Solution: Use Thvenins theorem to find Io in the network in

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

Determine the relative phase relationship of the two waves 1(t) = 10 cos (377t 30) V 2(t) = 10 cos (377t + 90) V

Given the following voltage and current: i(t) = 5 sin (377t 20) V (t) = 10 cos (377t + 30) V Determine the phase relationship between i(t) and (t).

Write the expression for the waveform shown in Fig. P8.4 as a cosine function with numerical values for the amplitude, frequency, and phase. 1 2345 24 V 24 V 12 V 4 3 2 1 6 7 8 9 10 11 12 ms (t) Figure P8.4

Calculate the current in the resistor in Fig. P8.5 if the voltage input is (a) 1(t) = 10 cos (377t + 180) V. (b) 2(t) = 12 sin (377t + 45) V. Give the answers in both the time and frequency domains. 2 + i(t) (t) Figure P8.5

Calculate the current in the capacitor shown in Fig. P8.6 if the voltage input is (a) 1(t) = 10 cos (377t 30) V. (b) 2(t) = 12 sin (377t + 60) V. Give the answers in both the time and frequency domains. (t) i(t) C = 1 F + Figure P8.6

Determine the phase angles by which 1(t) leads i1(t) and 1(t) leads i2(t), where 1(t) = 4 sin (377t + 25) V i1(t) = 0.05 cos (377t 20) A i2(t) = 0.1 sin (377t + 45) A

Find the frequency-domain impedance. Z, as shown in Fig. P8.8. Z 3 j4 Figure P8.8

Calculate the current in the inductor shown in Fig. P8.9 if the voltage input is (a) 1(t) = 10 cos (377t + 45) V (b) 2(t) = 5 sin (377t 90) V Give the answers in both the time and frequency domains. i(t) L = 1 mH + (t) Figure P8.9

Find the frequency-domain impedance, Z, in the network in Fig. P8.10. j1 j2 1 Z Figure P8.10

Find Z in the network in Fig. P8.11. 2 1 2 2 j1 Z j2 j2 Figure P8.11

Find the impedance, Z, shown in Fig. P8.12 at a frequency of 400 Hz. 1 10 mH 2 Z 10 F Figure P8.12

Find the frequency-domain impedance, Z, as shown in Fig. P8.13. Z 2 j1 j2 Figure P8.13

Find the impedance, Z, shown in Fig. P8.14 at a frequency of 60 Hz. Z 1 10 F 10 mH 2 Figure P8.14

Find Y in the network in Fig. P8.15. j2 S j1 S j1 S j2 S 1 S 2 S 2 S Y Figure P8.15

Find the equivalent impedance for the circuit in Fig. P8.16. Zeq 8 j10 j5 4 10 j2 j8 Figure P8.16

Find the frequency-domain impedance, Z, shown in Fig. P8.17. Z j1 j2 1 j2 2 Figure P8.17

Find the impedance, Z, shown in Fig. P8.18 at a frequency of 60 Hz. Z 10 mH 500 F 2 4 Figure P8.18

Find the frequency-domain impedance, Z, shown in Fig. P8.19. Z 1 4 2 j2 j4 j2 j1 j1 6 Figure P8.19

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. + 12 cos (1000t + 75) V 100 F 4 L Figure P8.20

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. Z C 1 5 mH Figure P8.21

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? 6 10 mH Z C Figure P8.22

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

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

Draw the frequency-domain network and calculate o(t) in the circuit shown in Fig. P8.25 if i1(t) is 200 cos (105 t + 60) mA, i2(t) is 100 sin 105 (t + 90) mA, and S(t) = 10 sin (105 t) V. Also, use a phasor diagram to determine C(t). 30 250 nF i 1(t) i 2(t) + o(t) + + S(t) C(t) Figure P8.25

The impedance of the circuit in Fig. P8.26 is real at f = 60 Hz. What is the value of L? 2 L Z 10 mF Figure P8.26

Find the frequency at which the circuit shown in Fig. P8.27 is purely resistive. Z 1 5 mH 1 mF Figure P8.27

