1) Connect each set of resistors in Figure 5-67 in series between points A and B.
R1
A
A B A
R2
B
R2
B
R1 R2 R3 R1
R3
R4 R5
R3
Figure 5-67(a) Figure 5-67(b) Figure 5-67(c)
7) The current from the source in Figure 5-70 is 5mA. How much current does each milliammeter in the circuit indicate?
The current is the same everywhere in a series circuit, therefore each meter will read 5mA
12) Calculate RT for each circuit of Figure 5-71.
1kohm
Es 5.6kohm
R
T
= Ω +
5.6
k
Ω +
2.2
k
Ω ⇒
8.8
k
Ω
2.2kohm
Figure 5-71(a)
4.7ohm
10ohm
Es
R
=
4.7
10 12 1
T
27.7
Ω
12ohm
1ohm
Figure 5-71(b)

1Mohm 560kohm
5.6Mohm
Es
R 1 M
T
= Ω +
560 k
Ω +
5.6
M
Ω +
680 k
Ω +
10 M
Ω ⇒
17.84
M
Ω
680kohm
10Mohm
Figure 5-71(c)
13) What is the total resistance of twelve 5.6kΩ resistor is series?
R
T
=
12(5.6
k ) 67.2
k
Ω
15) If the total resistance if Figure 5-72 is 17.4kΩ, what is the value of R
5
?
R
T
=
R
1
+
R
2
+
R
3
+
R
4
+
R
5
R
T
−
R
1
−
R
2
−
R
3
−
R
4
=
R
5
17.4
k
Ω −
5.6
k 1 k 2.2
k
Ω −
4.7
k
Ω =
R
5
R
5
=
3.9
k
Ω
18) What is the total resistance from A to B for each switch position in Figure 5-73.
Position 1 - R
T
=
R
1
+
R
3
+
R
5
⇒
2.01
k
Ω
Position 2 - R
T
=
R
1
+
R
2
+
R
3
+
R
4
+
R
5
⇒
3.67
k
Ω

19) What is the current in each of the following circuits?
R1
2.2kohm
R
T
=
R
1
+
R
2
+
R
3
⇒
8.8
k
Ω
I
⇒
625
µ
A
Es
R2
5.6kohm
=
Es
=
R
T
16 V
8.8
k
Ω
5.5V
R3
1kohm
Figure 5-74 (a)
Es
16V
R1
1Mohm
R2
2.2Mohm
R
T
=
R
1
+
R
2
+
R
3
⇒
3.76
M
Ω
I
=
Es
⇒
R
T
16 V
3.76
M
Ω
⇒
4.26
µ
A
R3
560kohm
I A
(a)
Figure 5-74 (b)
20) Determine the voltage drop across each resistor in Figure 5-74:
=
625
µ
VR
1
=
IR
1
⇒
VR
2
=
IR
2
⇒
(625
µ
A )(2.2
k
Ω ⇒
1.38
V
(625
µ
A )(5.6
k
Ω ⇒
3.5
V
(625
µ
A )(1.0
k
Ω ⇒
0.625
V
⇒
625 mV VR
3
=
IR
3
⇒

(b) I
=
4.26
µ
A
VR
1
=
IR
1
⇒
(4.26
µ
A )(1 M
Ω ⇒
4.26
V
VR
2
=
IR
2
⇒
(4.26
µ
A )(2.2
M
Ω ⇒
9.36
V
VR
3
=
IR
3
⇒
(4.26
µ
A )(560 k
Ω ⇒
2.38
V
29) Determine the total source in each circuit of Figure 5-79
-
5V
+
10V
+
-
+
8V
-
Figure 5-79(a)
R
E
T
=
10 V
+
8 V
+
5 V
⇒
23 V 23V
-
+ R
+
50V
-
25V
+
35V
+
-
10V
+
-
E
T
=
10 V
+
50 V
−
25 V
⇒
35 V
R
R
Figure 5-79(b)
8V
-
+ R
0V
+
R
E
T
=
8 V
−
8 V
⇒
0 V
8V
+ -
-
Figure 5-79(c)
Es 5.5
V
+
8.2
V
+
12.3
V 26 V
30) The following voltage drops are measured across three resistors in series: 5.5V, 8.2V, and
12.3V. What is the value of the source voltage to which these resistors are connected?
= ⇒

