5.6: Exercises
- Page ID
- 52922
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Analysis
1. Given the circuit in Figure 7.6.1 , write the mesh loop equations.
Figure 7.6.1
2. Using mesh analysis, determine the value of \(V_b\) for the circuit shown in Figure 7.6.1 .
3. For the circuit shown in Figure 7.6.1 , use mesh analysis to determine the current through the 1 k\(\Omega\) resistor.
4. Given the circuit in Figure 7.6.2 , write the mesh loop equations and the associated determinants.
Figure 7.6.2
5. Using mesh analysis, determine the value of \(V_b\) for the circuit shown in Figure 7.6.2 .
6. For the circuit shown in Figure 7.6.2 , use mesh analysis to determine the current through the 500 \(\Omega\) resistor.
7. Given the circuit in Figure 7.6.3 , write the mesh loop equations.
Figure 7.6.3
8. Using mesh analysis, determine the value of \(V_b\) for the circuit shown in Figure 7.6.3 .
9. For the circuit shown in Figure 7.6.3 , use mesh analysis to determine the current through the 75 \(\Omega\) resistor.
10. Given the circuit in Figure 7.6.4 , write the mesh loop equations and the associated determinants.
Figure 7.6.4
11. Using mesh analysis, determine the value of \(V_{bc}\) for the circuit shown in Figure 7.6.4 .
12. For the circuit shown in Figure 7.6.4 , use mesh analysis to determine the current through the 10 k\(\Omega\) resistor.
13. Given the circuit in Figure 7.6.5 , write the mesh loop equations.
Figure 7.6.5
14. Using mesh analysis, determine the value of \(V_{ac}\) for the circuit shown in Figure 7.6.5 .
15. For the circuit shown in Figure 7.6.5 , use mesh analysis to determine the current through the 4 k\(\Omega\) resistor.
16. Given the circuit in Figure 7.6.6 , write the mesh loop equations and the associated determinants.
Figure 7.6.6
17. Using mesh analysis, determine the value of \(V_c\) for the circuit shown in Figure 7.6.6 .
18. For the circuit shown in Figure 7.6.6 , use mesh analysis to determine the current through the 10 k\(\Omega\) resistor.
19. Given the circuit in Figure 7.6.7 , write the mesh loop equations.
Figure 7.6.7
20. Using mesh analysis, determine the value of \(V_{bd}\) for the circuit shown in Figure 7.6.7 .
21. For the circuit shown in Figure 7.6.7 , use mesh analysis to determine the current through the 500 \(\Omega\) resistor.
22. Given the circuit in Figure 7.6.8 , write the mesh loop equations.
Figure 7.6.8
23. Using mesh analysis, determine the value of \(V_{ad}\) for the circuit shown in Figure 7.6.8 .
24. For the circuit shown in Figure 7.6.8 , use mesh analysis to determine the current through the 3 k\(\Omega\) resistor.
25. Given the circuit in Figure 7.6.9 , write the mesh loop equations.
Figure 7.6.9
26. Using mesh analysis, determine the value of \(V_e\) for the circuit shown in Figure 7.6.9 .
27. For the circuit shown in Figure 7.6.9 , use mesh analysis to determine the current through the 9 k\(\Omega\) resistor.
28. Given the circuit in Figure 7.6.10 , write the mesh loop equations and the associated determinants.
Figure 7.6.10
29. Using mesh analysis, determine the value of \(V_{bc}\) for the circuit shown in Figure 7.6.10 .
30. Given the circuit shown in Figure 7.6.10 , use mesh analysis to determine the current through the 600 \(\Omega\) resistor.
31. Given the circuit in Figure 7.6.11 , write the mesh loop equations.
Figure 7.6.11
32. Using mesh analysis, determine the value of \(V_{bc}\) for the circuit shown in Figure 7.6.11 .
33. Given the circuit shown in Figure 7.6.11 , use mesh analysis to determine the current through the 800 \(\Omega\) resistor.
