Answer: Find RL for maximum power transfer and the maximum

Find Io in the network in Fig. P5.1 using linearity and the assumption that Io = 1 mA. 2 k 3 k 6 k 6 k 2 k Io 64 V + Figure P5.1

Find Io in the network in Fig. P5.2 using linearity and the assumption that Io = 1 mA. 3 k V2 3 k 4 k 4 k 8 k Io I1 I2 I3 2 mA + Figure P5.2

Find Io in the network in Fig. P5.3 using linearity and the assumption that Io = 1 mA. 2 k 2 k 4 k 2 k 2 k 2 k Io 12 mA Figure P5.3

Find Vo in the network in Fig. P5.4 using linearity and the assumption that Vo = 1 V. 3 k 3 k 3 k 6 k 8 V 3 k 3 k 3 k I3 I3 Vo I1 I2 V2 V4 + + + + Figure P5.4

Find Io in the circuit in Fig. P5.5 using linearity and the assumption that Io = 1 mA. 12 k 4 k 4 k 4 k 4 k 2 k Io 4 mA Figure P5.5

Find Io in the network in Fig. P5.6 using superposition. 6 k 3 k 3 k Io 6 V + 2 k 2 mA Figure P5.6

Find Io in the circuit in Fig. P5.7 using superposition. 6 k 2 k 2 k 2 k Io 30 V + 12 k 30 mA Figure P5.7

Find Vo in the network in Fig. P5.8 using superposition. 2 k 1 k 2 k 2 k 6 mA Vo 12 V + + Figure P5.8

Find Vo in the network in Fig. P5.9 using superposition. 3 k 3 k 3 k 3 k V 3 k 6 V o + + 9 V + Figure P5.9

In the network in Fig. P5.10, find Io using superposition. 6 k 6 k 6 k Io 12 V + 6 k 6 mA Figure P5.10

Find Io in the network in Fig. P5.11 using superposition. 12 k 6 V 12 k 12 k 4 mA Io 12 k + Figure P5.11

Find Io in the network in Fig. P5.12 using superposition. 6 V 6 k 5 mA 6 k 6 k 6 k + Io Figure P5.12

Find IA in the network in Fig. P5.13 using superposition. 5 20 5 10 4 A 2 A 40 V IA + Figure P5.13

Using superposition, find IA in the circuit in Fig. P5.14. + + 12 k 2 k 4 k 8 k 6 V 12 V IA Figure P5.14

Find IA in the network in Fig. P5.15 using superposition. 3 k 6 k 2 k 6 k 12 k 6 V + IA 2 mA Figure P5.15

Use superposition to find Vo in the network in Fig. P5.16. 12 V 6 k 6 V 6 mA 6 k 6 k 6 k 6 k + + Vo + Figure P5.16

Use superposition to find Io in the circuit in Fig. P5.17. 6 k 6 k 12 V 6 k 6 mA 4 mA 6 k 12 k + Io Figure P5.17

Use superposition to find Io in the network in Fig. P5.18. 4 k 6 V 12 V 6 mA 3 k 6 k + + Io Figure P5.18

Use superposition to find Vo in the circuit in Fig. P5.19. 12 V 6 mA 3 k 3 k 3 k 3 k + Vo + Figure P5.19

Find Vo in the circuit in Fig. P5.20 using superposition. + + 2 k 1 k 2 k 1 k 1 k 6 V 12 V 4 mA Vo + Figure P5.20

Find Io in the circuit in Fig. P5.21 using superposition. 1 k 1 k 1 k 2 V 4 k 4 V 2 mA + Io + Figure P5.21

Use superposition to find Io in the circuit in Fig. P5.22. 2 k 6 V 6 k 12 V 2 mA 4 k 3 k 12 V + + Io + Figure P5.22

Use superposition to find Io in the network in Fig. P5.23. 4 mA 6 mA 2 k 4 k 2 mA 12 k Io 4 k Figure P5.23