31) Five resistors are in series with a 20V source. The voltage drops across four of the resistors are 1.5V, 5.5V, 3V, and 6V. How much voltage is dropped across the fifth resistor?
Es
=
V
R 1
+
V
R 2
+
V
R 3
+
V
R 4
+
V
R 5
Es V
R 1
−
V
R 2
−
V
R 3
−
V
R 4
=
V
R 5
20 V
−
1.5
V
−
5.5
V
−
3 V
−
6 V
=
V
R 5
4 V
=
V
R 5
32) Determine the unspecified voltage drop(s) in each circuit of Figure 5-80. Show how to connect a voltmeter to measure each unknown voltage drop.
2V VR2 3.2V
15V
1V
15 V
−
0.5
V
−
1.5
V
−
1 V
−
3.2
V
−
V
R 2
−
2 V
=
0
V
R 2
=
6.8
V
0.5V
1.5V
Figure 5-80(a)
Es
R
8V
R
2R
R
=
8 V
2 R
=
16 V
3 R
=
24 V
4 R
=
32 V
R
+ +
2 R
+
3 R
+
4 R
=
Es
4R 3R 8 V
+
8 V
+
16 V
+
24 V
+
32 V
=
88 V
Figure 5-80(b)
33) In the circuit of Figure 5-81, determine the resistance of R
4

Es
56ohm
11.2V
27ohm 5.4V
4.7ohm
0.94V
R4
4.4V
Figure 5-81
I
=
V
R
R 1
1
⇒
11.2
56
V
Ω
⇒
0.2
A
⇒
200 mA
R 4
=
VR 4
I
⇒
4.4
V
200 mA
⇒
22
Ω

41) What is the voltage across each resistor in Figure 5-86? R is the lowest-value resistor, and all others are multiples of that value as indicated.
R
2R
R
T
=
R
1
+
R
2
+
R
3
+
R
4
+
R
5
RT
= +
2 R
+
3 R
+
4 R
+
5 R
⇒
15 R
Voltage Division Rule
Es
90V
5R
3R
4R
V
R
V
2 R
=
R
×
Es
⇒
V
R
=
R
T
= ×
V
⇒
12 V
V
3 R
= ×
V
⇒
18 V
V
4 R
= ×
V
⇒
24 V
V
5 R
= ×
V
⇒
30 V
R
15 R
×
90 V
⇒
6 V
Figure 5-86
49) Find RT in Figure 5-89.
R1 5.6Mohm
I
R
1
=
V
R 1
⇒
R
1
12
5.6
V
M
Ω
⇒
=
5.6
M
Ω given
2.14
µ
A
12V
R2
4.8V
R3
Es R 2
=
V
I
R 2
⇒
R 3
=
P
I
R
2
3
⇒
4.8
V
2.14
µ
A
⇒
21.5
µ
W
(2.14
µ
A )
2
2.24
M
Ω
⇒
4.69
M
Ω
P=21.5uW
Figure 5-89
RT
=
R 1
+
R 2
+
R 3
⇒
5.6
M
Ω +
2.24
M
Ω +
4.69
M
51) Determine the voltage at each point with respect to ground in Figure 5-90.
Ω ⇒
12.53
M
Ω

Es
100V
A
R1
5.6kohm
R4
1kohm
Figure 5-89
D
B
R2
5.6kohm
C
R3
1kohm
V
V
V
A
B
C
V
D
=
100 V
=
( R
2
+
R
3
+
R
4
)
×
E
S
⇒
7.6
k
Ω
13.2
k
Ω
×
100 V
⇒
55.53
V
=
( 3
+
R
T
R 4)
×
E
S
⇒
2 k
Ω
13.2
k
Ω
×
100 V
R
T
=
R
4
×
E
S
⇒
R
T
1 k
Ω
13.2
k
Ω
×
100
⇒
7.58
V
⇒
15.15
V