Fundamentals of Electric Circuits

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96 Chapter 3 Methods of Analysis We obtain the determinants Thus, ¢ 1 2 1 ` 1 2 ` 2 2 4, 3 2 ¢ ` 1 2 ` 6 2 4 3 1 ¢ 2 ` 1 1 ` 3 1 4 as before. i 1 ¢ 1 ¢ 1 A, i 2 ¢ 2 ¢ 1 A Practice Problem 3.5 i 1 Calculate the mesh currents and of the circuit of Fig. 3.19. i 2 Answer: i 1 2 A, i 2 0 A. 2 Ω 9 Ω 12 Ω 36 V + i 1 + − 24 V i − 2 4 Ω 3 Ω Figure 3.19 For Practice Prob. 3.5. Example 3.6 Use mesh analysis to find the current in the circuit of Fig. 3.20. I o 24 V i 2 i 1 A I o 10 Ω i 2 24 Ω 4 Ω 12 Ω i 3 + − + − i 1 Figure 3.20 For Example 3.6. 4I o Solution: We apply KVL to the three meshes in turn. For mesh 1, or For mesh 2, or For mesh 3, 24 10 (i 1 i 2 ) 12 (i 1 i 3 ) 0 11i 1 5i 2 6i 3 12 24i 2 4 (i 2 i 3 ) 10 (i 2 i 1 ) 0 5i 1 19i 2 2i 3 0 4I o 12(i 3 i 1 ) 4(i 3 i 2 ) 0 (3.6.1) (3.6.2)
3.4 Mesh Analysis 97 But at node A, I o i 1 i 2 , so that 4(i 1 i 2 ) 12(i 3 i 1 ) 4(i 3 i 2 ) 0 or i 1 i 2 2i 3 0 (3.6.3) In matrix form, Eqs. (3.6.1) to (3.6.3) become We obtain the determinants as ¢ 418 30 10 114 22 50 192 12 5 6 0 19 2 ¢ 1 5 0 1 25 456 24 432 12 5 6 0 19 2 ¢ 2 ¢ 3 11 5 6 £ 5 19 2 1 1 2 11 5 12 5 19 0 5 1 1 05 11 5 12 5 19 0 We calculate the mesh currents using Cramer’s rule as i 1 ¢ 1 , ¢ 432 192 2.25 A, i 2 ¢ 2 ¢ 144 192 0.75 A Thus, I o i 1 i 2 1.5 A. 11 5 6 5 19 2 5 1 1 25 11 5 6 5 19 2 11 12 6 5 0 2 5 1 0 25 11 12 6 5 0 2 i 1 § £ i 2 § £ i 3 i 3 ¢ 3 ¢ 288 192 1.5 A 12 0 § 0 24 120 144 60 228 288
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 and 10: 3.3 Nodal Analysis with Voltage Sou
Page 11 and 12: 3.3 Nodal Analysis with Voltage Sou
Page 13 and 14: 3.4 Mesh Analysis 93 Find v 1 , v 2
Page 15: 3.4 Mesh Analysis 95 The third step
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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