244 S S P P SERIES-PARALLEL NETWORKS FIG. 7.63 C response to an analysis of the ladder network of Fig. 7.60 without the elements R5 and R6. PROBLEMS SECTION 7.2 Descriptive Examples 1. Which elements of the networks in Fig. 7.64 are in series or parallel? In other words, which elements of the given networks have the same current (series) or voltage (parallel)? Restrict your decision to single elements, and do not include combined elements. R2 R1 R1 R3 E R4 E R4 R2 (a) R3 (b) R4 R5 R1 R2 E R3 E R1 R7 R2 R4 R5 R6 R3 (c) (d) FIG. 7.64 Problem 1. S S P P PROBLEMS 2. Determine RT for the networks of Fig. 7.65. 4 4 4 4 RT 4 4 RT 4 4 (a) (b) 4 4 4 4 4 RT 4 4 RT (c) (d) FIG. 7.65 Problem 2. 3. For the network of Fig. 7.66: a. Does I I3 I6? Explain. b. If I 5 A and I1 2 A, find I2. c. Does I1 I2 I4 I5? Explain. d. If V1 6 V and E 10 V, find V2. e. If R1 3 , R2 2 , R3 4 , and R4 1 , what is RT? f. If the resistors have the values given in part (e) and E 10 V, what is the value of I in amperes? g. Using values given in parts (e) and (f), find the power delivered by the battery E and dissipated by the resistors R1 and R2. + V1 – + V2 – R1 R3 I1 I4 + I I3 I2 I6 I5 E – R2 RT R4 FIG. 7.66 Problem 3. 4. For the network of Fig. 7.67: a. Calculate RT. b. Determine I and I1. c. Find V3. 5. For the network of Fig. 7.68: a. Determine RT. b. Find Is, I1, and I2. c. Calculate Va. I1 Is R1 I1 R3 12 E I E RT 64 V I2 R2 6 FIG. 7.67 Problem 4. 36 V R1 10 R2 15 10 Va + R3 12 V3 – R4 RT FIG. 7.68 Problem 5. 2 245 246 S S P P SERIES-PARALLEL NETWORKS 6. Determine the currents I1 and I2 for the network of Fig. 7.69. 16 + 20 V 5 –7V I2 I1 25 FIG. 7.69 Problem 6. 7. a. Find the magnitude and direction of the currents I, I1, I2, and I3 for the network of Fig. 7.70. b. Indicate their direction on Fig. 7.70. *8. For the network of Fig. 7.71: a. Determine the currents Is, I1, I3, and I4. b. Calculate Va and Vbc. +24 V Va I I1 20 V I1 R1 3 I2 R2 Vb R5 6 R3 6 FIG. 7.72 Problem 9. 20 V R3 Is 9. For the network of Fig. 7.72: a. Determine the current I1. b. Calculate the currents I2 and I3. c. Determine the voltage levels Va and Vb. Va 3 I3 R4 I3 FIG. 7.71 Problem 8. FIG. 7.70 Problem 7. E b 10 I1 I3 R5 R2 R1 10 R3 14 20 c –8 V 4 R1 I4 2 R2 6 R4 I2 3 5 S S P P PROBLEMS 247 10. For the network of Fig. 7.73: a. Find the currents I and I6. b. Find the voltages V1 and V5. c. Find the power delivered to the 6-k resistor. R4 9 k R5 I I6 6 k + E = 28 V V1 R1 – 12 k R2 12 k R3 3 k + V5 – R6 10.4 k FIG. 7.73 Problem 10. *11. For the series-parallel network of Fig. 7.74: a. Find the current I. b. Find the currents I3 and I9. c. Find the current I8. d. Find the voltage Vab. R6 R2 b 5 8 R3 R1 10 6 I3 R7 80 V 6 I R4 = 4 8 R5 Vab a I8 R8 FIG. 7.74 Problem 11. *12. Determine the dc levels for the transistor network of Fig. 7.75 using the fact that VBE 0.7 V, VE 2 V, and IC IE. That is: a. Determine IE and IC. b. Calculate IB. c. Determine VB and VC. d. Find VCE and VBC. VCC = 8 V IC 2.2 k RC 220 k RB VBC– C VC + + VB B IB VCE + VBE – – E VE = 2 V RE 1 k IE FIG. 7.75 Problem 12. R9 2 I9 4 248 S S P P SERIES-PARALLEL NETWORKS VDD = 16 V I1 R1 ID RD 2 M 2.5 k D G VG I2 VGS = –1.75 V IG = 0 A R2 ID = IS + IG VGS – 270 k RS S IS VS 1.5 k *13. The network of Fig. 7.76 is the basic biasing arrangement for the field-effect transistor (FET), a device of increasing importance in electronic design. (Biasing simply means the application of dc levels to establish a particular set of operating conditions.) Even though you may be unfamiliar with the FET, you can perform the following analysis using only the basic laws introduced in this chapter and the information provided on the diagram. a. Determine the voltages VG and VS. b. Find the currents I1, I2, ID, and IS. c. Determine VDS. d. Calculate VDG. FIG. 7.76 Problem 13. *14. For the network of Fig. 7.77: a. Determine RT. b. Calculate Va. c. Find V1. d. Calculate V2. e. Determine I (with direction). 