Use superposition to find Io in the circuit in Fig. P5.24. Io 3 k 2 k 4 mA 12 V 2 mA 4 k 6 k 6 k + Figure P5.24

Use Thvenins theorem to find Vo in the network in Fig. P5.25. Vo + 2 k 4 k 2 k 6 V 12 V + + Figure P5.25

Use Thvenins theorem to find Io in the network in Fig. P5.26. 2 k 1 k 1 k 4 mA 2 mA 6 mA Io Figure P5.26

Use Thvenins theorem to find Vo in the network in Fig. P5.27. 3 k 4 k 12 V + 6 k 2 k 2 mA + Vo Figure P5.27

Find Io in the network in Fig. P5.28 using Thvenins theorem. 12 V 3 k 6 k 2 k 2 mA Io 4 k + Figure P5.28

Find Vo in the circuit in Fig. P5.29 using Thvenins theorem. 12 V 2 k 1 k 2 mA 1 k Vo 2 k + + Figure P5.29

Use Thvenins theorem to find Io in the network in Fig. P5.30. Io 12 V 6 k 1 k 2 k 2 mA + 2 k Figure P5.30

Find Vo in the network in Fig. P5.31 using Thvenins theorem. 6 k 3 k 3 V 6 k 2 k 1 mA Vo + + Figure P5.31

Find Io in the circuit in Fig. P5.32 using Thvenins theorem. 4 k 6 k 6 k 4 k 6 mA 12 V + Io Figure P5.32

Find Io in the network in Fig. P5.33 using Thvenins theorem. 2 k 2 k 6 V 2 k 2 mA + 1 k Io Figure P5.33

Find Io in the network in Fig. P5.34 using Thvenins theorem. 1 k 6 V 1 mA 1 k 1 k Io 2 mA + Figure P5.34

Find Io in the circuit in Fig. P5.35 using Thvenins theorem. 2 k 2 k 1 k 4 mA 2 mA + 12 V Io Figure P5.35

Find Io in the network in Fig. P5.36 using Thvenins theorem. Io 6 V 2 mA 1 k 1 mA 1 k 1 k + Figure P5.36

Using Thvenins theorem, find IA in the circuit in Fig. P5.37. 5 20 5 10 4 A 2 A 40 V IA + Figure P5.37

Find Vo in the network in Fig. P5.38 using Thvenins theorem. 4 k 2 k 4 k 5 k 8 k 6 k + 2 mA 20 V 40 V + Vo + Figure P5.38

Find Vo in the circuit in Fig. P5.39 using Thvenins theorem. 12 V 2 mA 2 k 1 k 1 k 2 k + Vo + Figure P5.39

Find Io in the circuit in Fig. P5.40 using Thvenins theorem. 12 V 2 mA 2 k 1 k 2 k 1 k + Io Figure P5.40

Find Vo in the network in Fig. P5.41 using Thvenins theorem. 12 V 4 mA 1 k 1 k 2 k 2 k Vo + + Figure P5.41

Find Io in the network in Fig. P5.42 using Thvenins theorem. 6 V 12 V 2 k 1 k 1 k 2 k + + Io Figure P5.42

Find Vo in Fig. P5.43 using Thvenins theorem. + 4 k 12 k 2 k 4 k 2 k 3 mA 6 V 1 mA Vo + Figure P5.43

Use Thvenins theorem to find Vo in the circuit in Fig. P5.44. 2 k 2 k 1 k 1 k 1 k 2 mA 2 mA 4 mA Vo + Figure P5.44

Use Thvenins theorem to find Io in Fig. P5.45. Io 12 V 8 V 16 V 4 k 2 mA 2 k 4 k 2 k + + + Figure P5.45

Find Vo in the network in Fig. P5.46 using Thvenins theorem. 1 mA 2 mA 2 mA 6 V 0.5 k 0.5 k 1 k 1 k + Vo + Figure P5.46

Use Thvenins theorem to find Io in the network in Fig. P5.47. 2 mA 2 mA 24 V 2 k 4 k 6 k 3 k Io + Figure P5.47

