Ch08 Solution

Irwin, Basic Engineering Circuit Analysis, 11/E

1

8.1 Given i(t) = 5 cos (400t − 120°) A, determine the period of the current and the frequency in Hertz.

SOLUTION:

Chapter 8: AC Steady-State Analysis

Problem 8.1


1

8.2 Determine the relative phase relationship of the two waves

υ1(t) = 10 cos (377t − 30°) V υ2(t) = 10 cos (377t + 90°) V

SOLUTION:


Problem 8.2


1

8.3 Given the following voltage and current:

i(t) = 5 sin (377t − 20°) V

υ(t) = 10 cos (377t + 30°) V Determine the phase relationship between i(t) and υ(t).

SOLUTION:


Problem 8.3


1

8.4 Write the expression for the waveform shown in Fig. P8.4 as a cosine function with numerical values for the

amplitude, frequency, and phase. υ(t) 24 V 12 V –4 –3 –2 –1

1 2 3 4 5 6 7 8 9 10 11 12 – 24 V

ms

Figure P8.4

SOLUTION:


Problem 8.4


1

8.5 Calculate the current in the resistor in Fig. P8.5 if the voltage input is

(a) υ1(t) = 10 cos (377t + 180°) V. (b) υ2(t) = 12 sin (377t + 45°) V. Give the answers in both the time and frequency domains. i(t) + υ(t)

2Ω

− Figure P8.5

SOLUTION:


Problem 8.5


1

8.6 Calculate the current in the capacitor shown in Fig. P8.6 if the voltage input is

(a) υ1(t) = 10 cos (377t − 30°) V. (b) υ2(t) = 12 sin (377t + 60°) V. Give the answers in both the time and frequency domains. i(t) + υ(t)

C = 1 μF

− Figure P8.6

SOLUTION:


Problem 8.6


1

8.7 Determine the phase angles by which υ1(t) leads i1(t) and υ1(t) leads i2(t), where

υ1(t) = 4 sin (377t + 25°) V i1(t) = 0.05 cos (377t − 20°) A i2(t) = −0.1 sin (377t + 45°) A

SOLUTION:


Problem 8.7


1

8.8 Find the frequency-domain impedance. Z, as shown in Fig. P8.8.

Z

3Ω

j4 Ω

Figure P8.8

SOLUTION:


Problem 8.8


1

8.9 Calculate the current in the inductor shown in Fig. P8.9 if the voltage input is

(a) υ1(t) = 10 cos (377t + 45°) V (b) υ2(t) = 5 sin (377t − 90°) V Give the answers in both the time and frequency domains. i(t) + υ(t)

L = 1 mH

− Figure P8.9

SOLUTION:


Problem 8.9


1

8.10 Find the frequency-domain impedance, Z, in the network in Fig. P8.10. 1Ω

Z

j1 Ω

−j2 Ω

Figure P8.10

SOLUTION:


Problem 8.10


1

8.11 Find Z in the network in Fig. P8.11. 2Ω

Z

1Ω

j2 Ω

2Ω

−j1 Ω

2Ω

j2 Ω

Figure P8.11

SOLUTION:


Problem 8.11


1

8.12 Find the impedance, Z, shown in Fig. P8.12 at a frequency of 400 Hz. 10 mH

Z

2Ω

1Ω

10 μF

Figure P8.12

SOLUTION:


Problem 8.12


1

8.13 Find the frequency-domain impedance, Z, as shown in Fig. P8.13.

Z

2Ω

j1 Ω

−j2 Ω

Figure P8.13

SOLUTION:


Problem 8.13


1

8.14 Find the impedance, Z, shown in Fig. P8.14 at a frequency of 60 Hz. 10 mH

Z

2Ω

1Ω

10 μF

Figure P8.14

SOLUTION:


Problem 8.14


1

8.15 Find Y in the network in Fig. P8.15.

1S

j1 S –j2 S

Y 2S

j2 S

2S

–j1 S

Figure P8.15

SOLUTION:


Problem 8.15


1

8.16 Find the equivalent impedance for the circuit in Fig. P8.16. 8Ω

−j8 Ω

10 Ω j5 Ω −j2 Ω Zeq

j10 Ω 4Ω

Figure P8.16

SOLUTION:


Problem 8.16


1

8.17 Find the frequency-domain impedance, Z, shown in Fig. P8.17. 2Ω

−j1 Ω

1Ω

Z

j2 Ω

−j2 Ω Figure P8.17

SOLUTION:


Problem 8.17


1

8.18 Find the impedance, Z, shown in Fig. P8.18 at a frequency of 60 Hz. 2Ω

Z

4Ω

10 mH

500 μF

Figure P8.18

SOLUTION:


Problem 8.18


1

8.19 Find the frequency-domain impedance, Z, shown in Fig. P8.19. 6Ω 1Ω

2Ω

Z

j1 Ω

–j1 Ω

4Ω

j2 Ω

j2 Ω

j4 Ω Figure P8.19

SOLUTION:


Problem 8.19


1

8.20 In the circuit shown in Fig. P8.20, determine the value of the inductance such that the current is in phase with

the source voltage. 4Ω

12 cos (1000t + 75°) V

+ –

L

100 μF Figure P8.20

SOLUTION:


Problem 8.20


1

8.21 Find the value of C in the circuit shown in Fig. P8.21 so that Z is purely resistive at a frequency of 60 Hz. 1Ω

5 mH

Z

C

Figure P8.21

SOLUTION:


Problem 8.21


1

8.22 The impedance of the network in Fig. P8.22 is found to be purely real at f = 400 Hz. What is the value of C?

6Ω C

Z 10 mH

Figure P8.22

SOLUTION:


Problem 8.22


1

8.23 The admittance of the box in Fig. P8.23 is 0.1 + j0.2 S at 500 rad/s. What is the impedance at 300 rad/s?

Y

Figure P8.23

SOLUTION:


Problem 8.23


1

8.24 The impedance of the box in Fig. P8.24 is 5 + j4 Ω at 1000 rad/s. What is the impedance at 1300 rad/s?

Z

Figure P8.24

SOLUTION:


Problem 8.24


1

8.25 Draw the frequency-domain network and calculate υo(t) in the circuit shown in Fig. P8.25 if i1(t) is 200 cos (105t + 60°)

mA, i2(t) is 100 sin 105 (t + 90°) mA, and υS(t) = 10 sin (105t) V. Also, use a phasor diagram to determine υC (t). − +

i1(t)

i2(t)

30 Ω

υo(t)

υC(t)

+

250 nF

+ −

υS(t)

− Figure P8.25

SOLUTION:


Problem 8.25

2

Problem 8.25




1

8.26 The impedance of the circuit in Fig. P8.26 is real at f = 60 Hz. What is the value of L? L

Z

2Ω

10 mF

Figure P8.26

SOLUTION:


Problem 8.26


1

8.27 Find the frequency at which the circuit shown in Fig. P8.27 is purely resistive.

Z

1Ω

5 mH

1 mF

Figure P8.27

SOLUTION:


Problem 8.27


1

8.28 Find υS (t) in the circuit in Fig. P8.28. 40 Ω υS(t)

+ −

25 μF

+ υC(t) = 80 cos (1000t − 60°) V −

Figure P8.28

SOLUTION:


Problem 8.28


1

8.29 Draw the frequency-domain network and calculate i(t) in the circuit shown in Fig. P8.29 if υS(t) is 15 sin

(10,000t) V. Also, using a phasor diagram, show that υC(t) + υR(t) = υS(t). i(t)

υC(t) + − 66.67 μF

υS(t)

+ −

20 Ω

+ υR(t) −

Figure P8.29

SOLUTION:


Problem 8.29

2

Problem 8.29




1

8.30 Draw the frequency-domain network and calculate υo(t) in the circuit shown in Fig. P8.30 if iS(t) is 1 cos (2500t −

45°) A. Also, using a phasor diagram, show that iC(t) + iR(t) = iS(t). iC(t)

iS(t)

20 μF

iR(t) 10 Ω

+ υo(t) −

Figure P8.30

SOLUTION:


Problem 8.30

2

Problem 8.30




1

8.31 Find iC(t) and i(t) in the network in Fig. P8.31. i(t)

iC(t) 60 Ω

υ(t) = 120 cos (5000t) V

+ −

2.5 μF 16 mH

Figure P8.31

SOLUTION:


Problem 8.31


1

8.32 If υs(t) = 20 cos 5t volts, find υo(t) in the network in Fig. P8.32. 3Ω

0.5 H +

υs(t)

+ −

1H

10 Ω

0.02 F

υo(t) −

Figure P8.32

SOLUTION:


Problem 8.32


1

8.33 Find υo(t) in the circuit in Fig. P8.33. 20 Ω 200 μF

30 mH 100 μF +

170 cos 377t V

+ −

10 Ω 20 mH

15 Ω

υo(t) −

Figure P8.33

SOLUTION:


Problem 8.33

2

Problem 8.33




1

8.34 Find υo(t) in the network in Fig. P8.34.

0.1 F 5 cos 10t A

5Ω

0.4 H

0.02 F

5Ω

+ υo(t) −

Figure P8.34

SOLUTION:


Problem 8.34


1

8.35 Find io(t) in the circuit in Fig. P8.35 if υ (t) = 50 cos 100t V. 4Ω

20 mH

6Ω

5Ω

2000 μF υ(t)

+ –

io(t) 3Ω

1000 μF 50 mH

Figure P8.35

SOLUTION:


Problem 8.35

2

Problem 8.35




1

8.36 Find υo(t) and io(t) in the network in Fig. P8.36. io(t) 0.01 F 25 cos 20t V

+ −

5Ω

0.4 H

0.02 F

5Ω

+ υo(t) −

Figure P8.36

SOLUTION:


Problem 8.36


1

8.37 Calculate υo(t) in Fig. P8.37. 2H

6Ω

2Ω

+ −

50 cos 5t V

1H

0.2 F

5Ω

3Ω

+ 0.05 F

υo(t)

4Ω

− Figure P8.37

SOLUTION:


Problem 8.37

2

Problem 8.37




1

8.38 Find i2(t) in the circuit in Fig. P8.38. i2(t) 5Ω 8Ω

625 μF

25 mH

2Ω 2 cos 400t A

10 mH

4Ω

6Ω

Figure P8.38

SOLUTION:


Problem 8.38


1

8.39 Find the voltage Vo shown in Fig. P8.39. 2Ω

j10 Ω +

10 120° V

+ −

−j12 Ω

Vo −

Figure P8.39

SOLUTION:


Problem 8.39


1

8.40 Find the frequency-domain current I shown in Fig. P8.40.

10 0° A

80 Ω

−j60 Ω I

Figure P8.40

SOLUTION:


Problem 8.40


1

8.41 Find the frequency-domain voltage Vo shown in Fig. P8.41. + 0.5 25° A

j2 Ω

−j5 Ω

10 Ω

Vo −

Figure P8.41

SOLUTION:


Problem 8.41


1

8.42 Find the voltage V shown in Fig. P8.42. + 1 30° A

Z

j1 Ω

−j2 Ω

1Ω

V −

Figure P8.42

SOLUTION:


Problem 8.42


1

8.43 Find the frequency-domain current I shown in Fig. P8.43. 5Ω

37 −145° V

+ −

j6 Ω

−j 4 Ω

10 Ω I

Figure P8.43

SOLUTION:


Problem 8.43


1

8.44 Find υx(t) in the circuit in Fig. P8.44. 10 Ω

0.005 F

0.1 H +

100 cos 40t V

+ −

+ 40 cos (40t − 30°) V −

υx(t) − 5Ω

0.2 H

Figure P8.44

SOLUTION:


Problem 8.44

2

Problem 8.44




1

8.45 Find υo(t) in the network in Fig. P8.45.

50 cos 25t V

0.008 F

0.1 H

10 Ω

υo(t)

+ – +

υx(t)

+ –

2υx(t)

−

5Ω

0.2 H

Figure P8.45

SOLUTION:


Problem 8.45

2

Problem 8.45




1

8.46 Find υ1(t) and υ2(t) in the circuit in Fig. P8.46. 2Ω

4 cos 10t A

12 cos (10t − 25°) V

+−

0.2 H +

υ2(t)

0.02 F

υ1(t)

2 cos (10t + 15°) A

−

Figure P8.46

SOLUTION:


Problem 8.46

2

Problem 8.46




1

8.47 Find the voltage V shown in Fig. P8.47. 1Ω + 100 0° V

+ −

−j1 Ω

V −

Figure P8.47

SOLUTION:


Problem 8.47


1

8.48 Find the voltage Vo shown in Fig. P8.48. 2Ω

j10 Ω +

10 30° V

+ −

−j12 Ω

Vo −

Figure P8.48

SOLUTION:


Problem 8.48


1

8.49 Find the frequency-domain voltage Vo shown in Fig. P8.49. 1Ω + 15 Ω

5 30° A

−j12 Ω

Vo −

Figure P8.49

SOLUTION:


Problem 8.49


1

8.50 Find Vo in the network in Fig. P8.50. 2Ω

−j1 Ω +

j1 Ω

12 0° V

− +

4Ω

2Ω

Vo −

Figure P8.50

SOLUTION:


Problem 8.50


1

8.51 Determine Io in the network shown in Fig. P8.51 if VS = 12 0° V.

2Ω

2Ω

2Ω

+

− +

VS

j2 Ω

V1

+ j2 Ω

−

V2

Io

−

Figure P8.51

SOLUTION:


Problem 8.51


1

8.52 Given the network in Fig. P8.52, determine the value of Vo if VS = 24 0° V. j2 Ω

2Ω + VS

+ −

−j1 Ω

V1

+ 2Ω

−

Vo −

Figure P8.52

SOLUTION:


Problem 8.52


1

8.53 Find VS in the network in Fig. P8.53 if V1 = 4 0° V. −j1 Ω

−+

+ 1Ω

V1

VS

2Ω

j1 Ω

−j1 Ω

2Ω

− Figure P8.53

SOLUTION:


Problem 8.53


1

8.54 If V1 = 4 0° V, find Io in Fig. P8.54. −j2 Ω

−

V1

+

2Ω

j1 Ω

IS

1Ω Io

Figure P8.54

SOLUTION:


Problem 8.54


1

8.55 In the network in Fig. P8.55, Io = 4 0° A. Find Ix.

j1 Ω

1Ω

−j1 Ω 1Ω

2 0° A 1Ω

+ −

12 0° V

Ix

1Ω Io

Figure P8.55

SOLUTION:


Problem 8.55


1

8.56 If Io = 4 0° A in the circuit in Fig. P8.56, find Ix.

+ –

1Ω 1Ω

j1 Ω

Ix

1Ω

−j1 Ω

1Ω

2 0° A

12 0° V Io

1Ω

+ −

4 0° V

Figure P8.56

SOLUTION:


Problem 8.56

2

Problem 8.56




1

8.57 If Io = 4 0° A in the network in Fig. P8.57, find Ix. Ix j1 Ω

1Ω

1Ω 1Ω

R2

1Ω

+ −

12 0° V

2 0° A 1Ω

−j1 Ω

1Ω Io

Figure P8.57

SOLUTION:


Problem 8.57

2

Problem 8.57




1

8.58 In the network in Fig. P8.58, Vo is known to be 4 45° V. Find Z. 2Ω 12 0° V

+ −

+

−j1 Ω Z

1Ω

Vo −

Figure P8.58

SOLUTION:


Problem 8.58


1

8.59 In the network in Fig. P8.59, V1 = 5 −120° V. Find Z. 2Ω

+

V1

−

0.25 Ω

j1 Ω −j0.25 Ω

6 0° A

Z

Figure P8.59

SOLUTION:


Problem 8.59

2

Problem 8.59




1

8.60 Find Vo in the circuit in Fig. P8.60. −j2 Ω

2Ω

+

j2 Ω 24 0° V

+ −

2 90° A

2Ω

Vo −

Figure P8.60

SOLUTION:


Problem 8.60

2

Problem 8.60




1

8.61 Find Vo in the network in Fig. P8.61. 10 Ω + 30 Ω

Vo

j10 Ω

− +

2 60° A

10 30° V

− Figure P8.61

SOLUTION:


Problem 8.61

2

Problem 8.61




1

8.62 Using nodal analysis, find Io in the circuit in Fig. P8.62. V1

V2 1Ω

1Ω

+ −

−j1 Ω

1Ω 12 0° V

2 0° A

4 0° A

Io

Figure P8.62

SOLUTION:


Problem 8.62

2

Problem 8.62




1

8.63 Use nodal analysis to find Io in the circuit in Fig. P8.63. V

−j1 Ω

2Ω

j2 Ω

4 0° A 12 0° V

+ −

+ −

2Ω

6 0° V Io

Figure P8.63

SOLUTION:


Problem 8.63


1

8.64 Find Vo in the network in Fig. P8.64 using nodal analysis. V 2Ω

1Ω

−j1 Ω j2 Ω

12 0° V

+ −

2 0° A

+ 2Ω

+ −

4 0° V

Vo −

Figure P8.64

SOLUTION:


Problem 8.64


1

8.65 Use the supernode technique to find Io in the circuit in Fig. P8.65. 12 0° V

−j1 Ω

2Ω

−+ 1Ω

j2 Ω

2Ω

−j2 Ω

Io Figure P8.65

SOLUTION:


Problem 8.65

2

Problem 8.65




1

8.66 Find I1 and Vo in the network in Fig. P8.66.

+− 12 45° V

+ −

2Ω

−j1 Ω

6 0° V 1Ω

j4 Ω I1

+ −j1 Ω

Vo −

Figure P8.66

SOLUTION:


Problem 8.66


1

8.67 Use nodal analysis to find Vo in the network in Fig. P8.67. 12 0° V −+

+

−j 2 Ω 2 0° A

j4 Ω

2Ω

Vo −

Figure P8.67

SOLUTION:


Problem 8.67


1

8.68 Use nodal analysis to find Io in the circuit in Fig. P8.68. 1Ω −j1 Ω 1Ω 2 0° A

Io

j1 Ω

+ −

12 0° V

Figure P8.68

SOLUTION:


Problem 8.68

2

Problem 8.68




1

8.69 Use nodal analysis to find Vo in the network in Fig. P8.69. −j1 Ω 1Ω

j1 Ω +

+ −

1Ω 6 0° V

2 0° A

Vo −

Figure P8.69

SOLUTION:


Problem 8.69

2

Problem 8.69




1

8.70 Use nodal analysis to find Vo in the circuit in Fig. P8.70. −+

12 0° V

1Ω

1Ω +

2 0° A

−j1 Ω

1Ω

Vo −

Figure P8.70

SOLUTION:


Problem 8.70

2

Problem 8.70




1

8.71 Use nodal analysis to find Vo in the network in Fig. P8.71. −j1 Ω 1Ω

+ Vo

4 0° V + −

1Ω

− + −

+ −

12 0° V

6 0° V

Figure P8.71

SOLUTION:


Problem 8.71


1

8.72 Use nodal analysis to find Io in the network in Fig. P8.72. 1Ω

12 0° V

2 0° A

−+ 1Ω

−j1 Ω

1Ω Io

Figure P8.72

SOLUTION:


Problem 8.72

2

Problem 8.72




1

8.73 Use nodal analysis to find Vo in the circuit in Fig. P8.73. 6 0° V

12 0° V

+−

−+

1Ω

−j1 Ω

+ j2 Ω

2 0° A

1Ω

1Ω

Vo −

Figure P8.73

SOLUTION:


Problem 8.73

2

Problem 8.73




1

8.74 Find Io in the circuit in Fig. P8.74 using nodal analysis. Io 2Ω

2Ω −j2 Ω

12 0° V

+ −

1Ω

2 0° A

j1 Ω

+ −

6 0° V

Figure P8.74

SOLUTION:


Problem 8.74

2

Problem 8.74




1

8.75 Use nodal analysis to find Io in the circuit in Fig. P8.75.

+ −

1Ω

6 0° V

j1 Ω

4 0° A 12 0° V

+− 2 0° A −j1 Ω

1Ω

1Ω

1Ω

Io Figure P8.75

SOLUTION:


Problem 8.75

2

Problem 8.75




1

8.76 Use nodal analysis to find Vo in the network in Fig. P8.76. + Vx −

+−

1Ω

12 0° V

+ −

–j1 Ω

2Vx + 1Ω

Vo −

Figure P8.76

SOLUTION:


Problem 8.76

2

Problem 8.76




1

8.77 Use nodal analysis to find Vo in the network in Fig. P8.77. 2 0° A

+

−j1 Ω

Vx −

+

1Ω + − 6 0° V

+ –

2Vx

1Ω

Vo −

Figure P8.77

SOLUTION:


Problem 8.77


1

8.78 Use nodal analysis to find Io in the network in Fig. P8.78. −j 1 Ω − 1Ω 2Vx

+ –

Vx + 1Ω

1Ω

+ −

12 0° V

Io Figure P8.78

SOLUTION:


Problem 8.78


1

8.79 Use nodal analysis to find Vo in the network in Fig. P8.79. + 4 0° V

+ –

j1 Ω 1Ω

1Ω

1Ω

+ –

Vo

4Vo −

Figure P8.79

SOLUTION:


Problem 8.79

2

Problem 8.79




1

8.80 Use nodal analysis to find Io in the network in Fig. P8.80.

1Ω

2Vx

− +

+ V − x

1Ω

−j 1 Ω 1Ω

1Ω Io

+ −

12 0° V

Figure P8.80

SOLUTION:


Problem 8.80

2

Problem 8.80




1

8.81 Use nodal analysis to find Vo in the circuit in Fig. P8.81.

4Vo

+ –

1Ω

1Ω 1Ω

−j Ω

+

+ –

4 0° V

Vo −

Figure P8.81

SOLUTION:


Problem 8.81


1

8.82 Use nodal analysis to find Vx in the circuit in Fig. P8.82. 12 0° V

+−

j1 Ω +

2Vx

1Ω

−j1 Ω

Vx

1Ω

− Figure P8.82

SOLUTION:


Problem 8.82

2

Problem 8.82




1

8.83 Find the voltage across the inductor in the circuit shown in Fig. P8.83 using nodal analysis. V1

10 30° V

+ −

−j2 Ω

4Ω

V2

j1 Ω

2Ix

Ix

Figure P8.83

SOLUTION:


Problem 8.83


1

8.84 Use nodal analysis to find Vo in the circuit in Fig. P8.84.

−j1 Ω

1Ω

4 0° V

+−

+ Vx

1Ω

+ 1Ω

−

+ −

4Vx

Vo −

Figure P8.84

SOLUTION:


Problem 8.84

2

Problem 8.84




1

8.85 Use nodal analysis to find Vo in the network in Fig. P8.85. + Vx

+ −j1 Ω

1Ω

−

2 0° A

1Ω

6 0° V

Vo

1Ω

−

1Ω

+ −

+ −

4Vx

Figure P8.85

SOLUTION:


Problem 8.85

2

Problem 8.85




1

8.86 Use nodal analysis to find Vo in the circuit in Fig. P8.86. + Vx

+ −

1Ω

6 0° V

2 0° A

−

4 0° A

+

1Ω

−j1 Ω 1Ω

+ −

4Vx

Vo −

Figure P8.86

SOLUTION:


Problem 8.86

2

Problem 8.86




1

8.87 Use nodal analysis to find Vo in the circuit in Fig. P8.87. Ix 4Ix

−j1 Ω + +

Vx

Vo

−

1Ω

1Ω

1Ω 1Ω

+ −

6 0° V

+ −

2Vx

− Figure P8.87

SOLUTION:


Problem 8.87

2

Problem 8.87




1

8.88 Use nodal analysis to find Io in the circuit in Fig. P8.88. Ix

+ 1Ω

−j1 Ω

Vx −

1Ω Io

1Ω

1Ω 4 Ix

+ –

4 0° V

+ –

2Vx

Figure P8.88

SOLUTION:


Problem 8.88

2

Problem 8.88




1

8.89 Use mesh analysis to find Vo in the circuit shown in Fig. P8.89. −j1 Ω

12 45° V

−+ 6 0° V

− +

j2 Ω I1

I2

+ 2Ω V o −

Figure P8.89

SOLUTION:


Problem 8.89

2

Problem 8.89




1

8.90 Solve problem 8.67 using loop analysis.

SOLUTION:


Problem 8.90


1


SOLUTION:


Problem 8.91


1


SOLUTION:


Problem 8.92


1

8.93 Find Vo in the network in Fig. P8.93 using loop analysis. − j1 Ω

j2 Ω 2 0° A

1Ω

+ 1Ω

+ –

12 0° V

Vo −

Figure P8.93

SOLUTION:


Problem 8.93


1

8.94 Find Vo in the network in Fig. P8.94 using loop analysis. + Vo − 1Ω 1Ω

+ −

12 0° V

−j1 Ω

1Ω 2 0° A

Figure P8.94

SOLUTION:


Problem 8.94

2

Problem 8.94




1

8.95 Find Io in the network in Fig. P8.95 using loop analysis.

1Ω

2 0° A

−j1 Ω

12 0° V

+ −

4 0° A

1Ω

1Ω

j1 Ω

Io Figure P8.95

SOLUTION:


Problem 8.95

2

Problem 8.95




1

8.96 Find Vo in the circuit in Fig. P8.96 using mesh analysis. j2 Ω

2Ω

+ 2 0° A

2Ω

−j1 Ω

+−

1Ω

Vo −

6 0° V 4 0° A

Figure P8.96

SOLUTION:


Problem 8.96


1

8.97 Find Vo in the network in Fig. P8.97. j1 Ω + 12 0° V

+ −

2Ω 2Ω

16 0° V

− +

−j1 Ω

Vo

2 0° A −

Figure P8.97

SOLUTION:


Problem 8.97

2

Problem 8.97




1

8.98 Determine Vo in the circuit in Fig. P8.98. 2Ω

−j1 Ω

2Ω +

6 0° A

+ −

j2 Ω 12 0° V

1Ω

Vo −

Figure P8.98

SOLUTION:


Problem 8.98


1

8.99 Use mesh analysis to find Vo in the circuit shown in Fig. P8.99. j2 Ω

4Ω

−j4 Ω

12 0° V

+ −

I1

I2

+ 2Ω

4 90° A

Vo −

Figure P8.99

SOLUTION:


Problem 8.99


1

8.100 Using loop analysis, find Io in the network in Fig. P8.100. 12 0°V

2Ω

−+

2 0° A

−j2 Ω

j1 Ω

2Ω

4 0° A

Io Figure P8.100

SOLUTION:


Problem 8.100

2

Problem 8.100




1

8.101 Use mesh analysis to find Vo in the circuit in Fig. P8.101.

j1 Ω

6 0° A −j2 Ω

4 0°A 1Ω

+ 2Ω

Vo

2Ω

2 0° A

− Figure P8.101

SOLUTION:


Problem 8.101


1

8.102 Use loop analysis to find Io in the network in Fig. P8.102. Io 4 30° A

−j1 Ω

1Ω 1Ω

1Ω 2Vx

+ −

+ 1Ω

2 0° A

Vx −

Figure P8.102

SOLUTION:


Problem 8.102

2

Problem 8.102




1

8.103 Find Vo in the network in Fig. P8.103. 4 0° A

−j1 Ω

1Ω

Ix +

2Ix

j1 Ω

1Ω

Vo −

Figure P8.103

SOLUTION:


Problem 8.103

2

Problem 8.103




1

8.104 Use loop analysis to find Vo in the circuit in Fig. P8.104. + 4Ix

−j1 Ω

1Ω

1Ω 1Ω

+ –

Vo

4 0° V

Ix

−

Figure P8.104

SOLUTION:


Problem 8.104

2

Problem 8.104




1

8.105 Use loop analysis to find Vo in the network in Fig. P8.105. + Vx

+ −

1Ω

2 0° A

6 0° V

−

4 0° A

+

1Ω

−j1 Ω 1Ω

+ −

Vx

Vo −

Figure P8.105

SOLUTION:


Problem 8.105


1

8.106 Use superposition to find Vo in the network in Fig. P8.106. 12 0° V

−+ 1Ω

4 0° A

1Ω −j1 Ω

+ Vo −

Figure P8.106

SOLUTION:


Problem 8.106


1

8.107 Solve problem 8.67 using superposition.

SOLUTION:


Problem 8.107


1


SOLUTION:


Problem 8.108


1


SOLUTION:


Problem 8.109

2

Problem 8.109




1

8.110 Use superposition to determine Vo in the circuit in Fig. P8.110. 1Ω

−j1 Ω

j1 Ω +

6 0° V

− +

6 0° A

1Ω

Vo −

Figure P8.110

SOLUTION:


Problem 8.110

2

Problem 8.110




1

8.111 Using superposition, find Vo in the circuit in Fig. P8.111. 1Ω

−j1 Ω j2 Ω

6 0° V

+ −

2 0° A

+ Vo

2Ω

− Figure P8.111

SOLUTION:


Problem 8.111


1

8.112 Find Vo in the network in Fig. P8.112 using superposition. 1Ω 16 0° V

+ −

2Ω −j2 Ω

4 0° A

+

2 Ω Vo j3 Ω −

Figure P8.112

SOLUTION:


Problem 8.112

2

Problem 8.112




1

8.113 Find Vo in the network in Fig. P8.113 using superposition. 2Ω

2 0° A

12 0° V

−+ −j2 Ω

j4 Ω

+ 2 Ω Vo −

Figure P8.113

SOLUTION:


Problem 8.113

2

Problem 8.113




1

8.114 Use superposition to find Vo in the circuit in Fig. P8.114.

j1 Ω

2 0° A

1Ω −j1 Ω

4 0° A

+

1Ω

+ −

6 0° V

1Ω

Vo −

Figure P8.114

SOLUTION:


Problem 8.114

2

Problem 8.114




1

8.115 Use superposition to find Vo in the network in Fig. P8.115. +

+ −

1Ω

6 0° V

1Ω

1Ω −j1 Ω

Vo

4 0° A −

Figure P8.115

SOLUTION:


Problem 8.115

2

Problem 8.115




1

8.116 Solve problem 8.68 using source exchange.

SOLUTION:


Problem 8.116


1

8.117 Use source exchange to find the current Io in the network in Fig. P8.117. 1Ω

2Ω

12 0° V

+ −

−j1 Ω

2Ω 2 0° A

Io

4 0° A

Figure P8.117

SOLUTION:


Problem 8.117


1

8.118 Use source exchange to determine Vo in the network in Fig. P8.118.

−+ −j1 Ω 12 0° V

+ −

6 0° V 1Ω

2 0° A

2Ω

+ Vo −

Figure P8.118

SOLUTION:


Problem 8.118


1

8.119 Use source transformation to find Vo in the circuit in Fig. P8.119. + 12 0° V

+ −

−j2 Ω

1Ω

Vo −

1Ω 12 Ω

1Ω 2 0° A

Figure P8.119

SOLUTION:


Problem 8.119

2

Problem 8.119




1

8.120 Use source transformation to find Vo in the circuit in Fig. P8.120. −j2 Ω + 2 0° A

5Ω

1Ω

Vo −

1Ω 4 0° V

+ −

2Ω

+ −

6 0° V

2Ω Figure P8.120

SOLUTION:


Problem 8.120

2

Problem 8.120




1

8.21 Use source transformation to find Io in the circuit in Fig. P8.121. 3Ω 6 0° V

Io

1Ω

+ −

12 Ω 4 0° A

2 0° A

+ −

6Ω

−j3 Ω

8 0° V

4Ω

Figure P8.121

SOLUTION:


Problem 8.21

2

Problem 8.21




1

8.122 Solve problem 8.67 using Thévenin’s theorem.

SOLUTION:


Problem 8.122


1


SOLUTION:


Problem 8.123


1


SOLUTION:


Problem 8.124


1

8.125 Use Thevenin’s theorem to find Vo in the circuit in Fig. P8.125. j2 Ω

4Ω

−j4 Ω

12 0° V

+ −

I1

I2

+ 2Ω

4 90° A

Vo −

Figure P8.125

SOLUTION:


Problem 8.125


1

8.126 Apply Thévenin’s theorem twice to find Vo in the circuit in Fig. P8.126. 1Ω

2Ω

1Ω +

6 0° V

+ −

−j1 Ω

j1 Ω

1Ω

Vo −

Figure P8.126

SOLUTION:


Problem 8.126

2

Problem 8.126




1

8.127 Use Thévenin’s theorem to find Vo in the network in Fig. P8.127. 1Ω

–j2 Ω + −

+ Vo

6 0° V

2 0° A 1Ω

− Figure P8.127

SOLUTION:


Problem 8.127

2

Problem 8.127




1

8.128 Use Thévenin’s theorem to find Io in the network in Fig. P8.128.

2 0° A 1Ω

j1 Ω −j1 Ω

+ −

12 0° V

1Ω Io

Figure P8.128

SOLUTION:


Problem 8.128

2

Problem 8.128




1

8.129 Use Thévenin’s theorem to find the voltage across the 2-Ω resistor in the network in Fig. P8.129. 2Ω

−+ −j1 Ω

12 0° V 1Ω

j1 Ω

2 0° A

Figure P8.129

SOLUTION:


Problem 8.129

2

Problem 8.129




1

8.130 Use Thévenin’s theorem to find Io in the network in Fig. P8.130. Io 1Ω

+ −

12 0° V

1Ω −j1 Ω

1Ω 2 0° A

Figure P8.130

SOLUTION:


Problem 8.130

2

Problem 8.130




1

8.131 Use Thévenin’s theorem to find Vo in the network in Fig. P8.131.

−+ 1Ω

12 0° V

1Ω +

2 0° A

−j 1 Ω

1Ω

Vo −

Figure P8.131

SOLUTION:


Problem 8.131

2

Problem 8.131




1


–j1 Ω

1Ω

4 0° A 1Ω

3 0° A

Io

12 0° V

−+ j1 Ω

1Ω

Figure P8.132

SOLUTION:


Problem 8.132

2

Problem 8.132




1

8.133 Use Thévenin’s theorem to find Vo in the network in Fig. P8.133. 1Ω 4 0° A 1Ω 6 0° A

−j1 Ω

+ 4 0° A

j2 Ω

2Ω

Vo −

Figure P8.133

SOLUTION:


Problem 8.133

2

Problem 8.133




1

8.134 Use Thévenin’s theorem to determine Io in the circuit in Fig. P8.134. 2 0° A

−+ −j2 Ω

6 0° V 1Ω

1Ω

1Ω

4 0° A

Io Figure P8.134

SOLUTION:


Problem 8.134

2

Problem 8.134




1

8.135 Use Thévenin’s theorem to find Vo in the network in Fig. P8.135. 2 0° A

+

−j1 Ω

Vx −

+

1Ω + − 6 0° V

2Vx

+ –

1Ω

Vo −

Figure P8.135

SOLUTION:


Problem 8.135

2

Problem 8.135




1

8.136 Use Thévenin’s theorem to find Io in the network in Fig. P8.136. −j 1 Ω − 1Ω 2Vx

+ –

Vx + 1Ω

1Ω

+ −

12 0° V

Io Figure P8.136

SOLUTION:


Problem 8.136

2

Problem 8.136




1

8.137 Find Vo in the network in Fig. P8.137 using Thévenin’s theorem. 12 0° V

+− + 2Vx

1Ω

−j1 Ω

Vx −

j1 Ω

+ 1Ω

Vo −

Figure P8.137

SOLUTION:


Problem 8.137

2

Problem 8.137




1

8.138 Find the Thévenin’s equivalent for the network in Fig. P8.138 at terminals A–B. A

+ −j1 Ω

4 0° A

1Ω

j1 Ω

Vx −

2Vx B

Figure P8.138

SOLUTION:


Problem 8.138

2

Problem 8.138





3

Problem 8.138


1

8.139 Given the network in Fig. P8.139, find the Thévenin’s equivalent of the network at terminals A–B.

+−

12 0° V

+−

V2

6 0° V

1Ω

A

−j1 Ω

1Ω V1

V3 j1 Ω

+ −

4 0° V B

Figure P8.139

SOLUTION:


Problem 8.139

2

Problem 8.139




1

8.140 Use Thévenin’s theorem to determine Io in the network in Fig. P8.140.

2 0° A

1Ω

1Ω 1Ω

−j1 Ω

4 0° A 1Ω

Io 12 0° V

+ −

1Ω

j1 Ω

+ −

6 0° V

Figure P8.140

SOLUTION:


Problem 8.140

2

Problem 8.140




1


1Ω

2Vx

− +

+ V − x

1Ω

−j1 Ω 1Ω

1Ω Io

+ −

12 0° V

Figure P8.141

SOLUTION:


Problem 8.141

2

Problem 8.141





3

Problem 8.141


1

8.142 Solve problem 8.68 using Norton’s theorem.

SOLUTION:


Problem 8.142


1

8.143 Solve problem 8.69 using Norton’s theorem.

SOLUTION:


Problem 8.143


1

8.144 Find Vx in the circuit in Fig. P8.144 using Norton’s theorem. 11.3 45° V

−+ 2 0° A

j4 Ω

+ 10 Ω −j3 Ω

Vx −

Figure P8.144

SOLUTION:


Problem 8.144

2

Problem 8.144




1

8.145 Find Io in the network in Fig. P8.145 using Norton’s theorem. −j2 Ω

j1 Ω

6 45° A

2Ω

2 0° A

Io

Figure P8.145

SOLUTION:


Problem 8.145

2

Problem 8.145




1

8.146 Use Norton’s theorem to find Vo in the network in Fig. P8.146. + −j1 Ω

4 0° A

1Ω

Vx

1Ω

− +

j1 Ω

2Vx

1Ω

Vo −

Figure P8.146

SOLUTION:


Problem 8.146

2

Problem 8.146




1

8.147 Find Vo using Norton’s theorem for the circuit in Fig. P8.147.

4 0° V

+ −

+ −

−j1 Ω 1Ω

Vx

+

8 0° V

− +

1Ω j1 Ω

+ −

2Vx

1Ω

Vo −

Figure P8.147

SOLUTION:


Problem 8.147

2

Problem 8.147




1

8.148 Use Norton’s theorem to find Vo in the circuit in Fig. P8.148.

−j1 Ω

4Ix

2 0° A

1Ω 1Ω 4 0° A

1Ω Ix

+ 2Ω

Vo −

Figure P8.148

SOLUTION:


Problem 8.148

2

Problem 8.148




1

8.149 Apply Norton’s theorem to find Vo in the network in Fig. P8.149. −j1 Ω +

1Ω 6 0° V

+ −

1Ω

1Ω

j1 Ω 4 0° A

Vo

1Ω −

Figure P8.149

SOLUTION:


Problem 8.149

2

Problem 8.149




1

8.150 Find Vo in the circuit in Fig. P8.150.

6 0° V

+ −

2 0° A

1Ω

−j1 Ω

+−

+ 1Ω

1Ω

1Ω

12 0° V

Vo

1Ω

j1 Ω

− Figure P8.150

SOLUTION:


Problem 8.150

2

Problem 8.150




1

8.151 Find the node voltages in the network in Fig. P8.151. 1Ω

−j1 Ω

2Ω

+ −

1Ω

j1 Ω

1Ω 12 0° V

2 0° A

2Ω

−j2 Ω

Figure P8.151

SOLUTION:


Problem 8.151

2

Problem 8.151




1

8.152 Determine Vo in the network in Fig. P8.152.

1Ω

2 0° A

+ −

1Ω

6 0° V

−+ −j1 Ω

1Ω 1Ω

j1 Ω

12 30° V

+ 1Ω

Vo −

Figure P8.152

SOLUTION:


Problem 8.152

2

Problem 8.152




1

8.153 Find Io in the network in Fig. P8.153.

2 0° A

1Ω

4 0° A

1Ω 1Ω Io

−j1 Ω 12 0° V

+ −

1Ω

1Ω j1 Ω

+ −

6 0° V

Figure P8.153

SOLUTION:


Problem 8.153

2

Problem 8.153




1

8.154 Use both nodal analysis and loop analysis to find Io in the network in Fig. P8.154.

2 0° A

1Ω 1Ω

Io

2Vx

1Ω

2Ix

1Ω

−+ +

+ −

−j1 Ω

12 0° V

Vx −

1Ω

j1 Ω

Ix

Figure P8.154

SOLUTION:


Problem 8.154

2

Problem 8.154




1


−j1 Ω

1Ω

1Ω

6 0° V

12 0° V

+−

−+

2 0° A

1Ω

1Ω Io 1Ω

4 0° A

j1 Ω

Figure P8.155

SOLUTION:


Problem 8.155

2

Problem 8.155




1


1Ω

1Ω j1 Ω

Ix

1Ω

1Ω

2Ix

Io 1Ω

1Ω

+ −

6 0° V

−j1 Ω

− +

4 0° V

Figure P8.156

SOLUTION:


Problem 8.156

2

Problem 8.156




1

8.157 Determine Io in the network in Fig. P8.157.

1Ω

j1 Ω

−j1 Ω

1Ω

1Ω

2 0° A

1Ω

12 0° V

−+ 2Vx

Io 1Ω

−+

+ Vx

1Ω

−

Figure P8.157

SOLUTION:


Problem 8.157

2

Problem 8.157




1

8.158 Find Io in the circuit in Fig. P8.158.

12 0° V

−j1 Ω

+ − 1Ω

1Ω

1Ω

2 0° A

Io

Ix 1Ω

6 0° V

1Ω 2Ix

+ −

j1 Ω

Figure P8.158

SOLUTION:


Problem 8.158

2

Problem 8.158



Ch08 Solution

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