Network Theorems

Abstract

Fundamental electrical laws and the associated methods of analysis, which have been discussed in the previous chapters, need tedious mathematical manipulation. These cumbersome mathematical analyses can be simplified by using advanced techniques known as network or circuit theorems. These include linearity property, superposition theorem, Thevenin’s theorem, Norton’s theorem and maximum power transfer theorem. Here, most of these theorems will be discussed with independent and dependent sources. In addition, PSpice simulation will also be used in some cases to verify the analytical results.

Exercise Problems

• 4.1 An electrical circuit is shown in Fig. 4.77. Assume $I_{p} = 1\,{\text{A}}.$ By using the linearity property find the actual value of $I_{p}$.

  Fig. 4.77

  

  Circuit for Exercise Problem 4.1

• 4.2 Figure 4.78 shows an electrical circuit with the source voltage assigned to V _s  = 16 V. Calculate the actual value of $I_{0}$.

  Fig. 4.78

  

  Circuit for Exercise Problem 4.2

• 4.3 Use linearity property to calculate the actual value of the voltage $V_{0}$ of the circuit in Fig. 4.79. Assume $V_{0} = 1\,{\text{V}}$.

  Fig. 4.79

  

  Circuit for Exercise Problem 4.3

• 4.4 Using superposition theorem determine the current in the $4\,{\Omega}$ resistor of the circuit in Fig. 4.80. Compare the result by PSpice simulation.

  Fig. 4.80

  

  Circuit for Exercise Problem 4.4

• 4.5 Using superposition theorem calculate the current in the $6\,{\Omega}$ resistor of the circuit in Fig. 4.81. Compare the result by PSpice simulation.

  Fig. 4.81

  

  Circuit for Exercise Problem 4.5

• 4.6 Using superposition theorem find the current in the $6\,{\Omega}$ resistor of the circuit in Fig. 4.82. Verify the result by PSpice simulation.

  Fig. 4.82

  

  Circuit for Exercise Problem 4.6

• 4.7 Using superposition theorem calculate the current in the $3\,{\Omega}$ resistor of the circuit in Fig. 4.83. Verify the result by PSpice simulation.

  Fig. 4.83

  

  Circuit for Exercise Problem 4.7

• 4.8 Use superposition theorem to calculate the current in the $4\,{\Omega}$ resistor of the circuit in Fig. 4.84. Verify the result by PSpice simulation.

  Fig. 4.84

  

  Circuit for Exercise Problem 4.8

• 4.9 Using superposition theorem calculate the current in the $2\,{\Omega}$ resistor of the circuit in Fig. 4.85. Verify the result by PSpice simulation.

  Fig. 4.85

  

  Circuit for Exercise Problem 4.9

• 4.10 Using superposition theorem determine the current in the $4\,{\Omega}$ resistor of the circuit in Fig. 4.86. Verify the result by PSpice simulation.

  Fig. 4.86

  

  Circuit for Exercise Problem 4.10

• 4.11 Using superposition theorem find the current in the $8\,{\Omega}$ resistor of the circuit in Fig. 4.87. Verify the result by PSpice simulation.

  Fig. 4.87

  

  Circuit for Exercise Problem 4.11

• 4.12 Using superposition theorem find the current in the $4\,{\Omega}$ resistor of the circuit in Fig. 4.88. Verify the result by PSpice simulation.

  Fig. 4.88

  

  Circuit for Exercise Problem 4.12

• 4.13 Using superposition theorem determine the current in the $6\,{\Omega}$ resistor of the circuit in Fig. 4.89. Verify the result by PSpice simulation.

  Fig. 4.89

  

  Circuit for Exercise Problem 4.13

• 4.14 Use superposition theorem to calculate the current in the $3\,{\Omega}$ resistor of the circuit in Fig. 4.90. Verify the result by PSpice simulation.

  Fig. 4.90

  

  Circuit for Exercise Problem 4.14

• 4.15 Using superposition theorem determine the current in the $5\,{\Omega}$ resistor of the circuit in Fig. 4.91. Verify the result by PSpice simulation.

  Fig. 4.91

  

  Circuit for Exercise Problem 4.15

• 4.16 Using superposition theorem find the current in the $1\,{\Omega}$ resistor of the circuit in Fig. 4.92. Verify the result by PSpice simulation.

