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4.9: Exercises

  • Page ID
    52915
  • Analysis

    1. For the circuit shown in Figure 6.9.1 , determine the equivalent current source.

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    Figure 6.9.1

    2. Given the circuit shown in Figure 6.9.2 , determine the equivalent current source.

    clipboard_e09d5138ca945e595e479dc7434d485e7.png

    Figure 6.9.2

    3. Determine the equivalent current source for the circuit shown in Figure 6.9.3 .

    clipboard_ece74ac752d0f0cb0c8fabcb36443490b.png

    Figure 6.9.3

    4. For the circuit shown in Figure 6.9.4 , determine the equivalent current source.

    clipboard_efa3d8bb12cf9ed108f4fbfa88c622187.png

    Figure 6.9.4

    5. For the circuit shown in Figure 6.9.5 , determine the equivalent voltage source.

    clipboard_e89c8191a44816d239f8a3843fbca1d9d.png

    Figure 6.9.5

    6. Given the circuit shown in Figure 6.9.6 , determine the equivalent voltage source.

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    Figure 6.9.6

    7. Determine the equivalent voltage source for the circuit shown in Figure 6.9.7 .

    clipboard_e48a0a23b434d6e031453b487750c1a78.png

    Figure 6.9.7

    8. For the circuit shown in Figure 6.9.8 , determine the equivalent voltage source.

    clipboard_e72e84eecfa231e241b480779e8687052.png

    Figure 6.9.8

    9. Given the circuit shown in Figure 6.9.9 , determine the equivalent voltage source.

    clipboard_e898e601ff9dfb53fde7a2ba268d2e7b3.png

    Figure 6.9.9

    10. Using source conversion, find \(V_b\) for the circuit shown in Figure 6.9.10 .

    clipboard_eac4b2e35c4086a58f87007ae994024d4.png

    Figure 6.9.10

    11. Using source conversion, find the current through the 3 k\(\Omega\) resistor in the circuit of Figure 6.9.11 .

    clipboard_ef66dd09be3aeaf21f00cea5231e3ed71.png

    Figure 6.9.11

    12. Using source conversion, find \(V_b\) for the circuit shown in Figure 6.9.12 .

    clipboard_eab66f7a3e72a757f8c455c8c041dcb99.png

    Figure 6.9.12

    13. Using source conversion, find \(V_a\) for the circuit shown in Figure 6.9.13 .

    clipboard_eb12a5db6a65a64c0b9b01e06c4115858.png

    Figure 6.9.13

    14. Using source conversion, find \(V_b\) for the circuit shown in Figure 6.9.14 .

    clipboard_ed8539ca1883c00f0a44687ada5b8c8e6.png

    Figure 6.9.14

    15. Using superposition, determine \(V_b\) for the circuit shown in Figure 6.9.10 .

    16. Using superposition, find the current through the 3 k\(\Omega\) resistor for the circuit of Figure 6.9.10 .

    17. Using superposition, find the current through the 3 k\(\Omega\) resistor for the circuit of Figure 6.9.11 .

    18. Using superposition, determine \(V_{ab}\) for the circuit shown in Figure 6.9.11 .

    19. Using superposition, determine \(V_b\) for the circuit shown in Figure 6.9.12 .

    20. Using superposition, find the current through the 4 k\(\Omega\) resistor for the circuit of Figure 6.9.12 .

    21. Using superposition, find the current through the 30 k\(\Omega\) resistor for the circuit of Figure 6.9.13 .

    22. Using superposition, determine \(V_a\) for the circuit shown in Figure 6.9.13 .

    23. Using superposition, determine \(V_{ba}\) for the circuit shown in Figure 6.9.14 .

    24. Using superposition, find the current through the 10 k\(\Omega\) resistor for the circuit of Figure 6.9.14 .

