1. Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] Introductory Circuit Analysis, 12/e Boylestad Chapter 7 Series-Parallel Circuits

2. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] OBJECTIVES Learn about the unique characteristics of series-parallel configurations and how to solve for the voltage, current, or power to any individual element or combination of elements. Become familiar with the voltage divider supply and the conditions needed to use it effectively. Learn how to use a potentiometer to control the voltage across any given load.

3. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] INTRODUCTION A series-parallel configuration is one that is formed by a combination of series and parallel elements. A complex configuration is one in which none of the elements are in series or parallel.

4. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] SERIES-PARALLEL NETWORKS FIG. 7.1 Series-parallel dc network.

5. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] REDUCE AND RETURN APPROACH FIG. 7.2 Introducing the reduce and return approach.

6. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] REDUCE AND RETURN APPROACH FIG. 7.3 Series-parallel network for Example 7.1. FIG. 7.4 Substituting the parallel equivalent resistance for resistors R 2 and R 3 in Fig. 7.3.

7. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] REDUCE AND RETURN APPROACH FIG. 7.5 Series-parallel network for Example 7.2. FIG. 7.6 Schematic representation of the network in Fig. 7.5 after substituting the equivalent resistance R for the parallel combination of R 2 and R 3.

8. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] REDUCE AND RETURN APPROACH FIG. 7.7 Inserting an ammeter and a voltmeter to measure I 4 and V 2, respectively.

9. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] BLOCK DIAGRAM APPROACH Once the grouping of elements reveals the most direct approach, you can examine the impact of the individual components in each group. This grouping of elements is called the block diagram approach

10. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] BLOCK DIAGRAM APPROACH FIG. 7.8 Introducing the block diagram approach. FIG. 7.9 Block diagram format of Fig. 7.3.

11. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] BLOCK DIAGRAM APPROACH FIG. 7.10 Example 7.3. FIG. 7.11 Reduced equivalent of Fig. 7.10.

12. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] BLOCK DIAGRAM APPROACH FIG. 7.12 Example 7.4.

13. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] BLOCK DIAGRAM APPROACH FIG. 7.13 Reduced equivalent of Fig. 7.12.

14. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] DESCRIPTIVE EXAMPLES FIG. 7.14 Example 7.5. FIG. 7.15 Block diagram of Fig. 7.14.

15. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] DESCRIPTIVE EXAMPLES FIG. 7.16 Alternative block diagram for the first parallel branch in Fig. 7.14.

16. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] DESCRIPTIVE EXAMPLES FIG. 7.17 Example 7.6.

17. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] DESCRIPTIVE EXAMPLES FIG. 7.18 Block diagram for Fig. 7.17. FIG. 7.19 Reduced form of Fig. 7.17.

18. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] DESCRIPTIVE EXAMPLES FIG. 7.20 Example 7.7.

19. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] DESCRIPTIVE EXAMPLES FIG. 7.21 Network in Fig. 7.20 redrawn.

20. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] DESCRIPTIVE EXAMPLES FIG. 7.22 Example 7.8.

21. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] DESCRIPTIVE EXAMPLES FIG. 7.23 Network in Fig. 7.22 redrawn.

22. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] DESCRIPTIVE EXAMPLES FIG. 7.24 Example 7.9. FIG. 7.25 Determining V C for the network in Fig. 7.24.

23. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] DESCRIPTIVE EXAMPLES FIG. 7.26 Example 7.10.

24. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] DESCRIPTIVE EXAMPLES FIG. 7.27 Network in Fig. 7.26 redrawn.

25. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] DESCRIPTIVE EXAMPLES FIG. 7.28 An alternative approach to Example 7.10.

26. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] DESCRIPTIVE EXAMPLES FIG. 7.29 Example 7.11. FIG. 7.30 Network in Fig. 7.29 redrawn to better define a path toward the desired unknowns.

27. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] DESCRIPTIVE EXAMPLES FIG. 7.31 Complex network for Example 7.11.

28. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] LADDER NETWORKS A three-section ladder network appears in Fig. 7.32. The reason for the terminology is quite obvious for the repetitive structure. Basically two approaches are used to solve networks of this type. FIG. 7.32 Ladder network.

29. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] LADDER NETWORKS FIG. 7.33 Working back to the source to determine R T for the network in Fig. 7.32.

30. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] LADDER NETWORKS FIG. 7.34 Calculating R T and I s. FIG. 7.35 Working back toward I 6.

31. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] LADDER NETWORKS FIG. 7.36 Calculating I 6.

32. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] LADDER NETWORKS FIG. 7.37 An alternative approach for ladder networks.

33. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] VOLTAGE DIVIDER SUPPLY (UNLOADED AND LOADED) When the term loaded is used to describe voltage divider supply, it refers to the application of an element, network, or system to a supply that draws current from the supply. –In other words, the loading down of a system is the process of introducing elements that will draw current from the system. The heavier the current, the greater is the loading effect.

34. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] VOLTAGE DIVIDER SUPPLY (UNLOADED AND LOADED) No-Load Conditions Through a voltage divider network such as that in Fig. 7.38, a number of different terminal voltages can be made available from a single supply. FIG.7.38 Voltage divider supply.

35. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] VOLTAGE DIVIDER SUPPLY (UNLOADED AND LOADED) No-Load Conditions In general, for a voltage divider supply to be effective, the applied resistive loads should be significantly larger than the resistors appearing in the voltage divider network.

36. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] VOLTAGE DIVIDER SUPPLY (UNLOADED AND LOADED) L oaded Conditions FIG. 7.39 Voltage divider supply with loads equal to the average value of the resistive elements that make up the supply.

37. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] VOLTAGE DIVIDER SUPPLY (UNLOADED AND LOADED) L oaded Conditions FIG. 7.40 Voltage divider supply for Example 7.12.

38. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] POTENTIOMETER LOADING For the unloaded potentiometer in Fig. 7.41, the output voltage is determined by the voltage divider rule, with R T in the figure representing the total resistance of the potentiometer. FIG. 7.41 Unloaded potentiometer.

39. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] POTENTIOMETER LOADING FIG. 7.42 Loaded potentiometer.

40. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] POTENTIOMETER LOADING In general, when hooking up a load to a potentiometer, be sure that the load resistance far exceeds the maximum terminal resistance of the potentiometer if good control of the output voltage is desired.

41. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] POTENTIOMETER LOADING FIG. 7.43 Loaded potentiometer with R L << R T. FIG. 7.44 Loaded potentiometer with RL >> RT.

42. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] POTENTIOMETER LOADING FIG. 7.45 Example 7.13.

43. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] AMMETER, VOLTMETER, AND OHMMETER DESIGN FIG. 7.46 Iron-vane movement.

44. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] AMMETER, VOLTMETER, AND OHMMETER DESIGN FIG. 7.47 Iron-vane movement; (a) photo, (b) symbol and ratings. FIG. 7.48 Basic ammeter.

45. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] AMMETER, VOLTMETER, AND OHMMETER DESIGN FIG. 7.49 Multirange ammeter.

46. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] AMMETER, VOLTMETER, AND OHMMETER DESIGN FIG. 7.50 Basic voltmeter.

47. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] AMMETER, VOLTMETER, AND OHMMETER DESIGN The Voltmeter A variation in the additional circuitry permits the use of the iron-vane movement in the design of a voltmeter. The 1 mA, 43 Ω movement can also be rated as a 43 mV (1 mA x 43 Ω), 43 movement, indicating that the maximum voltage that the movement can measure independently is 43 mV. The millivolt rating is sometimes referred to as the voltage sensitivity (VS).

48. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] AMMETER, VOLTMETER, AND OHMMETER DESIGN The Voltmeter FIG. 7.51 Multirange voltmeter.

49. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] AMMETER, VOLTMETER, AND OHMMETER DESIGN The Ohmmeter In general, ohmmeters are designed to measure resistance in the low, middle, or high range. The most common is the series ohmmeter, designed to read resistance levels in the midrange.

50. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] AMMETER, VOLTMETER, AND OHMMETER DESIGN The Ohmmeter FIG. 7.52 Series ohmmeter.

51. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] AMMETER, VOLTMETER, AND OHMMETER DESIGN The Ohmmeter FIG. 7.53 Nanovoltmeter.

52. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] AMMETER, VOLTMETER, AND OHMMETER DESIGN The Ohmmeter The megohmmeter (often called a megger) is an instrument for measuring very high resistance values. Its primary function is to test the insulation found in power transmission systems, electrical machinery, transformers, and so on. To measure the high-resistance values, a high dc voltage is established by a hand- driven generator.

53. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] AMMETER, VOLTMETER, AND OHMMETER DESIGN The Ohmmeter FIG. 7.54 Megohmmeter.

54. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] APPLICATIONS Boosting a Car Battery FIG. 7.55 Boosting a car battery.

55. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] APPLICATIONS Boosting a Car Battery FIG. 7.56 Current levels at starting.

56. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] APPLICATIONS Boosting a Car Battery FIG. 7.57 Current levels if the booster battery is improperly connected.

57. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] APPLICATIONS Electronic Circuits The operation of most electronic systems requires a distribution of dc voltages throughout the design. Although a full explanation of why the dc level is required (since it is an ac signal to be amplified) will have to wait for the introductory courses in electronic circuits, the dc analysis will proceed in much the same manner as described in this chapter.

58. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] APPLICATIONS Electronic Circuits FIG. 7.58 The dc bias levels of a transistor amplifier.

59. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] COMPUTER ANALYSIS PSpice FIG. 7.59 Using PSpice to verify the results of Example 7.12.