  Fig. 4.92

  

  Circuit for Exercise Problem 4.16

• 4.17 Using superposition theorem calculate the current in the $8\,{\Omega}$ resistor of the circuit in Fig. 4.93. Verify the result by PSpice simulation.

  Fig. 4.93

  

  Circuit for Exercise Problem 4.17

• 4.18 Using superposition theorem determine the current in the $5\,{\Omega}$ resistor of the circuit in Fig. 4.94. Verify the result by PSpice simulation.

  Fig. 4.94

  

  Circuit for Exercise Problem 4.18

• 4.19 Use superposition theorem to determine the current in the $3\,{\Omega}$ resistor of the circuit in Fig. 4.95. Verify the result by PSpice simulation.

  Fig. 4.95

  

  Circuit for Exercise Problem 4.19

• 4.20 Using superposition theorem calculate the through the $4\,{\Omega}$ resistor of the circuit in Fig. 4.96 and verify the result by PSpice simulation.

  Fig. 4.96

  

  Circuit for Exercise Problem 4.20

• 4.21 Figure 4.97 shows an electrical circuit. Use superposition theorem to calculate the current in the $6\,{\Omega}$ resistor and verify the result by PSpice simulation.

  Fig. 4.97

  

  Circuit for Exercise Problem 4.21

• 4.22 Using superposition theorem determine the current in the $5\,{\Omega}$ resistor of the circuit in Fig. 4.98. Verify the result by PSpice simulation.

  Fig. 4.98

  

  Circuit for Exercise Problem 4.22

• 4.23 Using superposition theorem calculate the voltage across the $12\,{\Omega}$ resistor of the circuit in Fig. 4.99. Verify the result by PSpice simulation.

  Fig. 4.99

  

  Circuit for Exercise Problem 4.23

• 4.24 Using superposition theorem find the voltage across the $4\,{\Omega}$ resistor of the circuit in Fig. 4.100. Verify the result by PSpice simulation.

  Fig. 4.100

  

  Circuit for Exercise Problem 4.24

• 4.25 Using superposition theorem calculate the voltage across the $6\,{\Omega}$ resistor of the circuit in Fig. 4.101. Verify the result by PSpice simulation.

  Fig. 4.101

  

  Circuit for Exercise Problem 4.25

• 4.26 Using superposition theorem find the voltage across the $3\,{\Omega}$ resistor of the circuit in Fig. 4.102. Verify the result by PSpice simulation.

  Fig. 4.102

  

  Circuit for Exercise Problem 4.26

• 4.27 Using Thevenin’s theorem find the current in the $5\,{\Omega}$ resistor of the circuit in Fig. 4.103. Verify the result by PSpice simulation.

  Fig. 4.103

  

  Circuit for Exercise Problem 4.27

• 4.28 Use Thevenin’s theorem to determine the current in the $6\,{\Omega}$ resistor of the circuit in Fig. 4.104. Verify the result by PSpice simulation.

  Fig. 4.104

  

  Circuit for Exercise Problem 4.28

• 4.29 Using Thevenin’s theorem find the current in the $4\,{\Omega}$ resistor of the circuit in Fig. 4.105. Verify the result by PSpice simulation.

  Fig. 4.105

  

  Circuit for Exercise Problem 4.29

• 4.30 Use Thevenin’s theorem to determine the current in the $3\,{\Omega}$ resistor of the circuit in Fig. 4.106. Verify the result by PSpice simulation.

  Fig. 4.106

  

  Circuit for Exercise Problem 4.30

• 4.31 Using Thevenin’s theorem calculate the current in the $8\,{\Omega}$ resistor of the circuit in Fig. 4.107. Verify the result by PSpice simulation.

  Fig. 4.107

  

  Circuit for Exercise Problem 4.31

• 4.32 Using Thevenin’s theorem determine the current in the $10\,{\Omega}$ resistor of the circuit in Fig. 4.108. Verify the result by PSpice simulation.

  Fig. 4.108

  

  Circuit for Exercise Problem 4.32

• 4.33 Use Thevenin’s theorem to find the current in the $6\,{\Omega}$ resistor of the circuit in Fig. 4.109. Verify the result by PSpice simulation.