    25. Using superposition, find the current through the 1.5 k\(\Omega\) resistor for the circuit of Figure 6.9.15 .

    clipboard_e994572058f0839c49db6de64fe3ce95a.png

    Figure 6.9.15

    26. Using superposition, determine \(V_{ab}\) for the circuit shown in Figure 6.9.15 .

    27. Using superposition, determine \(V_b\) for the circuit shown in Figure 6.9.16 .

    clipboard_ed74c0c240b3f7ddd9c08a491ba7c8bc1.png

    Figure 6.9.16

    28. Using superposition, find the current through the 200 \(\Omega\) resistor for the circuit of Figure 6.9.16 .

    29. Using superposition, find the current through the 4 k\(\Omega\) resistor for the circuit of Figure 6.9.17 .

    clipboard_e32defbb8a4cb69885e84f6042dd512c3.png

    Figure 6.9.17

    30. Using superposition, determine \(V_b\) for the circuit shown in Figure 6.9.17 .

    31. Is it possible to determine \(V_b\) in Figure 6.9.17 by using source conversions instead of superposition? Why/why not?

    32. Using superposition, determine \(V_{bc}\) for the circuit shown in Figure 6.9.18 .

    clipboard_e44ffb6dd8987fe048b7cea6cd784d08e.png

    Figure 6.9.18

    33. Using superposition, find the current through the 10 k\(\Omega\) resistor for the circuit of Figure 6.9.18 .

    34. Using superposition, find the currents through the 100 \(\Omega\) and 700 \(\Omega\) resistors for the circuit shown in Figure 6.9.19 .

    clipboard_edeb858476998fd507d1a207e79a96f73.png

    Figure 6.9.19

    35. Using superposition, determine \(V_{bd}\) for the circuit shown in Figure 6.9.19 .

    36. Is it possible to determine \(V_{bd}\) in Figure 6.9.19 by using source conversions instead of superposition? Why/why not?

    37. Using superposition, determine \(V_{ad}\) for the circuit shown in Figure 6.9.20 .

    clipboard_e611c21be889f774c94493bb82d2d4511.png

    Figure 6.9.20

    38. Using superposition, find the current through the 20 k\(\Omega\) resistor for the circuit shown in Figure 6.9.20 .

    39. Using superposition, find the current through the 12 k\(\Omega\) resistor for the circuit shown in Figure 6.9.21 .

    clipboard_e4c21f1521c0a0c27cadafa3217cc8bba.png

    Figure 6.9.21

    40. Using superposition, determine \(V_b\) for the circuit shown in Figure 6.9.21 .

    41. Using superposition, determine \(V_b\) for the circuit shown in Figure 6.9.22 .

    clipboard_ed42413d01574c80a351bcc29da871c3c.png

    Figure 6.9.22

    42. Using superposition, find the current through the 100 \(\Omega\) resistor for the circuit of Figure 6.9.22 .

    43. Using superposition, find the current through the 5 k\(\Omega\) resistor for the circuit of Figure 6.9.23 .

    clipboard_e3c8499063593e1eaca49c452d743589c.png

    Figure 6.9.23

    44. Using superposition, determine \(V_c\) for the circuit shown in Figure 6.9.23 .

    45. Given the circuit shown in Figure 6.9.24 , determine the Thévenin equivalent circuit that is driving the 4 k\(\Omega\) resistor.

    clipboard_ebda213867d530c70291dce73d4882749.png

    Figure 6.9.24

    46. Given the circuit shown in Figure 6.9.24 , determine the Norton equivalent circuit driving the 4 k\(\Omega\) resistor.

    47. Given the circuit shown in Figure 6.9.24 , determine the Norton equivalent circuit driving the 12 k\(\Omega\) resistor.

    clipboard_ef28b860d2e87e03f5e48bd55f295ba48.png

    Figure 6.9.25

    48. Determine the Thévenin equivalent circuit driving the 12 k\(\Omega\) resistor for the circuit shown in Figure 6.9.25 .

