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Potential Energy
If you do work against gravity, the gravitational field stores that energy as Gravitational Potential Energy, GPE
If you do work against an electrostatic force, the electric field stores that energy as electric Potential Energy, EPE
Low PE
High PE
Electric Potential Energy Electrostatic Force is conservative Electrical potential energy is
the energy contained in a configuration of charges.
Like all potential energies, when it goes up the configuration is less stable; when it goes down, the configuration is more stable.
The unit is the Joule.
Electric Potential EnergyElectrical potential energy increases when charges are brought into more unstable configurations.
+ + +
Lower PE Higher PE
dFe
+
Moving q1 closer to q2 requires work and that will increase the PE of the charge. Work against electric force increases electric PE
Stable Unstable
Electric Potential EnergyElectrical potential energy decreases when charges are brought into more stable configurations.
+ -
Higher PE Lower PE
d
Fe+ -
q1 will naturally move or fall towards q2 in the direction of E. No work is required and the PE of the charge will decrease. Work with the electric force decreases electric PE
StableUnstable
Electric Potential EnergyMoving a charge in an electric field requires work. This work stores potential energy.
Vq
U
q
W
UW
elel
elel
Electric Potential, V, is electric potential energy per charge. At every location, a charge has a position-dependent potential. Potential difference is simply the difference in electric potential at any 2 points
Electric PotentialUNITS: J/C or Volt
Electric energy provides the means to transfer large quantities of energy over great distances with little loss.
Producing Electric Energy
Because electric energy can so easily be changed into other forms, it has become indispensable in our daily lives.
Producing Electric Energy
Circuit
Low V
High V
Charges flow from high to low V through conducting wireThis flow of positive charge is called conventional current
The flow stops when the potential difference between A and B is zero.
A
B
Potential Difference and Current
Lower V
High V
To be a circuit, charges must flow continuously thru a loop, returning to their original position and cycling thru again. To do so requires energy input, a charge pump that raises the electric potential of the charge
Circuits require an electrical energy source – VOLTAGE SOURCE, DV
A circuit is simply a closed, conducting loop through which charges can continuously move
Flow of charge is CURRENT, I
Energy Pump +DV
1. Voltaic or galvanic cell converts chemical E to electric E.
A battery is made up of several galvanic cells connected together.
2. Photovoltaic cell, or solar cell—changes light energy into electric energy.
Producing Electric Current (Charge Pump)
Requirements of a Circuit1. Closed conducting loop
2. An energy source that maintains an electric potential difference, DV, across the ends of the circuit.
+-DV
Energy Source
Pumps charge from – to + terminal
maintains a DV across the circuit
Low VLow energy
High VHigh
energy
CurrentOnce the two requirements of a circuit are met, charge will flow.Rate of charge flow is called CURRENTElectric current is represented by I I = DQ/t
Unit of current:
Ampere (A)1 A = 1 C/s
Current A 2 mm long cross section of wire is isolated and 20 C of charge is determined to pass through it in 40 s.
I = _____________ A20C/40s = 0.5
Conventional Current DirectionCurrent is in the direction of + charge flow.
In reality, the particles that carry charge through a wire are mobile electrons which move in a direction opposite conventional current.
+-
I
DV
Vdrift ≈ 10-6 m/s or 1 m/hr (SLOW!!!)
DV
I = Q/t
The charge carriers are densely packed into the wire, so there does not have to be a high speed to have a high current. That is, the charge carriers do not have to travel a long distance in a second, there just has to be a lot of them passing through the cross section.
The amount of current in a circuit depends on BOTH the potential difference across the circuit, DV, AND the total resistance in the circuit, R.
Resistance
LOAD
Energy Source
II
An electron traveling through the wires and loads of a circuit encounters resistance, R. Resistance is a hindrance to the flow of charge.