Use Thvenins theorem to find Io in the circuit in Fig. P5.48. 2 mA 1 mA 3 k 4 k 6 k 6 k 4 k 6 k 18 V Io + Figure P5.48

Given the linear circuit in Fig. P5.49, it is known that when a 2-k load is connected to the terminals AB, the load current is 10 mA. If a 10-k load is connected to the terminals, the load current is 6 mA. Find the current in a 20-k load. RTh Voc A B + Figure P5.49

If an 8-k load is connected to the terminals of the network in Fig. P5.50, VAB = 16 . If a 2-k load is connected to the terminals, VAB = 8 V. Find VAB if a 20-k load is connected to the terminals. A B Linear circuit Figure P5.50

Use Nortons theorem to find I o in the circuit in Fig. P5.51. 2 k 4 mA 12 V 1 k 3 k 3 k 2 k Io + Figure P5.51

Find I o in the network in Fig. P5.52 using Nortons theorem. 12 V 3 k 1 mA 3 k 6 k 3 k + Io Figure P5.52

Use Nortons theorem to find I o in the circuit in Fig. P5.53. 2 k 4 mA 12 V 4 k 4 k 2 k 2 k Io + Figure P5.53

Use Nortons theorem to find V o in the network in Fig. P5.54. 12 V 2 k 1 k 2 mA 1 k + Vo 2 k + Figure P5.54

Find I o in the network in Fig. P5.55 using Nortons theorem. 2 k 2 k 4 k 6 k 3 k 12 V Io + Figure P5.55

Use Nortons theorem to find V o in the network in Fig. P5.56. 2 k 2 mA 4 k 2 k 4 k 24 V + Vo + Figure P5.56

Find V o in the network in Fig. P5.57 using Nortons theorem. 3 k 2 k 1 k 3 V 1 mA Vo + + 1 k Figure P5.57

Use Nortons theorem to find I o in the circuit in Fig. P5.58. 1 k 1 k 1 k 2 V 4 k 4 V 2 mA + Io + Figure P5.58

Find V o in the circuit in Fig. P5.59 using Nortons theorem. + + 2 k 1 k 2 k 1 k 1 k 6 V 12 V 4 mA Vo + Figure P5.59

Use Nortons theorem to find I o in the network in Fig. P5.60. 2 mA 2 mA 24 V 2 k 4 k 6 k 3 k Io + Figure P5.60

Use Nortons theorem to find I o in the circuit in Fig. P5.61. 2 mA 1 mA 3 k 4 k 6 k 6 k 4 k 6 k 18 V Io + Figure P5.61

In the network in Fig. P5.62, find V o using Thvenins theorem. + Vo Vo + 12 V 1 k 2 k 1 k + 1 2 Figure P5.62

Use Thvenins theorem to find I o in the circuit in Fig. P5.63. + Vx + 2Vx 20 V 2 k 2 k 4 k Io + Figure P5.63

Find V o in the network in Fig. P5.64 using Thvenins theorem. 2VA 4 k 12 V + 2 k 4 k + + VA Vo + Figure P5.64

Use Thvenins theorem to find V o in the circuit in Fig. P5.65. 2Ix Ix 6 V 2 k 1 k 1 k + Vo + Figure P5.65

Find I o in the circuit in Fig. P5.66 using Thvenins theorem. 12 V Io 1 k 1 k + 2 k 2Vx + Vx + Figure P5.66

Use Thvenins theorem to find I o in the circuit in Fig. P5.67. 8 k 12 V 12 k 4 k 2Vx Io 4 k 2 k + + Vx + Figure P5.67

Use Thvenins theorem to find V o in the circuit in Fig. P5.68. 2Ix 1 k 1 k 1 k 1 k 12 V Vo + Ix + Figure P5.68

Find V o in the network in Fig. P5.69 using Thvenins theorem. 3 V 1 mA 1000Ix Ix 6 k 1 k + 2 k 2 k Vo + + Figure P5.69

