Analysis
1. For the circuit of Figure 3.10.1
, determine the circulating current.
![clipboard_e861ac67a9086ae6f98757a3cf40347fc.png](https://eng.libretexts.org/@api/deki/files/27016/clipboard_e861ac67a9086ae6f98757a3cf40347fc.png?revision=1)
Figure 3.10.1
Answer 1
2. For the circuit of Figure 3.10.2
, determine the circulating current.
![clipboard_e263d89e1d31aa1a9c9982c7c6c018fdc.png](https://eng.libretexts.org/@api/deki/files/27017/clipboard_e263d89e1d31aa1a9c9982c7c6c018fdc.png?revision=1)
Figure 3.10.2
3. For the circuit of Figure 3.10.1
, determine the power dissipated in the resistor.
Answer 3
4. For the circuit of Figure 3.10.2
, determine the power dissipated in the resistor.
5. Determine the voltage at the open terminals of Figure 3.10.3
.
![clipboard_eca443708d526dd4b74aee760106b58ec.png](https://eng.libretexts.org/@api/deki/files/27018/clipboard_eca443708d526dd4b74aee760106b58ec.png?revision=1)
Figure 3.10.3
Answer 5
6. Determine the voltage at the open terminals of Figure 3.10.4
.
![clipboard_e1b226cc7e6a1650d443048f61dbb091e.png](https://eng.libretexts.org/@api/deki/files/27019/clipboard_e1b226cc7e6a1650d443048f61dbb091e.png?revision=1)
Figure 3.10.4
7. Determine the voltage at the open terminals of Figure 3.10.5
.
![clipboard_ed22d6b240cfcaad4b9f18a054dbd5aa3.png](https://eng.libretexts.org/@api/deki/files/27020/clipboard_ed22d6b240cfcaad4b9f18a054dbd5aa3.png?revision=1)
Figure 3.10.5
Answer 7
8. Determine the equivalent resistance of circuit shown in Figure 3.10.6
.
![clipboard_e31cc3d5e1472c3319dd00fadb0824f37.png](https://eng.libretexts.org/@api/deki/files/27021/clipboard_e31cc3d5e1472c3319dd00fadb0824f37.png?revision=1)
Figure 3.10.6
9. Determine the equivalent resistance of circuit shown in Figure 3.10.7
.
![clipboard_eb2310a8bf98e5f61375be4b5e345f7fb.png](https://eng.libretexts.org/@api/deki/files/27022/clipboard_eb2310a8bf98e5f61375be4b5e345f7fb.png?revision=1)
Figure 3.10.7
Answer 9
10. Determine the equivalent resistance of circuit shown in Figure 3.10.8
.
![clipboard_e075298609eeea0d90e5dacf51314325c.png](https://eng.libretexts.org/@api/deki/files/27023/clipboard_e075298609eeea0d90e5dacf51314325c.png?revision=1)
Figure 3.10.8
11. For the circuit of Figure 3.10.9
, determine the circulating current.
![clipboard_e0380b29e0af21b3afc6a36bff16eb150.png](https://eng.libretexts.org/@api/deki/files/27024/clipboard_e0380b29e0af21b3afc6a36bff16eb150.png?revision=1)
Figure 3.10.9
Answer 11
12. For the circuit of Figure 3.10.9
, determine the voltages across each resistor and find \(V_{ab}\).
13. Given the circuit of Figure 3.10.9
, determine the power dissipated by each resistor and the power delivered by the source.
Answer 13
- 320mW (200\(\Omega\))
- 160mW (100\(\Omega\))
- 480mW (source)
14. For the circuit of Figure 3.10.10
, determine the circulating current.
![clipboard_ef1688398efa7a3af06c65509d07dbc9b.png](https://eng.libretexts.org/@api/deki/files/27025/clipboard_ef1688398efa7a3af06c65509d07dbc9b.png?revision=1)
Figure 3.10.10
15. Given the circuit of Figure 3.10.10
, determine the voltages across each resistor and find \(V_{ba}\).
Answer 15
- 6V(2\(k\Omega\))
- 12V(4\(k\Omega\))
- -6V (\(V_{ba}\))
16. For the circuit of Figure 3.10.10
, determine the power dissipated by each resistor and the power delivered by the source.
17. For the circuit of Figure 3.10.11
, determine the circulating current.
![clipboard_e041167f9eef10a020f8ecb316b680ef2.png](https://eng.libretexts.org/@api/deki/files/27026/clipboard_e041167f9eef10a020f8ecb316b680ef2.png?revision=1)
Figure 3.10.11
Answer 17
18. For the circuit of Figure 3.10.11
, determine the voltages across each resistor and find \(V_a\).
19. For the circuit of Figure 3.10.12
, determine the circulating current and indicate all voltage polarities.
