24 a 12 a4 ω 48 v v 5 i 5 r 5 i 4 i 7 r 5 4 a6 ω

= (24 A − 12 A)4 Ω = 48 V
V
5
= I
5
R
5
= ( I
4
− I
7
) R
5
= (4 A)6 Ω = 24 V
V
7
= I
7
R
7
= (8 A)2 Ω = 16 V
d. P =
2
7 7
I R = (8 A)
2
2 Ω = 128 W
P = EI = (240 V)(24 A) = 5760 W
26. a. R ′
T
= R
4
|| ( R
6
+ R
7
+ R
8
) = 2 Ω || 7 Ω = 1.56 Ω
R ″
T
= R
2
|| ( R
3
+ R
5
+ R ′
T
) = 2 Ω || (4 Ω + 1 Ω + 1.56 Ω ) = 1.53 Ω
R
T
= R
1
+ R ″
T
= 4 Ω + 1.53 Ω = 5.53 Ω
b. I = 2 V/5.53 Ω = 361.66 mA
c. I
3
=
2 ( ) 2 (361.66 mA)
2 6.56 2 6.56
I Ω Ω
=
Ω + Ω Ω + Ω
= 84.50 mA
I
8
=
2 (84.5 mA)
2 + 7
Ω
Ω Ω
= 18.78 mA
27. The 12 Ω resistors are in parallel.
Network redrawn:
R
T
= 12 Ω
I
s
=
24 V
12
T
E
=
R Ω
= 2 A
I
2 Ω
=
2 A
2 2
s
I
= = 1 A
I
12 Ω
=
2
24 ( ) 2
A
24 12 3
I
Ω
Ω
=
Ω + Ω
P
10 Ω
= ( I
10 Ω
)
2
10 Ω =
2
2
A 10
3
⎛ ⎞
⋅ Ω
⎜ ⎟
⎝ ⎠
= 4.44 W
28. a. R
10
+ R
11
|| R
12
= 1 Ω + 2 Ω || 2 Ω = 2 Ω
R
4
|| ( R
5
+ R
6
) = 10 Ω || 10 Ω = 5 Ω
R
1
+ R
2
|| ( R
3
+ 5 Ω ) = 3 Ω + 6 Ω || 6 Ω = 6 Ω
R
T
= 2 Ω || 3 Ω || 6 Ω = 2 Ω || 2 Ω = 1 Ω
I = 12 V/1 Ω = 12 A
b. I
1
= 12 V/6 Ω = 2 A
I
3
=
6 (2 A)
6 + 6
Ω
Ω Ω
= 1 A
I
4
=
1 A
2
= 0.5 A
c. I
6
= I
4
= 0.5 A
d. I
10
=
12 A
2
= 6 A

Chapter 7 61
29. a. E = (40 mA)(1.6 k Ω ) = 64 V
b.
2
48 V
12 mA
L
R = = 4 k Ω
3
24 V
8 mA
L
R = = 3 k Ω
c.
1
R
I = 72 mA − 40 mA = 32 mA
2
R
I = 32 mA − 12 mA = 20 mA
3
R
I = 20 mA − 8 mA = 12 mA
R
1
=
1
1
64 V 48 V 16 V
=
32 mA 32 mA
R
R
V
=
I
−
= 0.5 k Ω
R
2
=
2
2
48 V 24 V 24 V
=
20 mA 20 mA
R
R
V
=
I
−
= 1.2 k Ω
R
3
=
3
3
24 V
12 mA
R
R
V
=
I
= 2 k Ω
30.
1
R
I = 40 mA
2
R
I = 40 mA − 10 mA = 30 mA
3
R
I = 30 mA − 20 mA = 10 mA
5
R
I = 40 mA
4
R
I = 40 mA − 4 mA = 36 mA
R
1
=
1
1
120 V 100 V 20 V
=
40 mA 40 mA
R
R
V
=
I
−
= 0.5 k Ω
R
2
=
2
2
100 V 40 V 60 V
=
30 mA 30 mA
R
R
V
=
I
−
= 2 k Ω
R
3
=
3
3
40 V
10 mA
R
R
V
=
I
= 4 k Ω
R
4
=
4
4
36 V
36 mA
R
R
V
=
I
= 1 k Ω
R
5
=
5
5
60 V 36 V 24 V
=
40 mA 40 mA
R
R
V
=
I
−
= 0.6 k Ω

