 What is the emf of the battery
A 2 VB 4 VC 36 VD 12 VE 18 V
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 21 70
20 What is the potential difference across the terminals A and B of the battery
A 12 VB 24 VC 36 VD 122 VE 184 V
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 22 70
21 What power is dissipated by the 2-ohm internal resistance of the battery
A 006 WB 12 WC 32 WD 008 WE 48 W
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 23 70
22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare
A It is greater for the series connection
B It is greater for the parallel connection
C It is the same for both connections
D It is different for each connection but one must know the values of R1 and R2 to know which is greater
E It is different for each connection but one must know the value of ε to know which is greater
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 24 70
23 The product 3 amperes x3 volts x 3 seconds is equal to
A 27 CB 27 NC 27 JD 27 WE 27 NA
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 25 70
24 The electrical resistance of the part of the circuit shown between point X and point Y is
A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 26 70
25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is
A the same everywhere in the circuit
B greater at point X than at point Y
C greater in the 2 Ω resistor than in the 5 Ω resistor
D the same in the 2 Ω resistor and in the 5 Ω resistor
E greater in the 3 Ω resistor than in the 5 Ω resistor
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 27 70
26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours
A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 28 70
27 What is the net capacitance of the circuit
A 3CB 2CC 32 CD 23 CE C
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 29 70
28 What is the net charge stored in the circuit
A CVB 3CV2C 2CV3D CV2E CV3
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 30 70
29 What is the potential difference between the points X and Y
A VB 13 VC 12 VD 23 VE 32 V
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 31 70
30 What is the net resistance of the circuit
A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 32 70
31 What is the current in the light bulb L1
A 1 AB 2 AC 3 AD 4 AE 5 A
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 33 70
32 Which light bulb or bulbs could burn out without causing others to go out
A Only L1
B Only L2
C Only L3 and L4
D Only L4
E Only L5
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 34 70
33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open
A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 35 70
Free Response
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 36 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
b When the switch is closed what is the current running through the battery
c What is the terminal voltage on the battery
d What is the rate of energy delivered by the heating system
e If the switch is closed for 5 min what is the total energy dissipated in the coils
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 37 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 38 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
First find the equivalent resistance
1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω
Req = R + rReq = 865Ω + 05Ω
Req = 915Ω
Then find the current
I = VRI = 12V 915 Ω = 13 A
c When the switch is closed what is the current running through the battery
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 39 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
c What is the terminal voltage on the battery
VT = E - Ir
VT = 12V - (13A)(05Ω)
VT = 1135 V
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 40 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
d What is the rate of energy delivered by the heating system
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
P1 = V12R1
P1 = (1135 V)2(865Ω)
P1 = 149 W
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 41 70
1 A physics student has an assignment to make an electrical heating system with the set of materials listed below
e If the switch is closed for 5 min what is the total energy dissipated in the coils
The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω
W = Pt
W = (149 W)(300 s)
W = 4470 J
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 42 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
b Calculate the net resistance of the circuit
c Calculate the power dissipated in the circuit
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 43 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
a Use given materials design an electric circuit in which the electric motor will operate properly
i Draw the circuit including all devices
ii Explain your reasoning in designing this particular circuit
12V
motorRmotor = 6V05A = 12 Ω
Req = 12V05A = 24 Ω
6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 44 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
b Calculate the net resistance of the circuit
Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 45 70
2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors
c Calculate the power dissipated in the circuit
P = I V = (05A)(12V) = 6 W
P = (05A)(12V) = 6 W
P = 6 W
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 46 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
b What is the power dissipated by the circuit
c How would you compare this power to the power when all bulbs are connected in parallel
d What is the current in light bulb L1
e What is the voltage across light bulb L1
f What is the voltage across light bulb L2
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 47 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
a What is the resistance of the circuit
P = V2R
R = V2P
R = (120V)2(75W)
R = 192 Ω for each light bulb
Req2amp3 = 96Ω
Rcircuit = 192Ω + 96Ω = 288Ω
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 48 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
b What is the power dissipated by the circuit
P = V2R
P = (120V)2288Ω
P = 50W
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 49 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
c How would you compare this power to the power when all bulbs are connected in parallel
This power is less
The power for bulbs connected in series is
P = 3(75W)
P = 225 W
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 50 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
d What is the current in light bulb L1
I1 = V1R1
I1 = 120V288Ω = 042A
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 51 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
e What is the voltage across light bulb L1
V = IR
V = (042A)(192Ω)
V = 80V
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 52 70
3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply
f What is the voltage across light bulb L2
V = IR
V = (042A)(96Ω)
V = 40V
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 53 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
b What is the voltage drop across 6-Ω resistor
c What is the current in 4-Ω resistor
d What is the emf of the battery
e What is the net power dissipation
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 54 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
a What is the net resistance of the circuit
Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω
Whole circuit
Req = 96Ω + 24Ω + 12Ω
Req = 24Ω
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 55 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
b What is the voltage drop across 6-Ω resistor
V = IR
V = (025A)(24Ω) = 06V
(24Ω is the equivalent resistance of the middle section)
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 56 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
c What is the current in 4-Ω resistor
I = VR
I = (06V)(4Ω)
I = 015A
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 57 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
d What is the emf of the battery
V = IR
V = (025A)(24Ω)
V = 6V
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 58 70
4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A
e What is the net power dissipation
P = IV
P = (025A)(6V)
P = 15 W
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 59 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
b Calculate the current in the battery
c Calculate the terminal voltage of the battery
d Calculate the power dissipation in the 3-Ω resistor
e Calculate the power dissipation in the internal resistance
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 60 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
a Calculate the external resistance of the circuit
Top part 2Ω + 4Ω = 6Ω
Middle 13Ω + 16Ω = 36Ω Req = 2Ω
Whole circuit
Req = 4Ω + 2Ω + 2Ω = 8Ω
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 61 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
b Calculate the current in the battery
I = VR
I = (12V)(8Ω+1Ω)
I = 13A
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 62 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
c Calculate the terminal voltage of the battery
VT = E - Ir
VT = 12V - (13A)(1Ω)
VT = 117 V
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 63 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
d Calculate the power dissipation in the 3-Ω resistor
Find the potential difference across the two side resistors
V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V
Find the potential difference across the 3Ω resistor
V3 = 117V - 52V - 26V = 39V
Find the power dissipation in the 3Ω resistor
P = V2R = (39V)2(3Ω) = 51W
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 64 70
5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω
e Calculate the power dissipation in the internal resistance
P = I2R
P = (13A)2(1Ω)
P = 17W
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 65 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
b Calculate the current in the 2-Ω resistor
c Calculate the current in the 3-Ω resistor
Switch is closed and the current reached constant value
d Calculate the charge on the capacitor
e Calculate the energy stored in the capacitor
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 66 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
a Calculate the net resistance of the circuit
Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω
Calculate Req of the previous branch and the 6Ω resistor
112Ω + 16Ω = 312Ω Req = 4Ω
Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 67 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
b Calculate the current in the 2-Ω resistor
Current in the 2Ω resistor is the same as the current in the battery
I = VR
I = (18V)(6Ω)
I = 3A
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 68 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
c Calculate the current in the 3-Ω resistor
Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V
Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V
Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 69 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value
d Calculate the charge on the capacitor
Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor
V = IR = (1A)(9Ω) = 9V
Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ
Slide 70 70
6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open
Switch is closed and the current reached constant value
e Calculate the energy stored in the capacitor
Uc = frac12CV2
Uc = frac12(2μF)(9V)2
Uc = 81μJ