Find S (t) in the circuit in Fig. P8.28. 40 + + S(t) 25 F C(t) = 80 cos (1000t 60) V Figure P8.28

Draw the frequency-domain network and calculate i(t) in the circuit shown in Fig. P8.29 if S(t) is 15 sin (10,000t) V. Also, using a phasor diagram, show that C(t) + R(t) = S(t). 20 i(t) + R(t) + + S(t) C(t) 66.67 F Figure P8.29

Draw the frequency-domain network and calculate o(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). 10 o(t) + i S(t) i C(t) i R(t) 20 F Figure P8.30

Find iC(t) and i(t) in the network in Fig. P8.31. + (t) = 120 cos (5000t) V 16 mH 60 2.5 F i C i(t) (t) Figure P8.31

If s(t) = 20 cos 5t volts, find o(t) in the network in Fig. P8.32. o(t) + 3 + 10 0.5 H 1 H 0.02 F s(t) Figure P8.32

Find o(t) in the circuit in Fig. P8.33. o(t) + 20 15 10 + 20 mH 200 F 30 mH 100 F 170 cos 377t V Figure P8.33

Find o(t) in the network in Fig. P8.34. Figure P8.34

Find io(t) in the circuit in Fig. P8.35 if (t) = 50 cos 100t V. 3 6 5 4 20 mH 50 mH 2000 F 1000 F i o(t) (t) + Figure P8.35

Find o(t) and io(t) in the network in Fig. P8.36. 5 5 0.4 H 0.02 F 0.01 F 25 cos 20t V o(t) + + i o(t) Figure P8.36

Calculate o(t) in Fig. P8.37. 4 5 3 6 2 H 2 1 H 0.05 F 50 cos 5t V + 0.2 F o(t) + Figure P8.37

Find i2(t) in the circuit in Fig. P8.38. 8 6 5 2 4 25 mH 625 F 2 cos 400t A 10 mH i 2(t) Figure P8.38

Find the voltage Vo shown in Fig. P8.39. 10 120 V 2 j12 j10 + Vo + Figure P8.39

Find the frequency-domain current I shown in Fig. P8.40. 10 0 A 80 j60 I Figure P8.40

Find the frequency-domain voltage Vo shown in Fig. P8.41. Vo + 0.5 25 A j2 j5 10 Figure P8.41

Find the voltage V shown in Fig. P8.42. V + 1 30 A Z j1 j2 1 Figure P8.42

Find the frequency-domain current I shown in Fig. P8.43. 37 145 V j6 j4 5 + 10 I Figure P8.43

Find x(t) in the circuit in Fig. P8.44. 10 5 + + 0.1 H 0.2 H 0.005 F 100 cos 40t V 40 cos (40t 30) V x(t) + Figure P8.44

Find o(t) in the network in Fig. P8.45. + 5 10 0.1 H 0.2 H 0.008 F 50 cos 25t V x + (t) 2x(t) o(t) + Figure P8.45

Find 1(t) and 2(t) in the circuit in Fig. P8.46. 2 0.2 H 0.02 F 1(t) + 2(t) + 4 cos 10t A 2 cos (10t + 15) A 12 cos (10t 25) V Figure P8.46

Find the voltage V shown in Fig. P8.47. 100 0 V V 1 + j1 + Figure P8.47

Find the voltage Vo shown in Fig. P8.48. 10 30 V 2 j12 j10 + Vo + Figure P8.48

Find the frequency-domain voltage Vo shown in Fig. P8.49. Vo 1 15 5 30 A j12 + Figure P8.49

Find Vo in the network in Fig. P8.50. 2 2 j1 j1 + 4 Vo + 12 0 V Figure P8.50

Determine Io in the network shown in Fig. P8.51 if VS = 12 0 V. 2 2 2 VS j2 j2 V2 Io + V1 + + Figure P8.51

Given the network in Fig. P8.52, determine the value of Vo if VS = 24 0 V. VS Vo 2 j2 j1 2 + V1 + + Figure P8.52