Use Nortons theorem to find V o in the network in Fig. P5.70. 2000Ix 6 k 4 k 6 V 2 k 3 mA 4 k Vo + Ix + + Figure P5.70

Find V o in the circuit in Fig. P5.71 using Thvenins theorem. 6 V 12 V Vx 1000 4 k 2 k 4 k Vx 2 k + + Vo + + Figure P5.71

Find V o in the network in Fig. P5.72 using Thvenins theorem. 12 V 2 mA 1 k 1 k 2Ix 1 k + Vo + Ix Figure P5.72

Find V o in the network in Fig. P5.73 using Nortons theorem. 3 k 1 k 1 mA 3 k Vo + 2 k Vx 4000 Vx + Figure P5.73

Use Thvenins theorem to find the power supplied by the 2-V source in the circuit in Fig. P5.74. 1 k 2 k 1 k 1 k 4 V + 1 k 2 V + + 2Vx Vx + Figure P5.74

Find V o in the circuit in Fig. P5.75 using Thvenins theorem. 1 k 1 k 1 k 1 k 1 k 2 mA 12 V Ix Vo + 2Ix + Figure P5.75

Find V o in the network in Fig. P5.76 using Thvenins theorem. 2 k 1 k 2 mA 2 k 12 V 1 k Vo + Vx 2Vx + + + 1 k Figure P5.76

Find V o in the network in Fig. P5.77 using Thvenins theorem. 1 k 1 k 1 k 1 k 2 k 2 k 1 mA 1 k 4 mA Vo Vx + 2Vx 1000 + Figure P5.77

Use Thvenins theorem to find I 2 in the circuit in Fig. P5.78. 12 5 A 6 7 9 3 12 V VA 2VA + + + I2 IA 4IA Figure P5.78

Use Thvenins theorem to find V o in the circuit in Fig. P5.79. 1 2 A 8 5 2 2 4 9 V 2VA VA + + + IA 3IA Vo + Figure P5.79

Use Thvenins theorem to find V o in the circuit in Fig. P5.80. 4 mA 2 mA 12 V + + 2Vx Vo + Vx + 1 k 1 k 1 k 1 k 1 k 1 k Figure P5.80

Use Thvenins theorem to find I o in the network in Fig. P5.81. 1 k 1 k 1 k 2 k Vx 2Vx 2 V 6 V Io + + + + 1 k Figure P5.81

Use Thvenins theorem to find V o in the network in Fig. P5.82. 2 mA 1 k 1 k 1 k 1 k 1 k 1 k 4 V 6 V Vo + Ix 2Ix + + Figure P5.82

Find the Thvenin equivalent of the network in Fig. P5.83 at the terminals AB. 1 k 2 k 1 k 1 k Vx 1000 A B Vx + Figure P5.83

Find the Thvenin equivalent of the network in Fig. P5.84 at the terminals AB. 1 k 1 k 2 k 2 k Ix 1000Ix + A B Figure P5.84

Find the Thvenin equivalent of the circuit in Fig. P5.85 at the terminals AB. 2 k 3 k 1 k A B Vx + 4Vx 1000 Figure P5.85

Find the Thvenin equivalent of the network in Fig. P5.86 at the terminals AB using a 1-mA current source. 2 k 1 k 2 k 4 k Vx 2000 Vx A B + Figure P5.86

Find the Thvenin equivalent circuit of the network in Fig. P5.87 at terminals AB. 6 k 2 k 4 k 4 k A B Ix 2000Ix + Figure P5.87

Find V o in the network in Fig. P5.88 using source transformation. 4 k 3 k 4 k 2 k 2 mA 12 k 12 k + 12 V + Vo Figure P5.88

Find I o in the network in Fig. P5.89 using source transformation. 6 V 6 k 6 k 6 k + 6 k Io 1 mA Figure P5.89

Use source transformation to find V o in the network in Fig. P5.90. 4 k 12 k 2 mA 6 k 6 V Vo 24 V + + + Figure P5.90