  Fig. 4.109

  

  Circuit for Exercise Problem 4.33

• 4.34 Using Thevenin’s theorem calculate the current in the $5\,{\Omega}$ resistor of the circuit in Fig. 4.110. Verify the result by PSpice simulation.

  Fig. 4.110

  

  Circuit for Exercise Problem 4.34

• 4.35 Use Thevenin’s theorem to find the current in the $10\,{\Omega}$ resistor of the circuit in Fig. 4.111. Verify the result by PSpice simulation.

  Fig. 4.111

  

  Circuit for Exercise Problem 4.35

• 4.36 Using Thevenin’s theorem determine the current in the $12\,{\Omega}$ resistor of the circuit in Fig. 4.112. Verify the result by PSpice simulation.

  Fig. 4.112

  

  Circuit for Exercise Problem 4.36

• 4.37 Use Thevenin’s theorem to determine the current in the $6\,{\Omega}$ resistor of the circuit in Fig. 4.113. Verify the result by PSpice simulation.

  Fig. 4.113

  

  Circuit for Exercise Problem 4.37

• 4.38 Using Thevenin’s theorem calculate the voltage across the $5\,{\Omega}$ resistor of the circuit in Fig. 4.114. Verify the result by PSpice simulation.

  Fig. 4.114

  

  Circuit for Exercise Problem 4.38

• 4.39 Use Thevenin’s theorem to determine the current in the $2\,{\Omega}$ resistor of the circuit in Fig. 4.115. Verify the result by PSpice simulation.

  Fig. 4.115

  

  Circuit for Exercise Problem 4.39

• 4.40 Using Thevenin’s theorem calculate the power absorbed by the $5\,{\Omega}$ resistor of the circuit in Fig. 4.116. Also, find the current by PSpice simulation.

  Fig. 4.116

  

  Circuit for Exercise Problem 4.40

• 4.41 Using Thevenin’s theorem determine the voltage across the $3\,{\Omega}$ resistor of the circuit in Fig. 4.117. Verify the result by PSpice simulation.

  Fig. 4.117

  

  Circuit for Exercise Problem 4.41

• 4.42 Use Thevenin’s theorem to find the current in the $11\,{\Omega}$ resistor of the circuit in Fig. 4.118. Verify the result by PSpice simulation.

  Fig. 4.118

  

  Circuit for Exercise Problem 4.42

• 4.43 Using Thevenin’s theorem determine the current in the $8\,{\Omega}$ resistor of the circuit in Fig. 4.119. Verify the result by PSpice simulation.

  Fig. 4.119

  

  Circuit for Exercise Problem 4.43

• 4.44 Using Thevenin’s theorem find the current in the $4\,{\Omega}$ resistor of the circuit in Fig. 4.120. Verify the result by PSpice simulation.

  Fig. 4.120

  

  Circuit for Exercise Problem 4.44

• 4.45 Use Thevenin’s theorem to determine the current in the $3\,{\Omega}$ resistor of the circuit in Fig. 4.121. Verify the result by PSpice simulation.

  Fig. 4.121

  

  Circuit for Exercise Problem 4.45

• 4.46 Using Thevenin’s theorem calculate the power absorbed by the $12\,{\Omega}$ resistor of the circuit in Fig. 4.122.

  Fig. 4.122

  

  Circuit for Exercise Problem 4.46

• 4.47 Using Thevenin’s theorem calculate the current in the $5\,{\Omega}$ resistor of the circuit in Fig. 4.123. Verify the result by PSpice simulation.

  Fig. 4.123

  

  Circuit for Exercise Problem 4.47

• 4.48 Using Thevenin’s theorem find the current in the $6\,{\Omega}$ resistor of the circuit in Fig. 4.124. Verify the result by PSpice simulation.

  Fig. 4.124

  

  Circuit for Exercise Problem 4.48

• 4.49 Using Thevenin’s theorem find the current in $2\,{\Omega}$ resistor of the circuit in Fig. 4.125.

  Fig. 4.125

  

  Circuit for Exercise Problem 4.49

• 4.50 Using Thevenin’s theorem determine the current in the $12\,{\Omega}$ resistor of the circuit in Fig. 4.126. Verify the result by PSpice simulation.