![clipboard_ef7651a621a32325b0e5563d03ec591ce.png](https://eng.libretexts.org/@api/deki/files/27027/clipboard_ef7651a621a32325b0e5563d03ec591ce.png?revision=1)
Figure 3.10.12
Answer 19
- I = 15mA
- \(V_{ab}\): + on left, - on right
- \(V_{bc}\): + on top, - on bottom
- \(V_{c}\): + on right, - on left
- \(V_{src}\): + on top, - on bottom
20. Given the circuit of Figure 3.10.12
, determine the voltages across each resistor and find \(V_b\), \(V_{bc}\), and \(V_{ca}\).
21. For the circuit of Figure 3.10.12
, determine the power delivered by the source.
Answer 21
22. For the circuit of Figure 3.10.13
, determine the circulating current and indicate all voltage polarities.
![clipboard_e65986e91155770aec6f516631ea0081c.png](https://eng.libretexts.org/@api/deki/files/27028/clipboard_e65986e91155770aec6f516631ea0081c.png?revision=1)
Figure 3.10.13
23. Given the circuit of Figure 3.10.13
, determine the voltages across each resistor and find \(V_c\), \(V_{ac}\), and \(V_a\).
Answer 23
- \(V_{50}=2.5V\)
- \(V_{10}=0.5V\)
- \(V_{60}=3V\)
- \(V_{c}=3V\)
- \(V_{ac}=3V\)
- \(V_{a}=6V\)
24. For the circuit of Figure 3.10.13
, determine the power dissipated by the 10 \(\Omega\) resistor.
25. For the circuit of Figure 3.10.14
, determine the circulating current and indicate all voltage polarities.
![clipboard_e511631e9694e8715074ba413aa11e526.png](https://eng.libretexts.org/@api/deki/files/27029/clipboard_e511631e9694e8715074ba413aa11e526.png?revision=1)
Figure 3.10.14
Answer 25
- I = 200mA
- \(V_{5}\): + on right, - on left
- \(V_{10}\): + on top, - on bottom
- \(V_{25}\): + on left, - on right
- \(V_{src}\): + on top, - on bottom
26. For the circuit of Figure 3.10.14
, determine the voltages across each resistor and find \(V_b\), \(V_c\), and \(V_{ca}\).
27. Referring to the circuit of 3.10.15
, determine the voltages across each resistor and find \(V_b\), \(V_c\), and \(V_{ac}\).
![clipboard_ef688270056c67d8cc46fbc9513aa2191.png](https://eng.libretexts.org/@api/deki/files/27030/clipboard_ef688270056c67d8cc46fbc9513aa2191.png?revision=1)
Figure 3.10.15
Answer 27
- \(V_{400}=2V\)
- \(V_{200}=1V\)
- \(V_{b}=10V\)
- \(V_{c}=1V\)
- \(V_{ac}=11V\)
28. Referring to the circuit of Figure 3.10.15
, determine the circulating current and indicate all voltage polarities.
29. Given the circuit of 3.10.16
, determine the voltages across each resistor and find \(V_b\), \(V_c\), and \(V_{ac}\).
![clipboard_e243414e271738a53886d88add17a887c.png](https://eng.libretexts.org/@api/deki/files/27031/clipboard_e243414e271738a53886d88add17a887c.png?revision=1)
Figure 3.10.16
Answer 29
- \(V_{2k}=3.6V\)
- \(V_{8k}=14.4V\)
- \(V_{b}=9.6V\)
- \(V_{c}=-14.4V\)
- \(V_{ac}=20.4V\)
30. Referring to the circuit of Figure 3.10.16
, determine the circulating current and indicate all voltage polarities.
31. Given the circuit of 3.10.17
, determine the circulating current and indicate all voltage polarities.
![clipboard_e192b37d8de3292f4f932e563a13a06f9.png](https://eng.libretexts.org/@api/deki/files/27032/clipboard_e192b37d8de3292f4f932e563a13a06f9.png?revision=1)
Figure 3.10.17
Answer 31
- I = 35mA
- \(V_{400}\): + on left, - on right
- \(V_{200}\): + on right, - on left
- \(V_{12Vsrc}\): + on top, - on bottom
- \(V_{9Vsrc}\): + on bottom, - on top
32. Referring to the circuit of Figure 3.10.17
, determine the voltages across each resistor and find \(V_b\), \(V_c\), and \(V_{ac}\).
33. Given the circuit of 3.10.18
, determine the circulating current and indicate all voltage polarities.