Find VS in the network in Fig. P8.53 if V1 = 4 0 V. V1 VS j1 1 2 j1 2 j1 + + Figure P8.53

If V1 = 4 0 V, find Io in Fig. P8.54. j2 2 j1 IS 1 V1 Io + Figure P8.54

In the network in Fig. P8.55, Io = 4 0 A. Find Ix. 1 1 1 j1 j1 1 Io Ix + 2 0 A 12 0 V Figure P8.55

If Io = 4 0 A in the circuit in Fig. P8.56, find Ix. 1 1 1 j1 j1 1 Io Ix + 1 12 0 V 2 0 A + 4 0 V Figure P8.56

If Io = 4 0 A in the network in Fig. P8.57, find Ix. 1 1 1 1 1 j1 j1 Io Ix R2 1 + 2 0 A 12 0 V Figure P8.57

In the network in Fig. P8.58, Vo is known to be 4 45 V. Find Z. 2 j1 + 1 12 0 V Z Vo + Figure P8.58

In the network in Fig. P8.59, V1 = 5 120 V. Find Z. Z 2 0.25 j1 j0.25 V1 + 6 0 A Figure P8.59

Find Vo in the circuit in Fig. P8.60. Vo + 24 0 V 2 90 A + 2 j2 2 j2 Figure P8.60

Find Vo in the network in Fig. P8.61. 2 60 A 30 10 30 V 10 V j10 o + + Figure P8.61

Using nodal analysis, find Io in the circuit in Fig. P8.62. Io V1 V2 + 4 0 A 12 0 V 2 0 A 1 1 1 j1 Figure P8.62

Use nodal analysis to find Io in the circuit in Fig. P8.63. Io V + + 6 0 V 4 0 A 12 0 V 2 2 j1 j2 Figure P8.63

Find Vo in the network in Fig. P8.64 using nodal analysis. 12 0 V 2 0 A 4 0 V 2 2 1 V j1 j2 Vo + + + Figure P8.64

Use the supernode technique to find Io in the circuit in Fig. P8.65. 12 0 V 2 1 2 Io + j2 j2 j1 Figure P8.65

Find I1 and Vo in the network in Fig. P8.66. Vo + 6 0 V 12 45 V 2 j1 j4 1 j1 + + I1 Figure P8.66

Use nodal analysis to find Vo in the network in Fig. P8.67. Vo + 2 0 A 12 0 V 2 j2 j4 + Figure P8.67

Use nodal analysis to find Io in the circuit in Fig. P8.68. 2 0 A 12 0 V j1 j1 1 + Io 1 Figure P8.68

Use nodal analysis to find Vo in the network in Fig. P8.69. Vo + + 6 0 V 2 0 A j1 j1 1 1 Figure P8.69

Use nodal analysis to find Vo in the circuit in Fig. P8.70. 1 1 1 Vo + 2 0 A 12 0 V + j1 Figure P8.70

Use nodal analysis to find Vo in the network in Fig. P8.71. + Vo 4 0 V 6 0 V 12 0 V j1 1 1 + + + Figure P8.71

Use nodal analysis to find Io in the network in Fig. P8.72. 1 1 1 Io j1 12 0 V 2 0 A + Figure P8.72

Use nodal analysis to find Vo in the circuit in Fig. P8.73. 6 0 V 2 0 A 12 0 V 1 1 j1 j2 1 + + Vo + Figure P8.73

Find Io in the circuit in Fig. P8.74 using nodal analysis. 2 0 A 12 0 V 6 0 V j2 2 2 1 j1 Io + + Figure P8.74

Use nodal analysis to find Io in the circuit in Fig. P8.75. 6 0 V 4 0 A 2 0 A 12 0 V j1 j1 1 1 1 1 Io + + Figure P8.75

Use nodal analysis to find Vo in the network in Fig. P8.76. Vo 1 j1 1 + + 12 0 V + 2Vx + Vx Figure P8.76

Use nodal analysis to find Vo in the network in Fig. P8.77. 2 0 A 6 0 V 1 Vo + + j1 1 + 2Vx + Vx Figure P8.77

