Fundamentals of Electric Circuits

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90 Chapter 3 Methods of Analysis 2 A Example 3.3 Figure 3.9 For Example 3.3. 2 V v 1 v 2 2 Ω 10 Ω + − 4 Ω 7 A For the circuit shown in Fig. 3.9, find the node voltages. Solution: The supernode contains the 2-V source, nodes 1 and 2, and the 10- resistor. Applying KCL to the supernode as shown in Fig. 3.10(a) gives 2 i 1 i 2 7 Expressing i 1 and in terms of the node voltages or (3.3.1) To get the relationship between v 1 and v 2 , we apply KVL to the circuit in Fig. 3.10(b). Going around the loop, we obtain From Eqs. (3.3.1) and (3.3.2), we write or 2 v 1 0 2 i 2 v 2 0 4 7 1 8 2v 1 v 2 28 v 2 20 2v 1 v 1 2 v 2 0 1 v 2 v 1 2 v 2 v 1 2 20 2v 1 3v 1 22 1 v 1 7.333 V (3.3.2) and v 2 v 1 2 5.333 V. Note that the 10- resistor does not make any difference because it is connected across the supernode. 2 A 1 v 1 2 v 2 i 1 i 2 7 A 2 V 1 2 + + − + 2 A 2 Ω 4 Ω 7 A v 1 v 2 − − (a) Figure 3.10 Applying: (a) KCL to the supernode, (b) KVL to the loop. (b) Practice Problem 3.3 Find v and i in the circuit of Fig. 3.11. 4 Ω 9 V Answer: 0.6 V, 4.2 A. 21 V + − + − i + 3 Ω v 2 Ω 6 Ω − Figure 3.11 For Practice Prob. 3.3.
3.3 Nodal Analysis with Voltage Sources 91 Find the node voltages in the circuit of Fig. 3.12. Example 3.4 3 Ω + v x − 20 V 3v 6 Ω x 2 1 + − + − 4 2 Ω 10 A 4 Ω 1 Ω Figure 3.12 For Example 3.4. Solution: Nodes 1 and 2 form a supernode; so do nodes 3 and 4. We apply KCL to the two supernodes as in Fig. 3.13(a). At supernode 1-2, i 3 10 i 1 i 2 Expressing this in terms of the node voltages, or At supernode 3-4, v 3 v 2 6 10 v 1 v 4 3 v 1 2 5v 1 v 2 v 3 2v 4 60 (3.4.1) or i 1 i 3 i 4 i 5 1 v 1 v 4 3 v 3 v 2 6 4v 1 2v 2 5v 3 16v 4 0 v 4 1 v 3 4 (3.4.2) 3 Ω + v i x − 1 i 1 6 Ω v v 2 v 3 1 v 4 i i i 3 3 2 i 5 i 4 2 Ω 10 A 4 Ω 1 Ω + 3 Ω v x − Loop 3 20 V i 3 3v x + + − + − + 6 Ω + + v 1 Loop 1 v 2 v 3 Loop 2 v 4 − − − − (a) Figure 3.13 Applying: (a) KCL to the two supernodes, (b) KVL to the loops. (b)
Page 1 and 2: c h a p t e r Methods of Analysis 3
Page 3 and 4: 3.2 Nodal Analysis 83 since it is a
Page 5 and 6: 3.2 Nodal Analysis 85 Now we have t
Page 7 and 8: 3.2 Nodal Analysis 87 Substituting
Page 9: 3.3 Nodal Analysis with Voltage Sou
Page 13 and 14: 3.4 Mesh Analysis 93 Find v 1 , v 2
Page 15 and 16: 3.4 Mesh Analysis 95 The third step
Page 17 and 18: 3.4 Mesh Analysis 97 But at node A,
Page 19 and 20: 3.5 Mesh Analysis with Current Sour
Page 21 and 22: 3.6 Nodal and Mesh Analyses by Insp
Page 23 and 24: 3.6 Nodal and Mesh Analyses by Insp
Page 25 and 26: 3.8 Circuit Analysis with PSpice 10
Page 27 and 28: 3.9 Applications: DC Transistor Cir
Page 33 and 34: Review Questions 113 4. A supermesh
Page 35 and 36: Problems 115 3.9 Determine in the c
Page 37 and 38: Problems 117 3.20 For the circuit i
Page 39 and 40: Problems 119 Sections 3.4 and 3.5 M
Page 41 and 42: Problems 121 3.47 Rework Prob. 3.19
Page 43 and 44: Problems 123 i 1 i 2 3.62 Find the
Page 45 and 46: Problems 125 3.77 Solve for V 1 and

Fundamentals of Electric Circuits

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