  Fig. 4.126

  

  Circuit for Exercise Problem 4.50

• 4.51 Using Thevenin’s theorem calculate the current in the $8\,{\Omega}$ resistor of the circuit in Fig. 4.127. Verify the result by PSpice simulation.

  Fig. 4.127

  

  Circuit for Exercise Problem 4.51

• 4.52 Using Thevenin’s theorem find the current in the $10\,{\Omega}$ resistor of the circuit in Fig. 4.128. Verify the result by PSpice simulation.

  Fig. 4.128

  

  Circuit for Exercise Problem 4.52

• 4.53 Using Thevenin’s theorem determine the current in the $12\,{\Omega}$ resistor of the circuit in Fig. 4.129. Verify the result by PSpice simulation.

  Fig. 4.129

  

  Circuit for Exercise Problem 4.53

• 4.54 Using Thevenin’s theorem calculate the current in the $6\,{\Omega}$ resistor of the circuit in Fig. 4.130. Verify the result by PSpice simulation.

  Fig. 4.130

  

  Circuit for Exercise Problem 4.54

• 4.55 Using Thevenin’s theorem find the current in the $3\,{\Omega}$ resistor of the circuit in Fig. 4.131. Verify the result by PSpice simulation.

  Fig. 4.131

  

  Circuit for Exercise Problem 4.55

• 4.56 Using Thevenin’s theorem determine the current in the $8\,{\Omega}$ resistor of the circuit in Fig. 4.132. Verify the result by PSpice simulation.

  Fig. 4.132

  

  Circuit for Exercise Problem 4.56

• 4.57 Use Thevenin’s theorem to calculate the current in the $6\,{\Omega}$ resistor of the circuit in Fig. 4.133. Verify the result by PSpice simulation.

  Fig. 4.133

  

  Circuit for Exercise Problem 4.57

• 4.58 Use Thevenin’s theorem to calculate the current in the $10\,{\Omega}$ resistor of the circuit in Fig. 4.134. Verify the result by PSpice simulation.

  Fig. 4.134

  

  Circuit for Exercise Problem 4.58

• 4.59 Using Thevenin’s theorem determine the current in the $10\,{\Omega}$ resistor of the circuit in Fig. 4.135. Verify the result by PSpice simulation.

  Fig. 4.135

  

  Circuit for Exercise Problem 4.59

• 4.60 Using Thevenin’s theorem calculate the current in the $8\,{\Omega}$ resistor of the circuit in Fig. 4.136. Verify the result by PSpice simulation.

  Fig. 4.136

  

  Circuit for Exercise Problem 4.60

• 4.61 Using Thevenin’s theorem calculate the current in the $4\,{\Omega}$ resistor of the circuit in Fig. 4.137. Verify the result by PSpice simulation.

  Fig. 4.137

  

  Circuit for Exercise Problem 4.61

• 4.62 Use Thevenin’s theorem to find the current in the $5\,{\Omega}$ resistor of the circuit in Fig. 4.138. Verify the result by PSpice simulation.

  Fig. 4.138

  

  Circuit for Exercise Problem 4.62

• 4.63 Use Thevenin’s theorem to find the current in the $4\,{\Omega}$ resistor of the circuit is shown in Fig. 4.139.

  Fig. 4.139

  

  Circuit for Exercise Problem 4.63

• 4.64 Use Thevenin’s theorem to find the current in the $6\,{\Omega}$ resistor of the circuit in Fig. 4.140.

  Fig. 4.140

  

  Circuit for Exercise Problem 4.64

• 4.65 Using Norton’s theorem calculate the current in the $8\,{\Omega}$ resistor of the circuit in Fig. 4.141. Verify the result by PSpice simulation.

  Fig. 4.141

  

  Circuit for Exercise Problem 4.65

• 4.66 Using Norton’s theorem find the current in the $4\,{\Omega}$ resistor of the circuit in Fig. 4.142. Verify the result by PSpice simulation.

  Fig. 4.142

  

  Circuit for Exercise Problem 4.66

• 4.67 Using Norton’s theorem calculate the current in the $5\,{\Omega}$ resistor of the circuit in Fig. 4.143. Verify the result by PSpice simulation.

  Fig. 4.143

  

  Circuit for Exercise Problem 4.67

• 4.68 Using Norton’s theorem determine the current in the $8\,{\Omega}$ resistor of the circuit in Fig. 4.144. Verify the result by PSpice simulation.