Find I o in the network in Fig. P5.91 using source transformation. 3 k 9 k 12 k 4 k 3 k 6 k 4 mA + 6 V Io Figure P5.91

Find V o in the network in Fig. P5.92 using source transformation. 4 k 3 k 6 k 2 k 12 V 6 V Vo + + + Figure P5.92

Use source transformation to find I o in the network in Fig. P5.93. 2 k 4 k 6 k 2 k 2 mA 3 V 6 V Io + + Figure P5.93

Find the Thvenin equivalent circuit of the network in Fig. P5.94 at the terminals AB. 12 6 7 9 3 5 VA 2VA + + IA 4IA A B Figure P5.94

Find I o in the circuit in Fig. P5.95 using source transformation. 4 k 8 k 3 k 3 k 4 k 2 mA 3 k 3 k 12 V 9 V + Io + Figure P5.95

Find I o in the network in Fig. P5.96 using source transformation. 2 k 4 k 3 k 6 V 2 mA Io 6 k 4 k + 1 mA 2 mA Figure P5.96

Find I o in the network in Fig. P5.97 using source transformation. 3 k 4 k 2 mA 6 k 18 k 1 mA 12 V 6 mA + Io Figure P5.97

Find V o in the network in Fig. P5.98 using source transformation. 3 k 3 k 4 k 3 k 2 mA 12 k 12 k + 6 V + Vo Figure P5.98

Find I o in the network in Fig. P5.99 using source transformation. 3 k 4 k 4 mA 3 k 12 k 2 mA 12 V 4 mA + Io Figure P5.99

Find I o in the circuit in Fig. P5.100 using source transformation. 6 k 6 k 3 k 4 k 3 k 2 mA 3 k 3 k 6 V 12 V + Io + Figure P5.100

Use source transformation to find I o in the network in Fig. P5.101. 6 k 6 k 3 k 3 k 6 k 12 k 2 mA 12 V + Io Figure P5.101

Using source transformation, find V o in the circuit in Fig. P5.102. 2 k 6 k 8 k 12 V 3 k 4 k 2 mA + Vo + Figure P5.102

Use source transformation to find I o in the circuit in Fig. P5.103. Io 3 k 2 k 4 mA 12 V 2 mA 4 k 6 k 6 k + Figure P5.103

Use source transformation to find Io in the circuit in Fig. P5.104. 2 k 6 V 6 k 12 V 2 mA 4 k 3 k 12 V + + Io + Figure P5.104

Use source transformation to find Io in the circuit in Fig. P5.105. 2 mA 1 mA 3 k 4 k 6 k 6 k 4 k 6 k 18 V Io + Figure P5.105

Using source transformation, find Io in the circuit in Fig. P5.106. 2 mA 2 mA 24 V 2 k 4 k 6 k 3 k Io + Figure P5.106

Use source exchange to find Io in the network in Fig. P5.107. 20 mA 6 k 3 k 4 k 6 V 8 V Io 6 k 3 k 12 k + + Figure P5.107

Use a combination of Y- transformation and source transformation to find Io in the circuit in Fig. P5.108. 2 mA 6 k 4 k 6 k 4 k 3 k 6 k 6 k 4 k 4 k 6 k 6 V 6 V Io + + Figure P5.108

Use source exchange to find Io in the circuit in Fig. P5.109. 2 mA 6 k 2 k 2 k 2 k 12 k 12 k 1 k 1 k 6 V 8 V 24 V 2 k Io + + + Figure P5.109

Use source exchange to find Io in the network in Fig. P5.110. 2 mA 4 k 8 k 4 k 8 k 2 k 3 k 2 k 2 k 4 V 8 k 12 V 6 k 12 k 12 k Io + + Figure P5.110

Use source exchange to find Io in the network in Fig. P5.111. 4 mA 2 mA 3 k 2 k 2 k 2 k 2 k 2 k 3 k 4 k 3 k 3 k 12 V 6 V 6 k 6 k 4 k 4 k 6 k Io + + Figure P5.111