15. For the network of Fig. 7.78: a. Determine the current I. b. Find V. + 400 + V1 = +9 V – 400 Va 220 V2 I – 100 I 32 V E V1 600 + V R1 220 R2 7 R3 8 5 – V2 = –19 V FIG. 7.77 Problem 14. R1 R3 I 4 k E 24 V R2 Vb 1 k R4 2 k R5 Va FIG. 7.78 Problem 15. 1.5 k FIG. 7.79 Problem 16. 0.5 k *16. Determine the current I and the voltages Va, Vb, and Vab for the network of Fig. 7.79. S S P P PROBLEMS 17. For the configuration of Fig. 7.80: a. Find the currents I2, I6, and I8. b. Find the voltages V4 and V8. + V4 – R3 R1 I2 10 10 E 100 V R4 R2 30 I6 R6 6 6 R5 R7 6 3 I8 R8 + 10 V8 – FIG. 7.80 Problem 17. 18. Determine the voltage V and the current I for the network of Fig. 7.81. I 8 6 + 8 8 30 V V – 6 FIG. 7.81 Problem 18. *19. For the network of Fig. 7.82: a. Determine RT by combining resistive elements. b. Find V1 and V4. c. Calculate I3 (with direction). d. Determine Is by finding the current through each element and then applying Kirchhoff’s current law. Then calculate RT from RT E/Is, and compare the answer with the solution of part (a). + V1 – R1 16 + V4 – R2 I3 8 R3 R4 4 32 R5 16 E RT Is 32 V FIG. 7.82 Problem 19. 20. For the network of Fig. 7.83: a. Determine the voltage Vab. (Hint: Just use Kirchhoff’s voltage law.) b. Calculate the current I. + 5 6V – a b 2 3 20 V FIG. 7.83 Problem 20. I 249 250 S S P P SERIES-PARALLEL NETWORKS *21. For the network of Fig. 7.84: a. Determine the current I. b. Calculate the open-circuit voltage V. *22. For the network of Fig. 7.85, find the resistance R3 if the current through it is 2 A. 20 V + R1 8 I V 120 V 2A 18 V – R2 6 3 12 FIG. 7.84 Problem 21. 20 R3 FIG. 7.85 Problem 22. *23. If all the resistors of the cube in Fig. 7.86 are 10 , what is the total resistance? (Hint: Make some basic assumptions about current division through the cube.) *24. Given the voltmeter reading V 27 V in Fig. 7.87: a. Is the network operating properly? b. If not, what could be the cause of the incorrect reading? V 6 k = 27 V 12 k RT 6 k E FIG. 7.86 Problem 23. I R4 R6 3 2 1 V3 R3 – R V5 R5 – 2 5 FIG. 7.88 Problem 25. SECTION 7.3 Ladder Networks + + 4 36 k FIG. 7.87 Problem 24. R1 + 240 V 45 V 6 V7 R7 – 2 I7 25. For the ladder network of Fig. 7.88: a. Find the current I. b. Find the current I7. c. Determine the voltages V3, V5, and V7. d. Calculate the power delivered to R7, and compare it to the power delivered by the 240-V supply. S S P P PROBLEMS 26. For the ladder network of Fig. 7.89: a. Determine RT. b. Calculate I. c. Find I8. R1 R3 R6 4 4 4 I RT R2 2V 2 2 R4 2 R7 R5 R8 1 1 251 I8 FIG. 7.89 Problem 26. 7 *27. Determine the power delivered to the 10- load of Fig. 7.90. E 24 V 2 2 4 12 P 24 10 12 FIG. 7.90 Problem 27. *28. For the multiple ladder configuration of Fig. 7.91: a. Determine I. b. Calculate I4. c. Find I6. d. Find I10. SECTION 7.4 Voltage Divider Supply (Unloaded and Loaded) R10 R8 12 R9 29. Given the voltage divider supply of Fig. 7.92: a. Determine the supply voltage E. b. Find the load resistors RL2 and RL3. c. Determine the voltage divider resistors R1, R2, and R3. 12 R7 3 I E R1 I10 1 R11 3 12 V 2 R3 = 1 R2 6 I4 R4 Is = 72 mA R5 = 6 10 I6 E 40 mA R6 R1 48 V FIG. 7.91 Problem 28. 12 mA R2 RL1 24 V 8 mA R3 2 R12 RL2 RL3 FIG. 7.92 Problem 29. 