![clipboard_eb10a2c271c71253d93acbf050d083e74.png](https://eng.libretexts.org/@api/deki/files/27033/clipboard_eb10a2c271c71253d93acbf050d083e74.png?revision=1)
Figure 3.10.18
Answer 33
- I = 1.89mA
- \(V_{2k}\): + on left, - on right
- \(V_{8k}\): + on right, - on left
- \(V_{6Vsrc}\): + on top, - on bottom
- \(V_{24Vsrc}\): + on top, - on bottom
34. Referring to the circuit of Figure 3.10.18
, determine the voltages across each resistor and find \(V_b\), \(V_c\), and \(V_{ac}\).
35. Using the voltage divider rule, determine the voltages \(V_b\), \(V_c\) and \(V_{ac}\) for the circuit shown in Figure 3.10.19
.
![clipboard_eaaa1d73c2a23d38b89e254a7a3d43941.png](https://eng.libretexts.org/@api/deki/files/27034/clipboard_eaaa1d73c2a23d38b89e254a7a3d43941.png?revision=1)
Figure 3.10.19
Answer 35
- \(V_{b} = 14.4V\)
- \(V_{c} = 9V\)
- \(V_{ac} = 6V\)
36. Using the voltage divider rule, determine the voltages \(V_b\), \(V_c\) and \(V_{bd}\) for the circuit shown in Figure 3.10.20
.
![clipboard_e75b3cf942c84777cf92505298ec58a88.png](https://eng.libretexts.org/@api/deki/files/27035/clipboard_e75b3cf942c84777cf92505298ec58a88.png?revision=1)
Figure 3.10.20
37. For the circuit of Figure 3.10.20
, determine \(V_b\) if the 4 k\(\Omega\) resistor is accidentally shorted. How does this compare to the original circuit?
Answer 37
- \(V_{b} = 1V\). The 2V is now split across the three remaining resistors
38. For the circuit of Figure 3.10.20
, determine \(V_b\) if the 4 k\(\Omega\) resistor is accidentally opened. How does this compare to the original circuit?
39. Given the circuit shown in Figure 3.10.21
, find the voltage drop across the resistor.
![clipboard_e1c01318cf83b54086df572c79872e597.png](https://eng.libretexts.org/@api/deki/files/27036/clipboard_e1c01318cf83b54086df572c79872e597.png?revision=1)
Figure 3.10.21
Answer 39
40. Given the circuit shown in Figure 3.10.22
, find the voltage drops across the resistor.
![clipboard_ea950ebe89e6870a65141642845408268.png](https://eng.libretexts.org/@api/deki/files/27037/clipboard_ea950ebe89e6870a65141642845408268.png?revision=1)
Figure 3.10.22
41. Find the voltage drops across the resistors in the circuit of Figure 3.10.23
.
![clipboard_e8d64c8f8f624da1e3167b63f35c0022d.png](https://eng.libretexts.org/@api/deki/files/27038/clipboard_e8d64c8f8f624da1e3167b63f35c0022d.png?revision=1)
Figure 3.10.23
Answer 41
- \(V_{20} = 40V\)
- \(V_{20} = 100V\)
42. Find the voltage drops across the resistors in the circuit of Figure 3.10.24
.
![clipboard_ede92d2ac151242235576fe373b226be2.png](https://eng.libretexts.org/@api/deki/files/27039/clipboard_ede92d2ac151242235576fe373b226be2.png?revision=1)
Figure 3.10.24
43. Find the voltage drops across the resistors in the circuit of Figure 3.10.25
.
![clipboard_ef396c9c96b8556702036412193a2331c.png](https://eng.libretexts.org/@api/deki/files/27040/clipboard_ef396c9c96b8556702036412193a2331c.png?revision=1)
Figure 3.10.25
Answer 43
- \(V_{4} = 12V\)
- \(V_{10} = 30V\)
- \(V_{5} = 15V\)
44. Find the voltage drops across the resistors in the circuit of Figure 3.10.26
.
![clipboard_e04ddcc51d39f6f866df9871d32bc85f8.png](https://eng.libretexts.org/@api/deki/files/27041/clipboard_e04ddcc51d39f6f866df9871d32bc85f8.png?revision=1)
Figure 3.10.26
45. The circuit of Figure 3.10.27
uses a linear taper potentiometer. Determine \(V_b\) when the wiper arm is at position \(a\), position \(b\), and at the halfway point.
![clipboard_e8e4d376e23c544d757f7f4330a688152.png](https://eng.libretexts.org/@api/deki/files/27042/clipboard_e8e4d376e23c544d757f7f4330a688152.png?revision=1)
Figure 3.10.27
Answer 45
- \(V_{b} = 0V\). This is true no matter where the wiper arm of the potentiometer is
46. What is the maximum current flowing through the potentiometer of Figure 3.10.27
? At what position(s) does this occur?
Design
47. Redesign the circuit of Figure 3.10.1
using a new resistor such that the current from the 12 volt battery is 0.1 A.