  Fig. 4.144

  

  Circuit for Exercise Problem 4.68

• 4.69 Using Norton’s theorem find the current in the $12\,{\Omega}$ resistor of the circuit in Fig. 4.145. Verify the result by PSpice simulation.

  Fig. 4.145

  

  Circuit for Exercise Problem 4.69

• 4.70 Using Norton’s theorem calculate the current in the $5\,{\Omega}$ resistor of the circuit in Fig. 4.146. Verify the result by PSpice simulation.

  Fig. 4.146

  

  Circuit for Exercise Problem 4.70

• 4.71 Using Norton’s theorem determine the current in the $3\,{\Omega}$ resistor of the circuit in Fig. 4.147. Verify the result by PSpice simulation.

  Fig. 4.147

  

  Circuit for Exercise Problem 4.71

• 4.72 Using Norton’s theorem calculate the current in the $6\,{\Omega}$ resistor of the circuit in Fig. 4.148. Verify the result by PSpice simulation.

  Fig. 4.148

  

  Circuit for Exercise Problem 4.72

• 4.73 Use Norton’s theorem to find the current in the $4\,{\Omega}$ resistor of the circuit in Fig. 4.149. Verify the result by PSpice simulation.

  Fig. 4.149

  

  Circuit for Exercise Problem 4.73

• 4.74 An electrical circuit is shown in Fig. 4.150. Use Norton’s theorem to find the current in the $6\,{\Omega}$ resistor and compare the result with PSpice simulation.

  Fig. 4.150

  

  Circuit for Exercise Problem 4.74

• 4.75 Fig. 4.151 shows an electrical circuit. Calculate the current in the $5\,{\Omega}$ resistor by using Norton’s theorem and verify the result by PSpice simulation.

  Fig. 4.151

  

  Circuit for Exercise Problem 4.75

• 4.76 An electrical circuit is shown in Fig. 4.152. Determine the current in the $3\,{\Omega}$ resistor by using Norton’s theorem and verify the result by PSpice simulation.

  Fig. 4.152

  

  Circuit for Exercise Problem 4.76

• 4.77 Use Norton’s theorem to calculate the current in the $3\,{\Omega}$ resistor of the circuit in Fig. 4.153. Verify the result by PSpice simulation.

  Fig. 4.153

  

  Circuit for Exercise Problem 4.77

• 4.78 An electrical circuit is shown in Fig. 4.154. Use Norton’s theorem to calculate the current in the $5\,{\Omega}$ resistor. Verify the result by PSpice simulation.

  Fig. 4.154

  

  Circuit for Exercise Problem 4.78

• 4.79 Figure 4.155 shows an electrical circuit. Use Norton’s theorem to calculate the current in the $3\,{\Omega}$ resistor. Verify the result by PSpice simulation.

  Fig. 4.155

  

  Circuit for Exercise Problem 4.79

• 4.80 Figure 4.156 shows an electrical circuit. Use Norton’s theorem to calculate the current in the $3\,{\Omega}$ resistor. Verify the result by PSpice simulation.

  Fig. 4.156

  

  Circuit for Exercise Problem 4.80

• 4.81 Using maximum power transfer theorem calculate the load resistance R of the circuit in Fig. 4.157, and also find the maximum power.

  Fig. 4.157

  

  Circuit for Exercise Problem 4.81

• 4.82 Using maximum power transfer theorem determine the load resistance R of the circuit in Fig. 4.158, and also find the maximum power.

  Fig. 4.158

  

  Circuit for Exercise Problem 4.82

• 4.83 Using maximum power transfer theorem calculate the load resistance R of the circuit in Fig. 4.159, and also find the maximum power.

  Fig. 4.159

  

  Circuit for Exercise Problem 4.83

• 4.84 Using maximum power transfer theorem calculate the load resistance R of the circuit in Fig. 4.160, and also find the maximum power.

  Fig. 4.160

  

  Circuit for Exercise Problem 4.84

• 4.85 Using maximum power transfer theorem calculate the load resistance R of the circuit in Fig. 4.161, and also find the maximum power.

  Fig. 4.161

  

  Circuit for Exercise Problem 4.85