DV
Flow rate depends on- pump pressure- resistance of pipe which depends on pipe length and diameter
Water Flow through pipe
Current depends on
- Voltage difference, DV- Resistance of circuit elements
Current through Circuit
ResistanceMaterials and elements in a circuit offer
resistance to the flow of charge.
A
LR
pHet Sim
A
L
Resistivity ( W m)Conductors: r ~10-8 WmInsulators: r ~1011-1016 Wm
d
L
d
2L
2d
L
2d
2L
ResistanceRank the following circuit elements from highest resistance to lowest resistance.
A.
B.
C.
D.
A > C > B > D
R
VI
Current flow does NOT depend only on voltage. Charge traveling through the wires and loads of a circuit encounters resistance, R. Resistance is a hindrance to the current. The higher the resistance, the smaller the current.
VI
To produce electric current, I, a potential difference, DV, is required. Simon Ohm established experimentally that the current in a metal wire is proportional to the potential difference applied to its ends.
Ohm’s Law
IRV ResistanceUnits: Ohms ( )W
CurrentUnits: Amperes ( )A
Electric potentialUnits: Volts (v)
Every element in a circuit obeys Ohm’s Law
In which circuit does the light bulb have highest resistance? What are the resistances of each bulb?
RA = ΔVA / I = 6/1 = 6 Ω RB = ΔVB / I = 6/2 = 3 Ω
A. B.
1A
+ -6 V
2A
+ -6 V
6V
6V
0V
0V
ΔVA = -6VΔVB = -6V
A
Which of the following will cause the current through an electrical circuit to decrease? Choose all that apply.
a. decrease the voltageb. decrease the resistancec. increase the voltaged. increase the resistance
Kirchoff’s Rules1. Junction Rule At any junction point
in a circuit, the sum of all the currents entering the junction must equal the sum of all currents leaving the junctionCurrent into junction = Current out of junction(Conservation of
charge)
I = I1 + I2
I
I2
I1I
R1
R2
outin II
4 A
10 A What is the current in the unknown wire and what are the directions of the currents?6 A
4 A
5 A
11 A
2 A
14 A AI
I
II outin
14
11524
?
Kirchoff’s Rules2. Loop Rule The sum of the potential
differences across all elements around any closed loop of a circuit must be zero. (Conservation of
energy) loop
V 0
+ -
R1
R2
R3
DVbat
DV is negative (voltage drop) across elements in the circuit.
DV is positive (voltage gain) across the battery.
+ -+6 V VV
VV
B
Bbat
6
0
VV
V
VVV
B
B
BBbat
3
026
0
Outer Loop
What is the voltage drop across each of the bulbs? The bulbs have the same resistance.
-6 V
-3 V -3 V
Inner Loop
Two Types of ConnectionsWhen there are 2 or more electrical devices in a circuit with an energy source, there are a couple of ways to connect them.
Series ConnectionWhen devices are in series, all of the current going through one device goes through the other 1 2 I
Device 1 and 2 are in series. To go from A to B, all the charge passing through 1 must go through 2.
The SAME CURRENT goes through resistors in series. The total R is greater than each individual resistor
A B
Parallel Connection When devices are in parallel, the current splits; some current goes through one device, some through the other. In going from A to B, a charge goes through one device only. 1
2
I
Device 1 and 2 are in parallel. More charge (current) goes through path of least resistance
Resistors in parallel have the SAME VOLTAGE DROP. The total R is less than each individual resistor
A BI1I2
IKJR
I = I1+I2
Series Circuit–How do the brightnesses compare?
Which circuit has the greater current flow?
Does the charge get used up?
+ - + -
1 2 3brighterdimmer
More I (less resistance)
less I(more resistance)
the circuit with less load or less resistance
In a closed loop, current flow is the same through every element (light bulbs 1, 2, and 3 are equally bright)
I + - + -
Parallel ConnectionsAs the number of light bulbs (resistance) increases,
• what happens to the current through the circuit?
