# 2.3.8: Exercises

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## Analysis

1. Determine the effective resistance of the network shown in Figure 4.8.1 . Figure 4.8.1

• 80 $$\Omega$$

2. Determine the effective resistance of the network shown in Figure 4.8.2 . Figure 4.8.2

3. Determine the effective resistance of the network shown in Figure 4.8.3 . Figure 4.8.3

• 14.3 $$\Omega$$

4. Find the effective source current of the network shown in Figure 4.8.4 . Figure 4.8.4

5. Determine the effective source current of the network shown in Figure 4.8.5 . Figure 4.8.5

• 4mA, down

6. Find the source and resistor currents for the circuit of Figure 4.8.6 . Figure 4.8.6

7. Determine the source and resistor currents for the circuit of Figure 4.8.7 . Figure 4.8.7

• $$I_{200} = 120mA$$
• $$I_{50} = 480mA$$
• $$I_{src} = 600mA$$

8. Find the source and resistor currents for the circuit of Figure 4.8.8 . Figure 4.8.8

9. For the circuit of Figure 4.8.9 , determine the source and resistor currents. Figure 4.8.9

• $$I_{82} = 219.5mA$$
• $$I_{69} = 264.7mA$$
• $$I_{src} = 484.2mA$$

10. Determine the current through each resistor in the circuit of Figure 4.8.10 . Also determine the total power generated by the source. Figure 4.8.10

11. Consider the circuit shown in Figure 4.8.10 . Assume that the 100 k$$\Omega$$ is replaced with another resistor ten times as large. Will this have a major impact on the current exiting source? Why/why not?

• No. It is already the smallest current by an order of magnitude, and this makes it smaller

12. Consider the circuit shown in Figure 4.8.10 . Assume that the 1 k$$\Omega$$ is replaced with another resistor ten times smaller. Will this have a major impact on the current exiting source? Why/why not?

13. Find the current through each resistor in the circuit of Figure 4.8.11 . Figure 4.8.11

• $$I_{36k} = 333.3uA$$
• $$I_{48k} = 250uA$$

14. Determine the current through each resistor in the circuit of Figure 4.8.12 . Also determine the total current exiting by the source. Figure 4.8.12

15. Determine the current through each resistor in the circuit of Figure 4.8.13 . Figure 4.8.13

• $$I_{47k} = 0.1915mA$$
• $$I_{5.1k} = 1.765mA$$
• $$I_{1.8k} = 5mA$$

16. For the circuit shown in Figure 4.8.14 , determine the current through each resistor and the source voltage. Figure 4.8.14

17. For the circuit shown in Figure 4.8.15 , determine the current through each resistor and the source voltage. Figure 4.8.15

• $$I_{10} = 1.6A$$
• $$I_{40} = 0.4mA$$
• $$V_{src} = 16V$$

18. For the circuit shown in Figure 4.8.16 , determine the current through each resistor and the source voltage. Figure 4.8.16

19. For the circuit shown in Figure 4.8.17 , determine the current through each resistor and the source voltage. Figure 4.8.17

• $$I_{200} = 50mA$$
• $$I_{400} = 25mA$$
• $$V_{src} = 10 V$$

20. For the circuit shown in Figure 4.8.18 , determine the current through each resistor and the source voltage. Figure 4.8.18

21. For the circuit shown in Figure 4.8.19 , determine the current through each resistor and the source voltage. Figure 4.8.19

• $$I_{3k} = 145.5uA$$
• $$I_{2k} = 218.2uA$$
• $$I_{12k} = 28.57uA$$
• $$V_{src} = 0.4364V$$

22. For the circuit shown in Figure 4.8.20 , determine the current through each resistor and the source voltage. Figure 4.8.20

23. Referring to the circuit of Figure 4.8.20 , determine the resistor currents if the right-most 75 k$$\Omega$$ resistor is accidentally opened (i.e., unconnected). How do these results compare to those of problem 22?

• $$I_{25k} = 2.571mA$$
• $$I_{75k} = 0.8571mA$$
• Currents will be higher in the 25k resistors because there is one fewer path for current to go

24. Referring to the circuit of Figure 4.8.20 , determine the resistor currents if the right-most 75 k$$\Omega$$ resistor is accidentally shorted. How do these results compare to those of problems 22 and 23?

25. For the circuit shown in Figure 4.8.21 , determine the current through each resistor and the source voltage. Figure 4.8.21

• $$I_{5k} = 15.714mA$$
• $$I_{10k} = 2.857mA$$
• $$I_{1k} = 28.57mA$$
• $$V_{src} = 28.57V$$

26. Given the circuit of Figure 4.8.22 , find the currents through the two resistors. Figure 4.8.22

27. If the 5 mA current source shown in Figure 4.8.22 is accidentally wired in upside down, does the voltage across the 12 k $$\Omega$$ resistor become more positive or more negative with respect to ground?

