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Homework

Reading: Chap. 30, Chap. 31 and Chap. 32

Suggested exercises: 31.1, 5, 6, 7, 8, 13, 14, 17,

23, 24, 25

Problems: 31.35, 31.38, 31.41, 31.42, 31.49,

31.54, 31.57, 31.63, 31.64, 31.67, 31.70, 31.73

(due: Fri., Nov. 13)

Final Exam

Wed., Dec. 16

12:00pm - 3:00 pm

Room 202

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Chapter 31. Fundamentals of Circuits

Surprising as it may seem,

the power of a computer is

achieved simply by the

controlled flow of charges

through tiny wires and

circuit elements.

Chapter Goal: To

understand the fundamental

physical principles that

govern electric circuits.

Topics:

• Circuit Elements and Diagrams

• Kirchhoff’s Laws and the Basic Circuit

• Energy and Power

• Series Resistors

• Real Batteries

• Parallel Resistors

• Resistor Circuits

• Getting Grounded

• RC Circuits

Chapter 31. Fundamentals of Circuits

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Chapter 31. Basic Content and Examples

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Example 1

Consider the following circuit. When the switch S1 is open and

switch S2 is closed, find (a) the equivalent resistance of the circuit;

(b) the total current in the source of emf; (c) the potential drop

across each resistor; and (d) the current carried by each resistor. (e)

if switch S1 is now closed, find the current in the 2- resistor; (f) if

switch S2 is now opened (while S1 remains closed), find the

potential drops across the 6- resistor and across switch S2.

18V

212

6S1

S2

Example 2

Consider the following circuit. We have є1 = 12 V, є2 = 4 V, r1 = r2

= 1 , R1 = R2 = 5 , and R3 = 4 . (a) Find the potentials at points

a through e in the figure, assuming that the potential at point e is

zero; (b) find the power input and output in the circuit?

12V

14V

1

55

4

a b

c

de0V

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Example 4

A fully charged car battery is to be connected by jumper cables to

a discharged car battery in order to charge it. (1) To which

terminal of the discharged battery should the positive terminal of

the charged battery be connected? (2) Assume that the charged

battery has an emf of є1 = 12 V and the discharged battery has an

emf of є2 = 11 V, that the internal resistances of the batteries are

r1 = r2 = 0.02 , and that the resistance of the jumper cables is R

= 0.01 . What will the charging current be? (3) What will the

current be if the batteries are connected incorrectly?

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Tactics: Using Kirchhoff’s loop law

Tactics: Using Kirchhoff’s loop law

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EXAMPLE 32.1 A single-resistor circuit

QUESTION:

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EXAMPLE 32.1 A single-resistor circuit

EXAMPLE 32.1 A single-resistor circuit

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EXAMPLE 32.1 A single-resistor circuit

EXAMPLE 32.1 A single-resistor circuit

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EXAMPLE 32.1 A single-resistor circuit

Energy and Power

The power supplied by a battery is

The units of power are J/s, or W.

The power dissipated by a resistor is

Or, in terms of the potential drop across the resistor

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EXAMPLE 32.4 The power of light

QUESTION:

EXAMPLE 32.4 The power of light

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EXAMPLE 32.4 The power of light

EXAMPLE 32.4 The power of light

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Series Resistors

• Resistors that are aligned end to end, with no

junctions between them, are called series resistors or,

sometimes, resistors “in series.”

• The current I is the same through all resistors placed

in series.

• If we have N resistors in series, their

equivalent resistance is

The behavior of the circuit will be unchanged if the N series

resistors are replaced by the single resistor Req.

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EXAMPLE 32.7 Lighting up a flashlight

QUESTION:

EXAMPLE 32.7 Lighting up a flashlight

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EXAMPLE 32.7 Lighting up a flashlight

EXAMPLE 32.7 Lighting up a flashlight

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EXAMPLE 32.7 Lighting up a flashlight

Parallel Resistors

• Resistors connected at both ends are called

parallel resistors or, sometimes, resistors “in parallel.”

• The left ends of all the resistors connected in parallel

are held at the same potential V1, and the right ends are

all held at the same potential V2.

• The potential differences ΔV are the same across

all resistors placed in parallel.

• If we have N resistors in parallel, their

equivalent resistance is

The behavior of the circuit will be unchanged if the N

parallel resistors are replaced by the single resistor Req.

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EXAMPLE 32.10 A combination of resistors

QUESTION:

EXAMPLE 32.10 A combination of resistors

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EXAMPLE 32.10 A combination of resistors

EXAMPLE 32.10 A combination of resistors

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Problem-Solving Strategy: Resistor circuits

Problem-Solving Strategy: Resistor circuits

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Problem-Solving Strategy: Resistor circuits

Problem-Solving Strategy: Resistor circuits

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RC Circuits• Consider a charged capacitor, an open switch, and

a resistor all hooked in series. This is an RC Circuit.

• The capacitor has charge Q0 and potential difference

ΔVC = Q0/C.

• There is no current, so the potential difference across

the resistor is zero.

