Chapter 26
Direct-Current Circuits
• Study resistors in series and parallel
• Consider Kirchoff’s Rules
• The design and use of electronic measuring
instruments
• R-C circuits
• The applications of circuits in household wiring
Resistors in Series and Parallel
Resistors in Series
Vab  Vax  Vxy  Vyb  IR1  IR2  IR3
Vab  I ( R1  R2  R3 )  IReq
Req  R1  R2  R3
Figure 26-1
Resistors in Parallel
Figure 26-1
Vab Vab Vab


R1 R2 R3
 1 
1
1
1 

I  Vab  
   Vab 
R 
 R1 R2 R3 
 eq 
1
1
1
1
 

Req R1 R2 R3
I  I1  I 2  I 3 
Chapter 26
2
Series and parallel combination resistors
– Consider Problem-Solving Strategy 26.1.
– Follow Example 26.1 guided by Figure 26.3 below.
– Follow Example 26.2.
Kirchoff’s Rules I—junctions
• The algebraic sum of the currents into any junction is zero.
Chapter 26
5
Kirchhoff’s Laws
Kirchhoff’s Current Law
Proof
Charge can’t build up at the junction.
Figure 26-7
Kirchhoff’s Current Law - Example
Figure 26-8
Chapter 26
6
Kirchoff’s Rules II—loops
• The algebraic sum of the potential differences in any loop,
including those associated with emfs and those of resistive
elements, must equal zero.
Kirchhoff’s Laws - A Single Loop Circuit
Example 26-3
a) Solve for I
b) Solve for Vab
c) Solve for power output of
the emf of each battery
Figure 26-10
Chapter 26
8
Kirchhoff’s Voltage Law – Two Loop Example
Figure 26-8
Loop 1
Loop 1
1  I1r1  I1R1  I 3 R3  0
1  I1r1  I1R1  ( I1  I 2 ) R3  0
Loop 2
Loop 2
 2  I 2 r2  I 3 R3  I 2 R2  0
 2  I 2 r2  ( I1  I 2 ) R3  I 2 R2  0
9
Apply the junction rule to a point a reduces the
number of unknown currents from three to two
Chapter 26
10
Kirchoff’s Rules III—examples and strategy
• Read through Problem-Solving Strategy 26.2. Figure 26.9
illustrates this strategy.
• Refer to Example 26.3, illustrated by Figure 26.10.
Chapter 26
12
Chapter 26
13
Chapter 26
14
Kirchoff’s Rules IV—examples
•
•
•
•
Refer to Example 26.4, illustrated by Figure 26.11.
Consider Example 26.5.
Refer to Example 26.6, illustrated by Figure 26.12.
Review Example 26.7.
D’Arsonval’s galvanometer
• We’ll call it simply ―meter‖ henceforth.
• The meter is a coil of wire mounted next to a permanent
magnet. Any current passing through the coil will induce
magnetism in the coil. The interaction of the new
electromagnetism and the permanent magnet will move the
meter indicator mounted to the coil.
The Ammeter and Voltmeter
• The ammeter (sometimes prefixed with milli or micro because
the currents to be measured are routinely thousandths or
millionths of an ampere) may be used to measure current OR
voltage. A shunt resistor makes this conversion as shown below
in Figure 26.15.
Chapter 26
18
Chapter 26
19
Ohmmeters and digital multimeters
• An ohmmeter is designed specifically to measure resistance.
• Refer to Figure 26.17 and Figure 26.18 below to see an
ohmmeter wiring diagram and a photograph of a digital
multimeter. The multimeter can measure current, voltage, or
resistance over a wide range.
Chapter 26
21
Capacitor Charging Solution
q (t )
0
C
dq
SubstitutingI 
dt
dq
q (t )
V0 
R
0
dt
C
dq V0
q
 
dt R RC
dq
dt

q  V0C
RC
V0  I (t ) R 
dq
1

0 q  V0C RC 0 dt
q
t
 q  V0C  t
ln 

 V0C  RC

q  V0C 1  e
Chapter 26
t
RC
dq
dt
V0  t RC
I (t )  e
R
Vc (t )  I (t ) R
I (t ) 