Chapter 7 62
P
1
=
2
1 1
I R = (40 mA)
2
0.5 k Ω = 0.8 W (1 watt resistor)
P
2
=
2
2 2
I R = (30 mA)
2
2 k Ω = 1.8 W (2 watt resistor)
P
3
=
2
3 3
I R = (10 mA)
2
4 k Ω = 0.4 W (1/2 watt or 1 watt resistor)
P
4
=
2
4 4
I R = (36 mA)
2
1 k Ω = 1.3 W (2 watt resistor)
P
5
=
2
5 5
I R = (40 mA)
2
0.6 k Ω = 0.96 W (1 watt resistor)
All power levels less than 2 W . Four less than 1 W .
31. a.
yes,
R
L
± R
max
(potentiometer)
b. VDR:
2
R
V = 3 V = 2 2
1 2
(12 V) (12 V)
=
1 k
R R
R R + Ω
R
2
=
3 V(1 k )
12 V
Ω
= 0.25 k Ω = 250 Ω
R
1
= 1 k Ω − 0.25 k Ω = 0.75 k Ω = 750 Ω
c.
1
R
V = E − V
L
= 12 V − 3 V = 9 V
1
R
V = 9 V = 1
1 2
(12 V)
( )
L
R
R R R + &
(Chose
1
R
V rather than
2 L
R R
V
&
since numerator of VDR
equation "cleaner")
9 R
1
+ 9( R
2
|| R
L
) = 12 R
1
1 2
1 2
3( )
2 eq. 2 unk( = 10 k )
1 k
L
L
R R R
R
R R
=
⎫
Ω
⎬
+ = Ω
⎭
&
R
1
=
2
2
3
L
L
R R
R R +
⇒
2
2
3 10 k
10 k
R
R
Ω
+ Ω
and R
1
( R
2
+ 10 k Ω ) = 30 k Ω R
2
R
1
R
2
+ 10 k Ω R
1
= 30 k Ω R
2
R
1
+ R
2
= 1 k Ω : (1 k Ω − R
2
) R
2
+ 10 k Ω (1 k Ω − R
2
) = 30 k Ω R
2
2
2
R + 39 k Ω R
2
− 10 k Ω
2
= 0
R
2
= 0.255 k Ω , − 39.255 k Ω
R
2
= 255 Ω
R
1
= 1 k Ω − R
2
= 745 Ω
32. a. V
ab
=
80 (40 V)
100
Ω
Ω
= 32 V
V
bc
= 40 V − 32 V = 8 V
b. 80 Ω || 1 k Ω = 74.07 Ω
20 Ω || 10 k Ω = 19.96 Ω
V
ab
=
74.07 (40 V)
74.07 + 19.96
Ω
Ω Ω
= 31.51 V
V
bc
= 40 V − 31.51 V = 8.49 V

Chapter 7 63
c. P =
2 2
(31.51 V (8.49 V ) )
+
80 20 Ω Ω
= 12.411 W + 3.604 W = 16.02 W
d. P =
2 2
(32 V (8 V ) )
+
80 20 Ω Ω
= 12.8 W + 3.2 W = 16 W
The applied loads dissipate less than 20 mW of power.
33. a. I
CS
= 1 mA
b. R
shunt
=
max
(100 )(1 mA)
=
20 A 1 mA
m CS
CS
R I
I I
Ω
− −
≅
0.1
20
Ω = 5 m Ω
34. 25 mA: R
shunt
=
(1 k )(50 A)
25 mA 0.05 mA
μ Ω
−
≅ 2 Ω
50 mA: R
shunt
=
(1 k )(50 A)
50 mA 0.05 mA
μ Ω
−
= 1 Ω
100 mA: R
shunt
≅ 0.5 Ω
35. a. R
s
=
max
15 V (50 A)(1 k )
=
50 A
VS
CS
V V
I
μ
μ
− − Ω
= 300 k Ω
b. Ω /V = 1/ I
CS
= 1/50 μ A = 20,000
36. 5 V: R
s
=
5 V (1 mA)(100 )
1 mA
−