Use nodal analysis to find Io in the network in Fig. P8.78. 1 1 1 + j1 + 12 0 V 2Vx + Vx Io Figure P8.78

Use nodal analysis to find Vo in the network in Fig. P8.79. + 1 j1 1 1 + + 4 0 V Vo 4Vo Figure P8.79

Use nodal analysis to find Io in the network in Fig. P8.80. 12 0 V j1 + 1 1 1 Io 1 + + 2Vx Vx Figure P8.80

Use nodal analysis to find Vo in the circuit in Fig. P8.81. 4Vo 1 j Vo + + + 1 1 4 0 V Figure P8.81

Use nodal analysis to find Vx in the circuit in Fig. P8.82. 12 0 V 1 j1 1 j1 2Vx + Vx + Figure P8.82

Find the voltage across the inductor in the circuit shown in Fig. P8.83 using nodal analysis. 10 30 V 4 j2 j1 2Ix V1 V2 Ix + Figure P8.83

Use nodal analysis to find Vo in the circuit in Fig. P8.84. Vo + Vx 4Vx + + 1 1 1 j1 4 0 V + Figure P8.84

Use nodal analysis to find Vo in the network in Fig. P8.85. 2 0 A 6 0 V 1 1 1 j1 1 + + Vx + Vo + 4Vx Figure P8.85

Use nodal analysis to find Vo in the circuit in Fig. P8.86. 6 0 V 2 0 A 4 0 A 1 j1 + Vx 1 1 + Vo + + 4Vx Figure P8.86

Use nodal analysis to find Vo in the circuit in Fig. P8.86. 6 0 V 2 0 A 4 0 A 1 j1 + Vx 1 1 + Vo + + 4Vx Figure P8.86

Use nodal analysis to find Io in the circuit in Fig. P8.88. 4 0 V 1 j1 1 + Vx 1 1 + Ix + 2Vx 4 Ix Io Figure P8.88

Use mesh analysis to find Vo in the circuit shown in Fig. P8.89. 6 0 V 12 45 V 2 j1 j2 I1 + Vo + + I2 Figure P8.89

Solve problem 8.67 using loop analysis

Solve problem 8.68 using loop analysis

Solve problem 8.69 using loop analysis.

Find Vo in the network in Fig. P8.93 using loop analysis. j2 j1 12 0 V 2 0 A 1 1 Vo + + Figure P8.93

Find Vo in the network in Fig. P8.94 using loop analysis. + + 12 0 V 2 0 A j1 1 1 1 Vo Figure P8.94

Find Io in the network in Fig. P8.95 using loop analysis. 2 0 A 4 0 A 12 0 V j1 j1 1 Io 1 1 + Figure P8.95

Find Vo in the circuit in Fig. P8.96 using mesh analysis. 2 0 A 6 0 V 4 0 A j1 + 2 1 2 j2 Vo + Figure P8.96

Find Vo in the network in Fig. P8.97. + + 16 0 V 2 0 A 12 0 V 2 2 j1 j1 Vo + Figure P8.97

Determine Vo in the circuit in Fig. P8.98. 6 0 A 12 0 V 2 2 1 j1 j2 Vo + + Figure P8.98

Use mesh analysis to find Vo in the circuit shown in Fig. P8.99. 12 0 V 4 90 A 4 j2 2 j4 I + 1 I2 Vo + Figure P8.99

Using loop analysis, find Io in the network in Fig. P8.100. 2 0 A 4 0 A 12 0V j2 2 Io 2 j1 + Figure P8.100

Use mesh analysis to find Vo in the circuit in Fig. P8.101. 2 0 A 6 0 A 4 0A j2 2 2 1 j1 Vo + Figure P8.101

Use loop analysis to find Io in the network in Fig. P8.102. 2 0 A 4 30 A 1 1 1 2Vx 1 Vx Io + j1 + Figure P8.102

Find Vo in the network in Fig. P8.103. 4 0 A j1 j1 1 2Ix 1 Vo + Ix Figure P8.103

Use loop analysis to find Vo in the circuit in Fig. P8.104. 4Ix 1 j1 + 1 Vo Ix + 1 4 0 V Figure P8.104

Use loop analysis to find Vo in the network in Fig. P8.105. 6 0 V 4 0 A 1 2 0 A 1 j1 + 1 Vx Vx + Vo + + Figure P8.105

Use superposition to find Vo in the network in Fig. P8.106. 12 0 V 1 4 0 A 1 j1 + Vo + Figure P8.106

Solve problem 8.67 using superposition

Solve problem 8.68 using superposition.

