Chapter 18Chapter 18Direct Current CircuitsDirect Current Circuits

Conceptual questions: 5,6,12,15,19,20

Problems: 1,8,13,40

Quick quizzes: 1,2,3

Sources of emfSources of emf

Electromotive forces are created Electromotive forces are created by batteries, generators, by batteries, generators, thermocouples, nuclear reactors, thermocouples, nuclear reactors, etc. by means of chemical etc. by means of chemical reactions or by conversion of reactions or by conversion of kinetic, thermal, nuclear, etc. kinetic, thermal, nuclear, etc. energy into electricity.energy into electricity.

Symbol Symbol emfemf or or Unit - VoltUnit - Volt

emf and Internal emf and Internal ResistanceResistance

A real battery has A real battery has some internal some internal resistanceresistance

Therefore, the Therefore, the terminal voltage terminal voltage is not equal to the is not equal to the emfemf

More About Internal More About Internal ResistanceResistance

The schematic The schematic shows the internal shows the internal resistance, rresistance, r

The terminal The terminal voltage, ΔV = Vvoltage, ΔV = Vbb--VVaa

ΔV = ε – IrΔV = ε – Ir For the entire For the entire

circuit, ε = IR + Ircircuit, ε = IR + Ir

Problem 18-1Problem 18-1

A battery having an emf of 9.00 V A battery having an emf of 9.00 V delivers 117 mA whendelivers 117 mA when connected connected to a 72.0-Ω load. Determine the to a 72.0-Ω load. Determine the internal resistanceinternal resistance of the battery.of the battery.

Resistors in SeriesResistors in Series The current is the same in The current is the same in

resistors because any charge resistors because any charge that flows through one that flows through one resistor flows through the resistor flows through the otherother

The sum of the potential The sum of the potential differences across the differences across the resistors is equal to the total resistors is equal to the total potential difference across potential difference across the combinationthe combination ΔV = IRΔV = IR11 + IR + IR22 = I (R = I (R11+R+R22)) ΔV = IRΔV = IReqeq

RReqeq = R = R11 + R + R22 + R + R33 + … + …

When a piece of wire is used to connect points b and c in this figure, the brightness of bulb R1 (a) increases, (b) decreases(c) stays the same. The brightness of bulb R2 (a) increases, (b) decreases, (c) stays the same.

QUICK QUIZ 18.1

QUICK QUIZ 18.2With the switch in this circuit (figure a) closed, no current exists in R2 because the current has an alternate zero-resistance path through the switch. Current does exist in R1 and this current is measured with the ammeter at the right side of the circuit. If the switch is opened (figure b), current exists in R2. After the switch is opened, the reading on the ammeter (a) increases, (b) decreases, (c) does not change.

Resistors Resistors in Parallelin Parallel

The potential difference across each resistor is The potential difference across each resistor is the same because each is connected directly the same because each is connected directly across the battery terminals, across the battery terminals, V = V = VV1 1 = = VV22

VV11=I=I11RR11 VV22=I=I22RR22 The current, I, that enters a point must The current, I, that enters a point must

be equal to the total current leaving be equal to the total current leaving that pointthat point I = II = I11 + I + I22

I = I = VV11/R/R1 1 + + VV22/R/R2 2 = = V (1/RV (1/R11 + 1/R + 1/R22) = ) = V/RV/Reqeq 321eq R

1

R

1

R

1

R

1 The inverse of the equivalent The inverse of the equivalent resistance of resistors connected resistance of resistors connected in parallel is the algebraic sum of in parallel is the algebraic sum of the inverses of the individual the inverses of the individual resistanceresistance

With the switch in this circuit (figure a) open, there is no current in R2. There is current in R1 and this current is measured with the ammeter at the right side of the circuit. If the switch is closed (figure b), there is current in R2. When the switch is closed, the reading on the ammeter (a) increases, (b) decreases, or (c) remains the same.

QUICK QUIZ 18.3

Find the equivalent resistance of the circuit in Figure 18.8. If the total power supplied to the circuit is 4.00 W, find the emf of the battery.

Problem 18.8.

Conceptual questionsConceptual questions5. If you have your headlines on while you 5. If you have your headlines on while you

start your car why do they dim while the start your car why do they dim while the car starts?car starts?

12. Two sets of Christmas tree lights are 12. Two sets of Christmas tree lights are available. For set A, when one bulb is available. For set A, when one bulb is removed the remaining bulbs remain removed the remaining bulbs remain illuminated. For set B, when one bulb is illuminated. For set B, when one bulb is removed the remaining bulbs do not removed the remaining bulbs do not operate. Explain the differences in operate. Explain the differences in wiring of the two sets.wiring of the two sets.

Additional question:Additional question:

Are the two headlights on a car wired in Are the two headlights on a car wired in series or in parallel?series or in parallel?

