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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.