Vc (t )  V0 1  e
t
RC

22

R-C Circuits (Chapter 26, Sec 4)
Charging a Capacitor

R
0.37 I0
  vab  vbc
C
q  vbcC
vbc 
vab  iR
i
0.63 Qf
q
C
vab
R
Time Constant
Figure 26-20
Figure 26-21
Chapter 26
  RC
(26-14)
23
R-C Circuits (Chapter 26, Sec 4)
Discharging a Capacitor
0  vab  vbc
vab  vbc
Q0
RC
q  vbcC
vbc 
vab  iR
i
q
C
vab
R
Time Constant
  RC
Figure 26-22
(26-14)
Figure 26-23
Chapter 26
24
Power Distribution Systems
240-V line
black, red Neutral
Black
White
120 v
One phase of the 240-V line
We buy energy from the Power Company, not power
kW x time = watt-seconds = Joules
1 kWh = (1000W) (3600 s ) = 3.6 x 106 W-s = 3.6 x 106 J
25
Fuses, circuit breakers, and GFI
• A fuse will melt and a breaker will
open the circuit if maximum
current is reached. See Figure
26.26.
• GFI stops further current flow
when a sudden drop in resistance
indicates that someone has offered
a new path to ground. I don’t know
if it will save this worker we see in
Figure 26.27 who didn’t use a
grounded drill.
The wiring diagram for a typical kitchen
– Consider Figure 26.28 below.
– Follow Example 26.14.
Average Retail Price of Electricity
cents per kilowatt-hour
Census Division
and State
Commercial1
Residential
Nov-07
Nov-06
Nov-07
Industrial1
Nov-06
Nov-07
Nov-06
New England
16.18
15.58
14.19
13.78
12.75
11.44
Connecticut
18.33
16.92
14.91
14.24
12.46
12.08
Maine
15.42
14.06
13.04
11.91
12.12
9.45
Massachusetts
15.69
15.74
14.38
14.22
14.01
12.53
14.8
14.22
13.26
13.28
12.32
10.78
Rhode Island
14.62
14.34
13.2
12.81
12.18
12.28
Vermont
14.35
13.57
12.36
11.84
8.79
8.31
New Hampshire
U.S. Total
10.69
10.18
9.6
9.24
6.22
6.04
28
Q26.1
Which of the two
arrangements shown has the
smaller equivalent resistance
between points a and b?
A. the series arrangement
B. the parallel arrangement
C. The equivalent resistance
is the same for both
arrangements.
D. The answer depends on
the values of the individual
resistances R1, R2, and R3.
A26.1
Which of the two
arrangements shown has the
smaller equivalent resistance
between points a and b?
A. the series arrangement
B. the parallel arrangement
C. The equivalent resistance
is the same for both
arrangements.
D. The answer depends on
the values of the individual
resistances R1, R2, and R3.
Q26.2
Three identical resistors,
each of resistance R, are
connected as shown. What is
the equivalent resistance of
this arrangement of three
resistors?
A. 3R
B. 2R
C. 3R/2
D. 2R/3
E. R/3
A26.2
Three identical resistors,
each of resistance R, are
connected as shown. What is
the equivalent resistance of
this arrangement of three
resistors?
A. 3R
B. 2R
C. 3R/2
D. 2R/3
E. R/3
Q26.3
A 120-V, 60-W light bulb, a 120-V,
120-W light bulb, and a 120-V,
240-W light bulb are connected in
parallel as shown.
120 V
60 W
The voltage between points a and b
is 120 V. Through which bulb is
there the greatest voltage drop?
120 V
120 W
a
A. the 120-V, 60-W light bulb
B. the 120-V, 120-W light bulb
120 V
240 W
C. the 120-V, 240-W light bulb
D. All three light bulbs have the same voltage drop.
b
A26.3
A 120-V, 60-W light bulb, a 120-V,
120-W light bulb, and a 120-V,
240-W light bulb are connected in
parallel as shown.
120 V
60 W
The voltage between points a and b
is 120 V. Through which bulb is
there the greatest voltage drop?
120 V
120 W
a
A. the 120-V, 60-W light bulb
B. the 120-V, 120-W light bulb
120 V
240 W
C. the 120-V, 240-W light bulb
D. All three light bulbs have the same voltage drop.
b
Q26.4
A 120-V, 60-W light bulb, a 120-V,
120-W light bulb, and a 120-V,
240-W light bulb are connected in
parallel as shown.
120 V
60 W
The voltage between points a and b
is 120 V. Which bulb glows the
brightest?
120 V
120 W
a
A. the 120-V, 60-W light bulb
B. the 120-V, 120-W light bulb
120 V
240 W
C. the 120-V, 240-W light bulb
D. All three light bulbs glow with equal brightness.
b
A26.4
A 120-V, 60-W light bulb, a 120-V,
120-W light bulb, and a 120-V,
240-W light bulb are connected in
parallel as shown.
120 V
60 W
The voltage between points a and b
is 120 V. Which bulb glows the
brightest?
120 V
120 W
a
A. the 120-V, 60-W light bulb
B. the 120-V, 120-W light bulb
120 V
240 W