Answer 47
- Change the 100 \(\Omega\) resistor to 120 \(\Omega\)
48. Redesign the circuit of Figure 3.10.2
using a new resistor such that the current from the 9 volt battery is 2 mA.
49. For the circuit of Figure 3.10.6
, find the value of a series voltage source that would generate 1 mA of current if it was connected across the terminals.
Answer 49
50. For the circuit of Figure 3.10.8
, find the value of a series voltage source that would generate 1 mA of current if it was connected across the terminals.
51. Determine values for the resistors in Figure 3.10.28
such that \(R_1\) is four times the size of \(R_2\) and \(R_2\) is three times the size of R3, with the total resistance equaling 8 k\(\Omega\).
![clipboard_e71c45f140f3f0e50948cf5e412d88a78.png](https://eng.libretexts.org/@api/deki/files/27043/clipboard_e71c45f140f3f0e50948cf5e412d88a78.png?revision=1)
Figure 3.10.28
Answer 51
- \(R_{1} = 6k\Omega\)
- \(R_{2} = 1.5k\Omega\)
- \(R_{3} = 500\Omega\)
52. For the circuit shown in Figure 3.10.29
, determine values for \(R_1\) and \(R_2\) such that \(V_{ab}\) is 6 volts if \(E\) is a 9 volt battery and the total current draw is 20 mA.
![clipboard_e71eb3d6fe6e69e5c9256c4929c032aed.png](https://eng.libretexts.org/@api/deki/files/27044/clipboard_e71eb3d6fe6e69e5c9256c4929c032aed.png?revision=1)
Figure 3.10.29
53. Consider the circuit shown in Figure 3.10.30
. If all resistors have the same value, determine that value if \(E\), a 24 volt source, generates a total power of 10 watts.
![clipboard_e3d9e8caa5cefd7830ea11deee19bcf79.png](https://eng.libretexts.org/@api/deki/files/27045/clipboard_e3d9e8caa5cefd7830ea11deee19bcf79.png?revision=1)
Figure 3.10.30
Answer 53
54. For the circuit shown in Figure 3.10.31
, determine values for \(R_1\) and \(R_2\) such that \(V_{ab}\) is 6 volts if \(I\) is a 2 mA source and the total voltage drop is 24 volts.
![clipboard_ec5007d97be7064fac90325f84736385f.png](https://eng.libretexts.org/@api/deki/files/27046/clipboard_ec5007d97be7064fac90325f84736385f.png?revision=1)
Figure 3.10.31
55. Consider the circuit of Figure 3.10.20
. Is it possible to add a fifth resistor such that the circulating current is 0.1 mA? If so, what is that resistor value?
Answer 55
56. Consider the circuit of Figure 3.10.20
. Is it possible to add a fifth resistor such that the circulating current is 2 mA? If so, what is that resistor value?
Challenge
57. Assume that two AA cells, \(E_1\) and \(E_2\), rated at 900 mAh each are used to drive a 2 watt lamp as shown in Figure 3.10.32
. Determine the expected life of the batteries.
![clipboard_e23902157db19368435d13da2322ca06b.png](https://eng.libretexts.org/@api/deki/files/27047/clipboard_e23902157db19368435d13da2322ca06b.png?revision=1)
Figure 3.10.32
58. Given the circuit of Figure 3.10.33
, determine the required values of \(E\), \(R_1\), \(R_2\) and \(R_3\) if there is one volt across \(R_3\), the total current draw is 10 mA, the voltage across \(R_1\) is twice the size of voltage across \(R_2\) and the power dissipation in \(R_2\) is 100 mW.
![clipboard_e9fca02db221aab379374d6278c459f05.png](https://eng.libretexts.org/@api/deki/files/27048/clipboard_e9fca02db221aab379374d6278c459f05.png?revision=1)
Figure 3.10.33
59. Given the circuit of Figure 3.10.33
, determine the required source voltage if \(R_1\) is 1 k\(\Omega\), \(R_2\) is 1 k\(\Omega\), the power dissipation in \(R_1\) is 4 mW and the power dissipation in \(R_3\) is 2 mW.
60. Given the circuit of Figure 3.10.34
, determine \(V_c\), \(V_{db}\) and \(V_{ce}\).
![clipboard_e7011b0f4a67ab37625d0529160660982.png](https://eng.libretexts.org/@api/deki/files/27049/clipboard_e7011b0f4a67ab37625d0529160660982.png?revision=1)
Figure 3.10.34
61. Given the circuit of Figure 3.10.34
, determine \(V_{ac}\), \(V_{eb}\) and \(V_d\).
62. Refer to the circuit of Figure 3.10.20
. Assuming each resistor has a 10% tolerance, determine the maximum and minimum values for \(V_c\).