Problem 18.13.Problem 18.13. Find the current in the 12-Ω resistor

Current from the battery

CircuitsCircuits

Kirchhoff’s RulesKirchhoff’s Rules Junction RuleJunction Rule

The sum of the currents The sum of the currents entering any junction entering any junction must equal the sum of must equal the sum of the currents leaving that the currents leaving that junctionjunction

Conservation of ChargeConservation of Charge

Loop RuleLoop Rule The sum of the potential The sum of the potential

differences across all differences across all the elements around the elements around any closed circuit loop any closed circuit loop must be zeromust be zero

Conservation of EnergyConservation of Energy

More About the Loop RuleMore About the Loop Rule Traveling around the loop Traveling around the loop

from a to bfrom a to b In a, the resistor is In a, the resistor is

transversed in the transversed in the direction of the current, direction of the current, the potential across the the potential across the resistor is –IRresistor is –IR

In b, the resistor is In b, the resistor is transversed in the transversed in the direction opposite of the direction opposite of the current, the potential current, the potential across the resistor is +IRacross the resistor is +IR

Loop Rule, finalLoop Rule, final In c, the source of In c, the source of

emf is transversed in emf is transversed in the direction of the the direction of the emf (from – to +), the emf (from – to +), the change in the electric change in the electric potential is +εpotential is +ε

In d, the source of In d, the source of emf is transversed in emf is transversed in the direction opposite the direction opposite of the emf (from + to of the emf (from + to -), the change in the -), the change in the electric potential is -εelectric potential is -ε

Effects of Various CurrentsEffects of Various Currents

5 mA or less5 mA or less can cause a sensation of shockcan cause a sensation of shock generally little or no damagegenerally little or no damage

10 mA10 mA hand muscles contracthand muscles contract may be unable to let go a of live wiremay be unable to let go a of live wire

100 mA 100 mA if passes through the body for 1 second or if passes through the body for 1 second or

less, can be fatalless, can be fatal

Ground WireGround Wire

Electrical Electrical equipment equipment manufacturers manufacturers use electrical use electrical cords that have a cords that have a third wire, called third wire, called a grounda ground

Prevents shocksPrevents shocks

HouseholHouseholddwiring wiring

Conceptual questionsConceptual questions15. Embodied in Kirchhoff’s rules are two 15. Embodied in Kirchhoff’s rules are two

conservation laws. What are they?conservation laws. What are they?

19. Suppose a parachutists lands on a high 19. Suppose a parachutists lands on a high voltage wire and grabs a wire as she prepares voltage wire and grabs a wire as she prepares to be rescued. Will she be electrocuted? If the to be rescued. Will she be electrocuted? If the wire breaks open, should she continue to hold wire breaks open, should she continue to hold onto the wire as she falls to the ground?onto the wire as she falls to the ground?

20. Would a fuse work successfully if it were 20. Would a fuse work successfully if it were placed in parallel with a device it was placed in parallel with a device it was supposed to protect?supposed to protect?

Problem 18-40Problem 18-40

Your toaster oven and coffeemaker Your toaster oven and coffeemaker each dissipate 1 200 Weach dissipate 1 200 W of power. of power. Can you operate them together if Can you operate them together if the 120-V linethe 120-V line that feeds them has that feeds them has a circuit breaker rated at 15 A? a circuit breaker rated at 15 A? Explain. Explain.

MCADMCADUseUse thethe followingfollowing informationinformation inin questionsquestions 1-4:1-4:

Four 6-V batteries are connected in series in order Four 6-V batteries are connected in series in order to power lights A and B. The resistance of light A is to power lights A and B. The resistance of light A is 40 40 and the resistance of light B is 20 and the resistance of light B is 20 ..

1. How does the current through light bulb A compare with the current through light bulb B?A. The current through light bulb A is less.B. The current through light bulb A is the same.C. The current through light bulb A is greater.D. None of the above is true.

X X

A B

2. What is the potential difference between points C and D?A. 6 volts B. 12 voltsC. 18 volts D. 24 volts

3. What is the current through the wire at point C?A. 0.1 A B. 0.2 AC. 0.4 A D. 1.0 A

4. How does the voltage drop across light A compare to the drop across light B?A. The voltage drop for A is less than that for B by a factor of 4.B. The voltage drop for A is less than that for B by a factor of 2.C. The voltage drop for A is the same as that for B.D. The voltage drop for A is greater than that for B by a factor of 2.

X X

A B

DC

40 20

6V

For a circuit with constant resistance, which graph represents the relation between current and potential?

I

V

I

V

I

V

I

V

What must be the reading in the ammeter A for the circuit below?

A. 0 A B. 6.0 A C. 8.0 A D. 12.0 A

4.0 A

6.0 A

2.0 A

A

A. B. C. D.