Solve problem 8.69 using superposition.

Use superposition to determine Vo in the circuit in Fig. P8.110. 6 0 V 6 0 A 1 1 j1 j1 Vo + + Figure P8.110

Using superposition, find Vo in the circuit in Fig. P8.111. 6 0 V 2 0 A 1 j1 j2 2 + Vo + Figure P8.111

Find Vo in the network in Fig. P8.112 using superposition. 4 0 A 16 0 V 2 2 1 j2 j3 Vo + + Figure P8.112

Find Vo in the network in Fig. P8.113 using superposition. 2 0 A 12 0 V 2 j2 j4 2 + Vo + Figure P8.113

Use superposition to find Vo in the circuit in Fig. P8.114. 6 0 V 2 0 A 4 0 A j1 1 j1 + 1 1 Vo + Figure P8.114

Use superposition to find Vo in the network in Fig. P8.115. j1 4 0 A 1 1 1 Vo + + 6 0 V Figure P8.115

Solve problem 8.68 using source exchange

Use source exchange to find the current Io in the network in Fig. P8.117. 2 0 A 12 0 V 2 2 Io j1 1 4 0 A + Figure P8.117

Use source exchange to determine Vo in the network in Fig. P8.118. + Vo + 6 0 V 12 0 V2 1 2 0 A j1 + Figure P8.118

Use source transformation to find Vo in the circuit in Fig. P8.119. 12 0 V 1 1 1 12 + 2 0 A Vo + j2 Figure P8.119

Use source transformation to find Vo in the circuit in Fig. P8.120. 1 1 2 2 5 + + 4 0 V 2 0 A 6 0 V j2 Vo + Figure P8.120

Use source transformation to find Io in the circuit in Fig. P8.121. 12 1 6 3 + + 6 0 V 2 0 A 4 0 A 8 0 V j3 4 Io Figure P8.121

Solve problem 8.67 using Thvenins theorem.

Solve problem 8.68 using Thvenins theorem.

Solve problem 8.69 using Thvenins theorem.

Use Thevenins theorem to find Vo in the circuit in Fig. P8.125. 12 0 V 4 90 A 2 4 j2 j4 I1 Vo + + I2 Figure P8.125

Apply Thvenins theorem twice to find Vo in the circuit in Fig. P8.126. 6 0 V 1 j1 j1 1 2 1 + Vo + Figure P8.126

Use Thvenins theorem to find Vo in the network in Fig. P8.127. 1 j2 + 2 0 A 6 0 V 1 + Vo Figure P8.127

Use Thvenins theorem to find Io in the network in Fig. P8.128. + 12 0 V 2 0 A j1 j1 1 1 Io Figure P8.128

Use Thvenins theorem to find the voltage across the 2- resistor in the network in Fig. P8.129. 2 2 0 A 1 12 0 V + j1 j1 Figure P8.129

Use Thvenins theorem to find Io in the network in Fig. P8.130. + 12 0 V 2 0 A j1 1 1 Io 1 Figure P8.130

Use Thvenins theorem to find Vo in the network in Fig. P8.131. 1 + Vo 2 0 A 12 0 V 1 1 j1 + Figure P8.131

Use Thvenins theorem to find Io in the network in Fig. P8.132. 12 0 V 4 0 A 3 0 A 1 j1 j1 Io 1 1 + Figure P8.132

Use Thvenins theorem to find Vo in the network in Fig. P8.133. 6 0 A 4 0 A 4 0 A 1 j2 j1 1 2 Vo + Figure P8.133