34. For the circuit in Figure 7.6.12 , write the mesh loop equations.
Figure 7.6.12
35. Using mesh analysis, determine the value of \(V_a\) for the circuit shown in Figure 7.6.12 .
36. For the circuit shown in Figure 7.6.12 , use mesh analysis to determine the current through the 3 k\(\Omega\) resistor.
37. Given the circuit in Figure 7.6.13 , write the mesh loop equations.
Figure 7.6.13
38. Using mesh analysis, determine the value of \(V_c\) for the circuit shown in Figure 7.6.13 .
39. For the circuit shown in Figure 7.6.13 , use mesh analysis to determine the current passing through the 8.5 k\(\Omega\) resistor.
40. Given the circuit in Figure 7.6.14 , write the mesh loop equations (consider using source conversion).
Figure 7.6.14
41. Using mesh analysis, determine the value of \(V_a\) for the circuit shown in Figure 7.6.14 .
42. For the circuit shown in Figure 7.6.14 , use mesh analysis to determine the current passing through the 30 k\(\Omega\) resistor.
43. Given the circuit in Figure 7.6.15 , write the mesh loop equations (consider using source conversion).
Figure 7.6.15
44. Using mesh analysis, determine the value of \(V_b\) for the circuit shown in Figure 7.6.15 .
45. For the circuit shown in Figure 7.6.15 , use mesh analysis to determine the current through the 5 k\(\Omega\) resistor.
46. Given the circuit in Figure 7.6.16 , write the node equations.
Figure 7.6.16
47. Using nodal analysis, determine the value of \(V_b\) for the circuit shown in Figure 7.6.16 .
48. For the circuit shown in Figure 7.6.16 , use nodal analysis to determine the current through the 3 k\(\Omega\) resistor.
49. Given the circuit in Figure 7.6.17 , write the node equations.
Figure 7.6.17
50. Using nodal analysis, determine the value of \(V_b\) for the circuit shown in Figure 7.6.17 .
51. For the circuit shown in Figure 7.6.17 , use nodal analysis to determine the current passing through the 12 k\(\Omega\) resistor.
52. Given the circuit in Figure 7.6.18 , write the node equations.
Figure 7.6.18
53. Using nodal analysis, determine the value of \(V_{ba}\) for the circuit shown in Figure 7.6.18 .
54. For the circuit shown in Figure 7.6.18 , use nodal analysis to determine the current passing through the 100 \(\Omega\) resistor.
55. Given the circuit in Figure 7.6.19 , write the node equations.
Figure 7.6.19
56. Using nodal analysis, determine the value of \(V_{ac}\) for the circuit shown in Figure 7.6.19 .
57. For the circuit shown in Figure 7.6.19 , use nodal analysis to determine the current passing through the 20 k\(\Omega\) resistor.
58. Given the circuit in Figure 7.6.20 , write the node equations.
Figure 7.6.20
59. Using nodal analysis, determine the value of \(V_b\) for the circuit shown in Figure 7.6.20 .
60. For the circuit shown in Figure 7.6.20 , use nodal analysis to determine the current through the 3 k\(\Omega\) resistor.
61. Given the circuit in Figure 7.6.21 , write the node equations.
Figure 7.6.21
62. Using nodal analysis, determine the value of \(V_b\) for the circuit shown in Figure 7.6.21 .
63. For the circuit shown in Figure 7.6.21 , use nodal analysis to determine the current through the 40 \(\Omega\) resistor.
64. Given the circuit in Figure 7.6.13 , write the node equations.
65. Using nodal analysis, determine the value of \(V_d\) for the circuit shown in Figure 7.6.13 .
66. For the circuit shown in Figure 7.6.13 , use nodal analysis to determine the current passing through the 20 k\(\Omega\) resistor.
67. Given the circuit in Figure 7.6.14 , write the node equations using the general approach. Do not use source conversions.
