1. 1 ELECTRICAL TECHNOLOGY EET 103/4  Explain and analyze series and parallel circuits  Explain, derive and analyze Ohm’s Law, Kirchhoff Current Law, Kirchhoff Voltage Law, Source Transformation, Thevenin theorem.

2. 2 (CHAPTER 7) SERIES-PARALLEL CIRCUIT

3. 3 7.1 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. 4 7.2 Series–parallel Networks  General approach to circuit analysis:  Study the problem in total and make a brief mental sketch of the overall approach you plan to use.  Examine each region of the network independently before tying them together in series-parallel combinations.  Redraw the network as often as possible with reduced branches and undisturbed unknown quantities to maintain clarity.

5. 5  When you have a solution, check to see that it is reasonable by considering the magnitudes of the energy source and the elements in the network. If it does not seem reasonable, either solve using another approach or check over your work very carefully 7.2 Series–parallel Networks

6. 6 7.3 Reduce and Return Approach  Reduce:  Reduce the circuit to its simplest form across the source and then determine the source current (I s ).  Return:  Using the resulting source current (I s ) to work back to the desired unknown.

7. 7 7.3 Reduce and Return Approach

8. 8

9. 9 Example 7.1 Find I 3 :

10. 10 7.3 Reduce and Return Approach Example 7.1 – solution

11. 11 7.3 Reduce and Return Approach Example 7.1 – solution (cont’d)

12. 12 7.3 Reduce and Return Approach Example 7.1 – solution (cont’d)

13. 13 7.3 Reduce and Return Approach Example 7.2 (a) Determine I 4, I s and V 2. (b) Insert the meters to measure I s and V 2.

14. 14 7.3 Reduce and Return Approach Example 7.2 – solution (a)

15. 15 7.3 Reduce and Return Approach Example 7.2 – solution (cont’d)

16. 16 7.3 Reduce and Return Approach Example 7.2 – solution (cont’d)

17. 17 7.3 Reduce and Return Approach Example 7.2 – solution (cont’d)

18. 18 7.3 Reduce and Return Approach Example 7.2 – solution (cont’d)

19. 19 (b) 7.3 Reduce and Return Approach Example 7.2 – solution (cont’d)

20. 20 7.4 Block Diagram Approach  Network is broken down into combinations of elements.  Initially, there will be some concern about identifying series and parallel elements, but that will come with practice.  In reverse, the block diagram approach can be used effectively to reduce the apparent complexity of a system by identifying the major series and parallel components of the network.

21. 21 7.4 Block Diagram Approach Determine all the currents and voltages: Example 7.3

22. 22 7.4 Block Diagram Approach Example 7.3 – solution Block A Block B

23. 23 7.4 Block Diagram Approach Example 7.3 – solution (cont’d) Block C

24. 24 7.4 Block Diagram Approach Example 7.3 – solution (cont’d)

25. 25 7.4 Block Diagram Approach Example 7.3 – solution (cont’d)

26. 26 7.4 Block Diagram Approach Example 7.3 – solution (cont’d)

27. 27 7.4 Block Diagram Approach Example 7.3 – solution (cont’d) = 2 A = 1 A I2I2 I3I3 I s = I A = I 1 = 2 A I B = 1 A I C = 1 A I 2 = 0.5 A I 3 = 0.5 A I 4 = I C = 1 A I 5 = I C = 1 A

28. 28 7.4 Block Diagram Approach Example 7.3 – solution (cont’d)

29. 29 7.4 Block Diagram Approach Example 7.4 Determine all the currents and voltages:

30. 30 7.4 Block Diagram Approach Example 7.4 – solution

31. 31 7.4 Block Diagram Approach Example 7.4 – solution (cont’d) Redraw the network;

32. 32 7.4 Block Diagram Approach Example 7.4 – solution (cont’d) (Current divider rule)

33. 33 7.4 Block Diagram Approach Example 7.4 – solution (cont’d) (Kirchhoff’s current law) (Ohm’s law)

34. 34 7.4 Block Diagram Approach Example 7.4 – solution (cont’d) (Ohm’s law)

35. 35 7.4 Block Diagram Approach Example 7.4 – solution (cont’d)

36. 36 7.4 Block Diagram Approach Example 7.4 – solution (cont’d)

37. 37 7.4 Block Diagram Approach Example 7.7 Find V 1, V 3, V ab and I s :

38. 38 7.4 Block Diagram Approach Example 7.7 – solution Redraw the circuit: Net supply voltage;

39. 39 7.4 Block Diagram Approach Example 7.7 – solution (cont’d)

40. 40 7.4 Block Diagram Approach Example 7.7 – solution (cont’d)

41. 41 7.4 Block Diagram Approach Example 7.7 – solution (cont’d)

42. 42 7.4 Block Diagram Approach Example 7.8 Find V 1, V 2 and I :

43. 43 7.4 Block Diagram Approach Example 7.8 – solution Redraw the circuit: (Note the currents)

44. 44 7.4 Block Diagram Approach Example 7.8 – solution (cont’d)

45. 45 7.4 Block Diagram Approach Example 7.8 – solution (cont’d)

46. 46 7.4 Block Diagram Approach Example 7.8 – solution (cont’d)

47. 47 7.4 Block Diagram Approach Example 7.11 (a) Determine; (b) Insert voltmeters and ammeter to measure and

48. 48 7.4 Block Diagram Approach Example 7.11 – solution Redraw the circuit: (i)

49. 49 7.4 Block Diagram Approach Example 7.11 – solution (cont’d) (ii)

50. 50 7.4 Block Diagram Approach Example 7.11 – solution (cont’d) (iii) (iv)

51. 51 7.4 Block Diagram Approach Example 7.11 – solution (cont’d) (b)