Use Thvenins theorem to determine Io in the circuit in Fig. P8.134. + 4 0 A 2 0 A 6 0 V 1 1 1 Io j2 Figure P8.134

Use Thvenins theorem to find Vo in the network in Fig. P8.135. 2 0 A 6 0 V 1 1 Vo + + j1 + 2Vx + Vx Figure P8.135

Use Thvenins theorem to find Io in the network in Fig. P8.136. 1 1 1 + j1 + 12 0 V 2Vx + Vx Io Figure P8.136

Find Vo in the network in Fig. P8.137 using Thvenins theorem. 12 0 V 1 j1 1 j1 2Vx + Vo + Vx + Figure P8.137

Find the Thvenins equivalent for the network in Fig. P8.138 at terminals AB. 2Vx 4 0 A 1 j1 j1 A B Vx + Figure P8.138

Find the Thvenins equivalent for the network in Fig. P8.138 at terminals AB. 2Vx 4 0 A 1 j1 j1 A B Vx + Figure P8.138

Use Thvenins theorem to determine Io in the network in Fig. P8.140. 4 0 A 12 0 V 1 1 1 Io j1 1 1 j1 2 0 A + + 6 0 V Figure P8.140

Use Thvenins theorem to find Io in the network in Fig. P8.141. 12 0 V j1 + 1 1 1 Io 1 + + 2Vx Vx Figure P8.141

Solve problem 8.68 using Nortons theorem

Solve problem 8.69 using Nortons theorem

Find Vx in the circuit in Fig. P8.144 using Nortons theorem. + 11.3 45 V 2 0 A j4 10 j3 Vx + Figure P8.144

Find Io in the network in Fig. P8.145 using Nortons theorem. j1 6 45 A 2 0 A Io 2 j2 Figure P8.145

Use Nortons theorem to find Vo in the network in Fig. P8.146. 4 0 A 2Vx 1 1 1 Vo + Vx + j1 j1 Figure P8.146

Find Vo using Nortons theorem for the circuit in Fig. P8.147. 4 0 V 8 0 V Vx 2Vx 1 1 1 + + + + Vo + j1 j1 Figure P8.147

Use Nortons theorem to find Vo in the circuit in Fig. P8.148. 1 1 j1 1 2 Ix 4Ix 2 0 A 4 0 A Vo + Figure P8.148

Apply Nortons theorem to find Vo in the network in Fig. P8.149. 4 0 A 6 0 V j1 1 1 1 1 j1 + Vo + Figure P8.149

Find Vo in the circuit in Fig. P8.150. 6 0 V 12 0 V 1 1 1 1 1 + 2 0 A + Vo + j1 j1 Figure P8.150

Find the node voltages in the network in Fig. P8.151. 2 0 A 12 0 V j1 2 2 1 1 1 j1 + j2 Figure P8.151

Determine Vo in the network in Fig. P8.152. 6 0 V 2 0 A j1 1 j1 1 1 1 1 + 12 30 V + Vo + Figure P8.152

Find Io in the network in Fig. P8.153. 4 0 A 12 0 V Io 1 1 1 1 1 j1 j1 2 0 A + + 6 0 V Figure P8.153

Use both nodal analysis and loop analysis to find Io in the network in Fig. P8.154. 2 0 A 12 0 V 1 1 1 1 1 2Ix 2Vx Io Ix + + Vx + j1 j1 Figure P8.154

Find Io in the network in Fig. P8.155. 2 0 A 6 0 V 12 0 V 4 0 A 1 1 1 1 1 j1 j1 + Io + Figure P8.155

Find Io in the network in Fig. P8.156. 6 0 V 4 0 V 1 1 1 1 1 1 j1 j1 2Ix Ix Io + + Figure P8.156

Determine Io in the network in Fig. P8.157. 2 0 A 12 0 V 1 1 1 1 1 1 2Vx + + Vx + j1 j1 Io Figure P8.157

Find Io in the circuit in Fig. P8.158. 12 0 V 2 0 A 1 6 0 V 1 j1 1 1 1 2Ix Ix Io + + j1 Figure P8.158