    49. Given the circuit shown in Figure 6.9.26 , determine the Thévenin equivalent circuit that is driving the 20 k\(\Omega\) resistor.

    clipboard_e05f7f1871e6a3552ce56d10962639127.png

    Figure 6.9.26

    50. For the circuit shown in Figure 6.9.26 , determine the Norton equivalent circuit driving the 4 k\(\Omega\) resistor.

    51. Given the circuit shown in Figure 6.9.27 , determine the Norton equivalent circuit driving the 40 \(\Omega\) resistor.

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    Figure 6.9.27

    52. Determine the Thévenin equivalent circuit driving the 10 \(\Omega\) resistor for the circuit shown in Figure 6.9.27 .

    53. Given the circuit shown in Figure 6.9.28 , determine the Norton equivalent circuit driving the 12 k\(\Omega\) resistor.

    clipboard_eea02490bf51e7bc8914d02b47504756e.png

    Figure 6.9.28

    54. Given the circuit of Figure 6.9.24 , determine the power in the 4 k\(\Omega\) resistor. If this resistor can be replaced with any other value, is it possible to achieve a higher power? Why/why not?

    55. Given the circuit of Figure 6.9.25 , determine the power in the 12 k\(\Omega\) resistor. If this resistor can be replaced with any other value, is it possible to achieve a higher power? Why/why not?

    56. Given the circuit of Figure 6.9.27 , determine the power in the 40 \(\Omega\) resistor. If this resistor can be replaced with any other value, is it possible to achieve a higher power? Why/why not?

    57. Given the circuit of Figure 6.9.28 , determine the power in the 6 k\(\Omega\) resistor. If this resistor can be replaced with any other value, is it possible to achieve a higher power? Why/why not?

    Design

    58. Consider the 4 k\(\Omega\) resistor to be the load in Figure 6.9.24 . Determine a new value for the load in order to achieve maximum load power. Also determine the maximum load power.

    59. Consider the 12 k\(\Omega\) resistor to be the load in Figure 6.9.25 . Determine a new value for the load in order to achieve maximum load power. Also determine the maximum load power.

    60. Consider the 40 \(\Omega\) resistor to be the load in Figure 6.9.27 . Determine a new value for the load in order to achieve maximum load power. Also determine the maximum load power.

    61. Consider the 6 k\(\Omega\) resistor to be the load in Figure 6.9.28 . Determine a new value for the load in order to achieve maximum load power. Also determine the maximum load power.

    62. Redesign the circuit of Figure 6.9.15 so that it uses only current sources and produces the same component currents and voltages as the original circuit.

    63. Redesign the circuit of Figure 6.9.17 so that it uses only current sources and produces the same component currents and voltages as the original circuit.

    64. Redesign the circuit of Figure 6.9.21 so that it uses only voltage sources and produces the same component currents and voltages as the original circuit.

    65. Redesign the circuit of Figure 6.9.23 so that it uses only voltage sources and produces the same component currents and voltages as the original circuit.

    66. Convert the delta network of Figure 6.9.29 into a Y network.

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    Figure 6.9.29

    67. Convert the pi network of Figure 6.9.30 into a T network.

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    Figure 6.9.30

    68. Convert the Y network of Figure 6.9.31 into a delta network.

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    Figure 6.9.31

    69. Convert the T network of Figure 6.9.32 into a pi network.

    clipboard_ea3e84cd041af3a1113e0935fe5857655.png

    Figure 6.9.32

    Challenge

    70. Redesign the circuit of Figure 6.9.33 so that it uses only current sources and produces the same node voltages as the original circuit.

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    Figure 6.9.33

    71. Using any combination of techniques, find the current through the 9 k\(\Omega\) resistor for the circuit of Figure 6.9.33 .