Find RL in the network in Fig. P5.112 in order to achieve maximum power transfer. RL 2 k 2 k 2 k 2 k + 12 V Figure P5.112

In the network in Fig. P5.113, find RL for maximum power transfer and the maximum power transferred to this load. RL 2 k 4 mA 4 k 1 k 2 k Figure P5.113

Find RL for maximum power transfer and the maximum power that can be transferred to the load in Fig. P5.114. RL 2 mA 6 V 2 k 6 k 3 k + Figure P5.114

Find RL for maximum power transfer and the maximum power that can be transferred to the load in the circuit in Fig. P.5.115. 1 mA 2 mA 2 mA 6 V 0.5 k 1 k 1 k RL + Figure P5.115

Find RL for maximum power transfer and the maximum power that can be transferred to the load in the network in Fig. P5.116. 2 k 2 k 2 mA 4 k RL 4 mA 8 mA 4 k Figure P5.116

Find RL for maximum power transfer and the maximum power that can be transferred to the load in the circuit in Fig. P5.117. 1 k 3 k 1 k 3 V 1 mA 0.5 mA + 2 k RL Figure P5.117

Determine the value of RL in the network in Fig. P5.118 for maximum power transfer. RL 100I I 12 V 5 k 5 k + Figure P5.118

Find RL for maximum power transfer and the maximum power that can be transferred to the load in Fig. P5.119. 4Vx 1000 RL 2 k 3 k Vx 1 k + 1 mA Figure P5.119

Find the value of RL in the network in Fig. P5.120 for maximum power transfer. 4V RL x 4 2 A 2 4 + + Vx Figure P5.120

Find the value of RL for maximum power transfer and the maximum power that can be transferred to RL in the circuit of Fig. P5.121. 12 4 30 V 4 + + + Vx RL 4Vx Figure P5.121

Find the maximum power that can be transferred to RL in the network in Fig. P5.122. 500 500 1000 + 12 V + RL 0.5Vo + Vo Figure P5.122

In the network in Fig. P5.123, find the value of RL for maximum power transfer. In addition, calculate the maximum power dissipated in RL under these conditions. RL 2Vx 2 k 12 V 2 mA 2 k 1 k Vx 1 k + + + Figure P5.123

In the network in Fig. P5.124, find the value of RL for maximum power transfer. In addition, calculate the power dissipated in RL under these conditions. 5 k 10 k 10 k 10 mA I1 RL 1000I1 + Figure P5.124

Find the value of RL in Fig. P5.125 for maximum power transfer. In addition, calculate the power dissipated in RL under these conditions. Vx RL 0.5Vx + 6 k 12 V 3 k 3 mA 2 k + + Figure P5.125

Calculate the maximum power that can be transferred to RL in the circuit in Fig. P5.126. 4 4 4 4 20 V 100 V + + 4Vx + Vx + RL Figure P5.126

Find RL for maximum power transfer and the maximum power that can be transferred in the network in Fig. P5.127. 2 k 2 k 2 k 4 k 1 mA RL Vx + 2000 Vx Figure P5.127

Find the value of RL in Fig. P5.128 for maximum power transfer and the maximum power that can be dissipated in RL. 2 VA 8 9 V 2VA RL 2 A IA 3IA 1 2 4 + + + Figure P5.128

A cell phone antenna picks up a call. If the antenna and cell phone are modeled as shown in Fig. P5.129, (a) Find Rcell for maximum output power. (b) Determine the value of Pout. (c) Determine the corresponding value of Pant. (d) Find VoVant. (e) Determine the amount of power lost in Rant.(f) Calculate the efficiency = Pout Pant. (g) Determine the value of Rcell such that the efficiency is 90%. (h) Given the change in (g), what is the new value of Pant? (i) Given the change in (g), what is the new value of Pout? (j) Comment on the results obtained in (i) and (b). V Rcell ant = 0.1 V Rant = 50 Vo + + Figure P5.129