1.6 k 4 252 S S P P SERIES-PARALLEL NETWORKS *30. Determine the voltage divider supply resistors for the configuration of Fig. 7.93. Also determine the required wattage rating for each resistor, and compare their levels. +120 V R1 10 mA R2 + 20 mA 100 V RL1 – + 40 mA 180 V R3 RL 40 V 2 – + R4 36 V RL3 – 4 mA R5 –60 V FIG. 7.93 Problem 30. SECTION 7.5 Potentiometer Loading 1 k Pot. E 12 V R1 R2 + 10 k 3 V RL – *31. For the system of Fig. 7.94: a. At first exposure, does the design appear to be a good one? b. In the absence of the 10-k load, what are the values of R1 and R2 to establish 3 V across R2? c. Determine the values of R1 and R2 when the load is applied, and compare them to the results of part (b). FIG. 7.94 Problem 31. a 100 Pot. + 1 k Vab E – 40 V 20 b + 10 k Vbc – c *32. For the potentiometer of Fig. 7.95: a. What are the voltages Vab and Vbc with no load applied? b. What are the voltages Vab and Vbc with the indicated loads applied? c. What is the power dissipated by the potentiometer under the loaded conditions of Fig. 7.95? d. What is the power dissipated by the potentiometer with no loads applied? Compare it to the results of part (c). SECTION 7.6 Ammeter, Voltmeter, and Ohmmeter Design FIG. 7.95 Problem 32. 33. A d’Arsonval movement is rated 1 mA, 100 . a. What is the current sensitivity? b. Design a 20-A ammeter using the above movement. Show the circuit and component values. S S P P PROBLEMS 34. Using a 50-mA, 1000- d’Arsonval movement, design a multirange milliammeter having scales of 25 mA, 50 mA, and 100 mA. Show the circuit and component values. 35. A d’Arsonval movement is rated 50 mA, 1000 . a. Design a 15-V dc voltmeter. Show the circuit and component values. b. What is the ohm/volt rating of the voltmeter? 36. Using a 1-mA, 100- d’Arsonval movement, design a multirange voltmeter having scales of 5 V, 50 V, and 500 V. Show the circuit and component values. 37. A digital meter has an internal resistance of 10 M on its 0.5-V range. If you had to build a voltmeter with a d’Arsonval movement, what current sensitivity would you need if the meter were to have the same internal resistance on the same voltage scale? *38. a. Design a series ohmmeter using a 100-mA, 1000- movement; a zero-adjust with a maximum value of 2 k; a battery of 3 V; and a series resistor whose value is to be determined. b. Find the resistance required for full-scale, 3/4-scale, 1/2-scale, and 1/4-scale deflection. c. Using the results of part (b), draw the scale to be used with the ohmmeter. 39. Describe the basic construction and operation of the megohmmeter. *40. Determine the reading of the ohmmeter for the configuration of Fig. 7.96. 18 18 18 R1 R2 R3 12 R1 R2 12 12 R3 (b) (a) FIG. 7.96 Problem 40. SECTION 7.9 Computer Analysis PSpice or Electronics Workbench 41. Using schematics, determine V1, V3, Vab, and Is for the network of Fig. 7.16. 42. Using schematics, determine Is, I5, and V7 for the network of Fig. 7.22. 253 254 SERIES-PARALLEL NETWORKS S S P P Programming Language (C, QBASIC, Pascal, etc.) 43. Write a program that will find the complete solution for the network of Fig. 7.6. That is, given all the parameters of the network, calculate the current, voltage, and power to each element. 44. Write a program to find all the quantities of Example 7.8 given the network parameters. GLOSSARY d’Arsonval movement An iron-core coil mounted on bearings between a permanent magnet. A pointer connected to the movable core indicates the strength of the current passing through the coil. Ladder network A network that consists of a cascaded set of series-parallel combinations and has the appearance of a ladder. Megohmmeter An instrument for measuring very high resistance levels, such as in the megohm range. Series ohmmeter A resistance-measuring instrument in which the movement is placed in series with the unknown resistance. Series-parallel network A network consisting of a combination of both series and parallel branches. Transistor A three-terminal semiconductor electronic device that can be used for amplification and switching purposes.
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