    72. Using any combination of techniques, determine \(V_{bc}\) for the circuit shown in Figure 6.9.33 .

    73. Is it possible to determine \(V_{bc}\) in Figure 6.9.33 by using just source conversions? Why/why not?

    74. Using superposition, find the current through the 25 \(\Omega\) resistor for the circuit of Figure 6.9.34 .

    clipboard_e32584d1d74cda73a77c3115bea866a89.png

    Figure 6.9.34

    75. Using superposition, find \(V_{ab}\) in the circuit of Figure 6.9.34 .

    76. Redesign the circuit of Figure 6.9.34 using only voltage sources so that it achieves the same node voltages as the original.

    clipboard_ed191ab00db9222d7df97bdd23893e7f0.png

    Figure 6.9.35

    77. Is it possible to determine \(V_{bc}\) in Figure 6.9.35 by using just source conversions or just superposition? Why/why not?

    78. Using any combination of techniques, find the current through the 100 \(\Omega\) resistor for the circuit shown in Figure 6.9.35 .

    79. Redesign the circuit of Figure 6.9.35 so that it uses only voltage sources and produces the same node voltages as the original circuit.

    80. Determine the Thévenin and Norton equivalents driving the 40 \(\Omega\) resistor for the circuit shown in Figure 6.9.16 .

    81. Determine the Thévenin and Norton equivalents driving the 12 k\(\Omega\) resistor for the circuit shown in Figure 6.9.17 .

    82. Given the circuit of Figure 6.9.26 , determine if the 4 k\(\Omega\) resistor is the optimal value to achieve maximum power dissipation in that resistor. If it is not, determine the value that will produce maximum power in the resistor along with the resulting power.

    83. For the circuit of Figure 6.9.36 , determine an equivalent circuit using just a single voltage source.

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    Figure 6.9.36

    Simulation

    84. Using DC bias simulations, compare the original circuit of problem 1 to its converted equivalent. Do this by connecting a resistor to the output terminals, trying several different resistance values and checking to see if the two circuits always produce the same voltage across this resistor.

    85. Using DC bias simulations, compare the original circuit of problem 5 to its converted equivalent. Do this by connecting a resistor to the output terminals, trying several different resistance values and checking to see if the two circuits always produce the same voltage across this resistor.

    86. Perform a DC bias simulation on the circuit of problem 11 to verify the node voltages.

    87. Perform a DC bias simulation on the circuit of problem 13 to verify the node voltages.

    88. Perform a DC bias simulation on the circuit of problem 19 to verify the node voltages.

    89. Perform a DC bias simulation on the circuit of problem 21 to verify the resistor current.

    90. Create DC bias simulations of the original and equivalent circuits generated in problem 45 to determine if the equivalent circuit is truly equivalent. Do this by substituting several different values for the 4 k\(\Omega\) resistor in both circuits to see if the same load voltage is obtained for both circuits.

    91. Create DC bias simulations of the original and equivalent circuits generated in problem 49 to determine if the equivalent circuit is truly equivalent. Do this by substituting several different values for the 20 k\(\Omega\) resistor in both circuits to see if the same load voltage is obtained for both circuits.

    92. Create DC bias simulations of the original and equivalent circuits generated in problem 53 to determine if the equivalent circuit is truly equivalent. Do this by substituting several different values for the 12 k\(\Omega\) resistor in both circuits to see if the same load voltage is obtained for both circuits.

    93. Perform a DC bias simulation on the circuit of problem 63 to verify that the node voltages of the new design match those of the original.

    94. Perform a DC bias simulation on the circuit of problem 65 to verify that the node voltages of the new design match those of the original.

    95. Using either Monte Carlo simulation or multiple DC bias simulations, verify that the resistance calculated in problem 55 achieves maximum power. Do this by trying several resistor values near the calculated value, and determining the power for each based on the squared load voltages.

    96. Using either Monte Carlo simulation or multiple DC bias simulations, verify that the resistance calculated in problem 56 achieves maximum power. Do this by trying several resistor values near the calculated value, and determining the power for each based on the squared load voltages.

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