68. Using nodal analysis, determine the value of \(V_{ab}\) for the circuit shown in Figure 7.6.14 .
69. For the circuit shown in Figure 7.6.14 , use nodal analysis to determine the current passing through the 30 k\(\Omega\) resistor.
70. Given the circuit in Figure 7.6.15 , write the node equations.
71. Using nodal analysis, determine the value of \(V_b\) for the circuit shown in Figure 7.6.15 .
72. For the circuit shown in Figure 7.6.15 , use nodal analysis to determine the current through the 4 k\(\Omega\) resistor.
73. For the circuit of Figure 7.6.22 , determine \(V_b\).
Figure 7.6.22
74. For the circuit of Figure 7.6.23 , determine \(V_c\).
Figure 7.6.23
75. Given the circuit of Figure 7.6.24 , determine \(V_b\).
Figure 7.6.24
76. Find the current through the 10 k\(\Omega\) resistor given the circuit of Figure 7.6.25 .
Figure 7.6.25
77. Given the circuit of Figure 7.6.26 , determine \(V_c\).
Figure 7.6.26
78. In the circuit of Figure 7.6.27 , determine \(V_a\).
Figure 7.6.27
79. For the circuit of Figure 7.6.28 , determine \(V_a\).
Figure 7.6.28
80. For the circuit of Figure 7.6.29 , determine \(V_a\).
Figure 7.6.29
Challenge
81. Given the circuit in Figure 7.6.8 , write the node equations.
82. Using nodal analysis, determine the value of \(V_b\) for the circuit shown in Figure 7.6.8 .
83. For the circuit shown in Figure 7.6.8 , use nodal analysis to determine the current through the 3 k\(\Omega\) resistor.
84. Given the circuit in Figure 7.6.6 , write the node equations.
85. Using nodal analysis, determine the value of \(V_c\) for the circuit shown in Figure 7.6.6 .
86. For the circuit shown in Figure 7.6.6 , use nodal analysis to determine the current through the 8 k\(\Omega\) resistor.
87. Given the circuit in Figure 7.6.10 , write the node equations and the associated determinants.
88. Using nodal analysis, determine the value of \(V_{bc}\) for the circuit shown in Figure 7.6.10 .
89. For the circuit shown in Figure 7.6.10 , use nodal analysis to determine the current through the 2 k\(\Omega\) resistor.
90. Given the circuit of Figure 7.6.30 , determine \(V_c\).
Figure 7.6.30
91. Find the current through the 10 k\(\Omega\) resistor in the circuit of Figure 7.6.31 .
Figure 7.6.31
92. Given the circuit of Figure 7.6.32 , determine \(V_c\).
Figure 7.6.32
93. Given the circuit of Figure 7.6.33 , determine the current through the 5 k\(\Omega\) resistor.
Figure 7.6.33
94. For the circuit of Figure 7.6.34 , determine \(V_b\).
Figure 7.6.34
95. For the circuit of Figure 7.6.35 , determine \(V_c\).
Figure 7.6.35
96. For the circuit of Figure 7.6.36 , determine \(V_a\).
Figure 7.6.36
97. For the circuit of Figure 7.6.37 , determine \(V_b\).
Figure 7.6.37
Simulation
98. Perform a DC bias simulation on the circuit depicted in Figure 7.6.7 to verify the component currents.
99. Perform a DC bias simulation on the circuit depicted in Figure 7.6.9 to verify the component currents.
100. Perform a DC bias simulation on the circuit depicted in Figure 7.6.7 to verify the loop currents and node voltages.
101. Perform a DC bias simulation on the circuit depicted in Figure 7.6.16 to verify the node voltages.
102. Perform a DC bias simulation on the circuit depicted in Figure 7.6.19 to verify the node voltages.
103. Perform a DC bias simulation on the circuit depicted in Figure 7.6.20 to verify the node voltages.