• At t = 0 the switch closes and the capacitor begins

to discharge through the resistor.

• The capacitor charge as a function of time is

where the time constant τ is

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EXAMPLE 32.14 Exponential decay in an RC

circuit

QUESTION:

EXAMPLE 32.14 Exponential decay in an RC

circuit

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EXAMPLE 32.14 Exponential decay in an RC

circuit

EXAMPLE 32.14 Exponential decay in an RC

circuit

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Chapter 32. Summary Slides

General Strategy

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General Strategy

General Strategy

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Important Concepts

Important Concepts

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Important Concepts

Applications

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Applications

Chapter 32. Clicker Questions

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Which of these diagrams represent the same circuit?

A. a and b

B. b and c

C. a and c

D. a, b, and d

E. a, b, and c

Which of these diagrams represent the same circuit?

A. a and b

B. b and c

C. a and c

D. a, b, and d

E. a, b, and c

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What is ∆V across the

unspecified circuit

element? Does the

potential increase or

decrease when

traveling through this

element in the direction

assigned to I?

A. ∆V decreases by 2 V in the direction of I.

B. ∆V increases by 2 V in the direction of I.

C. ∆V decreases by 10 V in the direction of I.

D. ∆V increases by 10 V in the direction of I.

E. ∆V increases by 26 V in the direction of I.

A. ∆V decreases by 2 V in the direction of I.

B. ∆V increases by 2 V in the direction of I.

C. ∆V decreases by 10 V in the direction of I.

D. ∆V increases by 10 V in the direction of I.

E. ∆V increases by 26 V in the direction of I.

What is ∆V across the

unspecified circuit

element? Does the

potential increase or

decrease when

traveling through this

element in the direction

assigned to I?

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Rank in order, from largest to smallest,

the powers Pa to Pd dissipated in

resistors a to d.

A. Pb > Pa = Pc = Pd

B. Pb = Pd > Pa > Pc

C. Pb = Pc > Pa > Pc

D. Pb > Pd > Pa > Pc

E. Pb > Pc > Pa > Pd

A. Pb > Pa = Pc = Pd

B. Pb = Pd > Pa > Pc

C. Pb = Pc > Pa > Pc

D. Pb > Pd > Pa > Pc

E. Pb > Pc > Pa > Pd

Rank in order, from largest to smallest,

the powers Pa to Pd dissipated in

resistors a to d.

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What is the potential at points a to e ?

A.

B.

C.

D.

E.

A.

B.

C.

D.

E.

What is the potential at points a to e ?

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Rank in order,

from brightest to

dimmest, the

identical bulbs A

to D.

A. C = D > B > A

B. A > C = D > B

C. A = B = C = D

D. A > B > C = D

E. A > C > B > D

A. C = D > B > A

B. A > C = D > B

C. A = B = C = D

D. A > B > C = D

E. A > C > B > D

Rank in order,

from brightest to

dimmest, the

identical bulbs A

to D.

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The time constant

for the discharge of

this capacitor is

A. 5 s.

B. 1 s.

C. 2 s.

D. 4 s.

E. The capacitor doesn’t discharge because

the resistors cancel each other.

A. 5 s.

B. 1 s.

C. 2 s.

D. 4 s.

E. The capacitor doesn’t discharge because

the resistors cancel each other.

The time constant

for the discharge of

this capacitor is

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Chapter 32. Reading Quizzes

How many laws are named after Kirchhoff?

A. 0

B. 1

C. 2

D. 3

E. 4

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How many laws are named after Kirchhoff?

A. 0

B. 1

C. 2

D. 3

E. 4

What property of a real battery makes

its potential difference slightly different

than that of an ideal battery?

A. Short circuit

B. Chemical potential

C. Internal resistance

D. Effective capacitance

E. Inductive constant

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A. Short circuit

B. Chemical potential

C. Internal resistance

D. Effective capacitance

E. Inductive constant

What property of a real battery makes

its potential difference slightly different

than that of an ideal battery?

A. Period

B. Torque

C. Terminal voltage

D. Time constant

E. Coefficient of thermal expansion

In an RC circuit, what is the

name of the quantity

represented by the symbol ?

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A. Period

B. Torque

C. Terminal voltage

D. Time constant

E. Coefficient of thermal expansion

In an RC circuit, what is the

name of the quantity

represented by the symbol ?

Which of the following are ohmic materials:

A. batteries.

B. wires.

C. resistors.

D. Materials a and b.

E. Materials b and c.

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Which of the following are ohmic materials:

A. batteries.

B. wires.

C. resistors.

D. Materials a and b.

E. Materials b and c.

The equivalent resistance for a group of

parallel resistors is

A. less than any resistor in the group.

B. equal to the smallest resistance in the group.

C. equal to the average resistance of the group.

D. equal to the largest resistance in the group.

E. larger than any resistor in the group.

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The equivalent resistance for a group of

parallel resistors is

A. less than any resistor in the group.

B. equal to the smallest resistance in the group.

C. equal to the average resistance of the group.

D. equal to the largest resistance in the group.

E. larger than any resistor in the group.