3I
More I
less I
Increases, There are more pathways so less
resistance
Series ConnectionsIf one resistor is turned off (a light bulb goes out), what happens to the other resistors in the circuit?
If one resistor goes out, there is no longer a closed loop for current flow and all other devices in series will go out. There is an OPEN CIRCUIT
Parallel ConnectionsIf on resistor is turned off (a light bulb goes out), what happens to the other resistors in the circuit?
If one resistor goes out, there is still a closed loop for current flow and so the other devices in series will stay on
Energy Transfer and Power When a LOAD is put on the circuit
(light bulb, beeper, motor…), electrical energy is transformed to other, useful forms of energy.
An electrical circuit is simply an energy transformation tool. Rate of energy transformation/transfer is POWER
LOAD
Energy Source
Energy Transfer and PowerPOWER, P, is the rate
that energy is supplied to the load or the rate of work done on the charge.
LOAD
Energy Source
RVRIIVP
t
qV
t
W
t
E
timeP
dtransformeEnergy
/22
Unit of Power: Watt (W)
1 W = 1 J/s
Energy transfer and PowerPOWER, P, is the rate that energy is
supplied to the load or the rate of work done on the charge.
LOAD
Energy Source
60 Watt light bulb means 60 J of
energy delivered to bulb every second
OR 60 J of energy used
by the bulb per second
Electric heater. An electric heater draws 15.0 A on a 120 V line. How much power does it use and how much does it cost per month (30 days) if it operates 3.0 h per day and the electric company charges 10.5 cents per kW-h?
kWWIVP 8.11800)120)(15( To operate it for 30 days, 3 hr/day would total 90hrs and would use
hrkWhrskW 162)90(8.1
17$)105.0($162 kWhrCost
Will a fuse blow? Determine the total current drawn by all the devices used at once. Will they blow a 20-A fuse?
AVWVPILB 8.0120/100/
AVWVPIH 15120/1800/
AVWVPIS 9.2120/350/
AVWVPID 10120/1200/
A7.28YES
Equivalent Resistance – Resistors in Series
0321 VVVVb
IRV Each element obeys
Ohms Law
)(
0
321
321
RRRIIR
IRIRIRIR
Total
Total
321 RRRReq
(Kirchoff’s Loop Rule)
I
R1 R2
+ -
R3
-DV1 -DV2 -DV3
DVbat
I
REq
+ -
DVbat
Equivalent Resistance – Resistors in Series
This circuit can be replaced by
...
...
...
...
321
321
321
321
PPPP
IIII
VVVV
RRRReq
+ -R1
R2
R3I
+ -
Req
I
this one whereV
V
I I2
I3
I1
321 IIII
311
311
3
3
2
2
1
1
1111
)111
(
RRRR
RRRV
R
V
R
V
R
V
R
VI
total
total
+ -
+DV
Equivalent Resistance – Resistors in Parallel
R1
R2
R3
Kirchoff’s Junction Rule:
Equivalent Resistance – Resistors in Parallel
This circuit can be replaced by
...
...
...
...1111
321
321
321
331
PPPP
IIII
VVVV
RRRReq
this one where
+- R1 R2 R3
I I1 I2 I3
I
V
+- Re
q
I
V
Series or Parallel? The light bulbs are identical and have identical resistance, R. Which configuration produces more light? Which way do you think the headlights of a car are wired?
More pathways,
Less resistance,
More current
More light
DO NOW What is the equivalent resistance of the circuit? What is the current through the circuit?
+ -4 W
I+ -
Req = 18W
I
12 V
6 W
8 W
12 V
AIIIRV eqReq67.01812
IRV Ohms Law
Rank, from highest to lowest, the voltage between A and B, C and D, D and EE and F
4W
12 V
6W
8W
AI 67.0
IRV
+ -
I
AB
C D E F1 (highest)
23
4
-5.36V
-4.02V
-2.68V
If the resistors were light bulbs, which would be brightest?The 8 W one
+ -
Example - What is the equivalent resistance of the circuit?