• The voltage is larger, but now negative, so it becomes more negative

28. Given the circuit of Figure 4.8.23 , find the voltages across the three resistors. Figure 4.8.23

29. Find the currents through the three resistors in Figure 4.8.23 .

• $$I_{2k} = 11.25mA$$
• $$I_{6k} = 3.75mA$$
• $$I_{4.5k} = 5mA$$

## Design

30. For the network shown in Figure 4.8.24 , determine a for values for $$R_1$$ given that $$R_2$$ is 12 k$$\Omega$$ and the equivalent combination is 8 k$$\Omega$$. Figure 4.8.24

31. Add a third parallel resistor to the circuit of Figure 4.8.8 such that the source current is 10 mA.

• 1.714k$$\Omega$$

32. Add a fourth parallel resistor to the circuit of Figure 4.8.10 such that the source current is 20 mA.

33. Consider the circuit shown in Figure 4.8.14 . Determine a new value for the current source such that the source voltage equals 10 volts.

• 6.667mA

34. Consider the circuit shown in Figure 4.8.16 . Determine a new value for the current source such that the source voltage equals 20 volts.

35. Given the circuit of Figure 4.8.25 , if the source is 6 volts and $$R_1$$ is 2 k$$\Omega$$, what must be the value of $$R_2$$ if the total current exiting the source is 10 mA? Figure 4.8.25

• 857$$\Omega$$

36. For the circuit shown in Figure 4.8.26 , determine values for resistors $$R_2$$ and $$R_3$$ such that the current through $$R_2$$ is twice the current through $$R_1$$ and the current through $$R_3$$ is half the current through $$R_1$$. The source is 6 volts and $$R_1$$ is 2 k$$\Omega$$. Figure 4.8.26

37. For the circuit shown in Figure 4.8.27 , determine values for resistors $$R_1$$ and $$R_2$$ such that the current through $$R_2$$ is twice the current through $$R_1$$. The source is 10 mA and $$R_1$$ is 6 k$$\Omega$$. Figure 4.8.27

• 3k$$\Omega$$

## Challenge

38. For the circuit shown in Figure 4.8.12 , determine a new value for the 11 k$$\Omega$$ resistor such that the supply current is 50 mA.

39. For the circuit shown in Figure 4.8.14 , determine a new value for the 2 k$$\Omega$$ resistor such that the voltage drop across the 6 k$$\Omega$$ is 15 volts.

40. Consider the circuit shown in Figure 4.8.21 . If the current source was replaced with a voltage source, what value is needed so that the same currents flow through the resistors as in the original circuit?

41. For the network shown in Figure 4.8.24 , determine values for $$R_1$$ and $$R_2$$ such that $$R_2$$ is twice the size of $$R_1$$ and the equivalent combination is 6 k$$\Omega$$.

42. Given the network of Figure 4.8.3 , is it possible to replace the 60 $$\Omega$$ resistor with another value such that the equivalent combination of the three resistors is 25 $$\Omega$$? If so, what is that value?

43. Given the network of Figure 4.8.11 , is it possible to add a fifth parallel resistor such that the source current is 1 mA? If so, what is that value?

44. For the circuit shown in Figure 4.8.26 , determine values for the three resistors such that the current through $$R_1$$ is twice the current through $$R_2$$ and four times the current through $$R_3$$. The source is 12 volts and should produce a total of 9 mA of current.

45. For the circuit shown in Figure 4.8.27 determine values for the two resistors such that the current through $$R_1$$ is half the current through $$R_2$$. The source is 24 mA and should produce a drop of 16 volts across $$R_1$$.

46. Given three current sources with values of 1 mA, 2 mA and 7 mA; how would they need to be connected in order to deliver 4 volts across a 1 k$$\Omega$$ load resistor? Figure 4.8.28

47. Consider the circuit of Figure 4.8.28 . Assume $$I$$ is a 4 mA source. Using only 5% standard resistor values (see Appendix A), pick values for the three resistors such that the voltage across $$R_1$$ is within 10% of 10 volts as long as the resistors are within tolerance.

## Simulation

48. Verify the currents found in problem 11 via a DC simulation.

49. Verify the currents found in problem 15 via a DC simulation.

50. Verify the currents and voltages found in problem 17 via a DC simulation.

51. Verify the results found in problem 25 via a DC simulation.

52. Verify the results found in problem 27 via a DC simulation.

53. Perform a DC simulation on the design of problem 44 to verify its performance.

54. Perform a DC simulation on the design of problem 45 to verify its performance.

55. Perform a DC simulation on the design of problem 46 to verify its performance.

56. Perform a Monte Carlo or worst-case simulation on the design of problem 47 to verify its performance.

2.3.8: Exercises is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by James M. Fiore.