C. the 120-V, 240-W light bulb
D. All three light bulbs glow with equal brightness.
b
Q26.5
A 120-V, 60-W light bulb, a 120-V, 120-W
light bulb, and a 120-V, 240-W light bulb are
connected in series as shown.
The voltage between points a and b is 120 V.
Through which bulb is there the greatest
voltage drop?
a
120 V
60 W
120 V
120 W
A. the 120-V, 60-W light bulb
B. the 120-V, 120-W light bulb
C. the 120-V, 240-W light bulb
D. All three light bulbs have the same voltage drop.
120 V
240 W
b
A26.5
A 120-V, 60-W light bulb, a 120-V, 120-W
light bulb, and a 120-V, 240-W light bulb are
connected in series as shown.
The voltage between points a and b is 120 V.
Through which bulb is there the greatest
voltage drop?
a
120 V
60 W
120 V
120 W
A. the 120-V, 60-W light bulb
B. the 120-V, 120-W light bulb
C. the 120-V, 240-W light bulb
D. All three light bulbs have the same voltage drop.
120 V
240 W
b
Q26.6
A 120-V, 60-W light bulb, a 120-V, 120-W
light bulb, and a 120-V, 240-W light bulb are
connected in series as shown.
The voltage between points a and b is 120 V.
Which bulb glows the brightest?
a
120 V
60 W
120 V
120 W
A. the 120-V, 60-W light bulb
B. the 120-V, 120-W light bulb
C. the 120-V, 240-W light bulb
D. All three light bulbs glow with equal brightness.
120 V
240 W
b
A26.6
A 120-V, 60-W light bulb, a 120-V, 120-W
light bulb, and a 120-V, 240-W light bulb are
connected in series as shown.
The voltage between points a and b is 120 V.
Which bulb glows the brightest?
a
120 V
60 W
120 V
120 W
A. the 120-V, 60-W light bulb
B. the 120-V, 120-W light bulb
C. the 120-V, 240-W light bulb
D. All three light bulbs glow with equal brightness.
120 V
240 W
b
Q26.7
Three identical light bulbs are
connected to a source of emf as
shown. Which bulb is brightest?
A. light bulb A
B. light bulb B
C. light bulb C
D. both light bulbs B and C
(Both are equally bright and are
brighter than light bulb A.)
E. All bulbs are equally bright.
A26.7
Three identical light bulbs are
connected to a source of emf as
shown. Which bulb is brightest?
A. light bulb A
B. light bulb B
C. light bulb C
D. both light bulbs B and C
(Both are equally bright and are
brighter than light bulb A.)
E. All bulbs are equally bright.
Q26.8
You wish to study a resistor in a circuit. To simultaneously
measure the current in the resistor and the voltage across the
resistor, you would place
A. an ammeter in series and an voltmeter in series.
B. an ammeter in series and an voltmeter in parallel.
C. an ammeter in parallel and an voltmeter in series.
D. an ammeter in parallel and an voltmeter in parallel.
A26.8
You wish to study a resistor in a circuit. To simultaneously
measure the current in the resistor and the voltage across the
resistor, you would place
A. an ammeter in series and an voltmeter in series.
B. an ammeter in series and an voltmeter in parallel.
C. an ammeter in parallel and an voltmeter in series.
D. an ammeter in parallel and an voltmeter in parallel.
Q26.9
A battery, a capacitor, and a resistor are connected in series.
Which of the following affect(s) the maximum charge stored
on the capacitor?
A. the emf  of the battery
B. the capacitance C of the capacitor
C. the resistance R of the resistor
D. both  and C
E. all three of , C, and R
A26.9
A battery, a capacitor, and a resistor are connected in series.
Which of the following affect(s) the maximum charge stored
on the capacitor?
A. the emf  of the battery
B. the capacitance C of the capacitor
C. the resistance R of the resistor
D. both  and C
E. all three of , C, and R
Q26.10
A battery, a capacitor, and a resistor are connected in series.
Which of the following affect(s) the rate at which the
capacitor charges?
A. the emf  of the battery
B. the capacitance C of the capacitor
C. the resistance R of the resistor
D. both C and R
E. all three of , C, and R
A26.10
A battery, a capacitor, and a resistor are connected in series.
Which of the following affect(s) the rate at which the
capacitor charges?
A. the emf  of the battery
B. the capacitance C of the capacitor
C. the resistance R of the resistor
D. both C and R
E. all three of , C, and R