+ -
Req = 1.8W
12 V
4 W6 W
8 W
12 V
The equivalent resistance of resistors in
parallel is less than the smallest single resistance
+ -
12 V
4 W
8 W
Rank the currents at points A-F from greatest to least
AB
CD
EF
A=B > F=E > D=C
If the resistors were light bulbs, which would be brighter?
The 4 W one
+ -
Series and Parallel Resistors – Two 100 W resistors are connected a) in series and b) in parallel to a 24.0 V battery. What is the current through each resistor? What is Req of each circuit?
+ -
Req = 33W
30 V
50 W
100 W
30 V
+ -I
+ -
Req = 150 W
I
30 V
100 W
30 V
50 W
I1
This is the current through each resistor
I3 I2
I1
I = 0.20 A
I1
I1 = 0.91 AI2 = 0.30AI3 = 0.61 A
+ -
Series and Parallel Resistors – Two 100 W resistors are connected a) in series and b) in parallel to a 24.0 V battery. What is the current through each resistor? What is Req of each circuit?
+ -
Req = 33W
30 V
50 W
100 W
30 V
AIII 90.060.030.032
I
I3I2
ARVI 30.0100/30/22 ARVI 60.050/30/3
12 V
I
I2
12W
2W 4W
I3
Find the current through each resistor and the current drawn from the battery.
1. Draw and label the current flow in the circuit2. Apply Kirchoff’s Rules
AIIIRIRIVV
204212012012
2
22
4222
42
Loop1
AIIRIV
101212012012
3
3
123
12
Loop2
Kirchoff’s Loop Rule
Kirchoff’s Junction Rule A
III312
32
Measuring Current
Current to be measured must pass through the ammeter, so it must be placed in SERIES mode in the circuit.
Ideally ammeters have ZERO resistance so that they do not affect the energy of the circuit
Ammeter – measures current
Measuring VoltageVoltmeter – measures
voltage
Does NOT require the current to pass through it. It must be placed in parallel to the circuit element.
Ideally voltmeters have INFINITE resistance so that they do not draw current away from circuit.
For the circuit below, all resistors have the same value, R (10 )Wa) Draw and label the current flow
b) Calculate the equivalent resistance of the circuit
c) Calculate the total current provided by the battery.
d) Calculate the current in resistor 3
e) Calculate the current in resistor 5
R282V
I I3
I2
I3
I4I5
R1 R3
R4
R5
R6
R7R8
R2
I I3
I2
I3
I4I5
R1 R3
R4
R5
R6
R7R8
R2
I I3
I2
I3
I4
I5
R1 R3
R4 R5
6
R7R8
R2
II3
I2
R1 R3
R456
R7R8
R2
II3
I2
R1
R34567
R8
Req = 2 8/11 R = 27.3W
For the circuit below, all resistors have the same value, R (10 )Wa) Draw and label the current flow
b) Calculate the equivalent resistance of the circuit
c) Calculate the total current provided by the battery.
d) Calculate the current in resistor 3
e) Calculate the current in resistor 5
I = 3A
R282V
I I3
I2
I3
I4I5
R1 R3
R4
R5
R6
R7R8
I3 = 33/40 A = 0.825AI5 = 0.275A
DV
bat
R1 R2
R3
R4R5
R6
I=2
I
I
I1I2=1.5
I3 = 1.0
I4
DV(v)
I(A)
R (W)
Bat 2.0
R1 5.0
R2 3.5
R3 1.5
R4 4.0
R5 1.0
R6 2.0
Example– Calculate the missing information in the table for the following series-parallel network. Find the equivalent resistance of the circuit.
Req = 7 W
14
2.5 0.5
0.5 7.0
6.0 4.0
1.0 4.0
4.0 4.0
4.0 2.0
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