1. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Chapter 36. AC Circuits Today, a “grid” of AC electrical distribution systems spans the United States and other countries. Any device that plugs into an electric outlet uses an AC circuit. In this chapter, you will learn some of the basic techniques for analyzing AC circuits. Chapter Goal: To understand and apply basic techniques of AC circuit analysis.

2. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Topics: AC Sources and Phasors Capacitor Circuits RC Filter Circuits Inductor Circuits The Series RLC Circuit Power in AC Circuits Chapter 36. AC Circuits

3. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Chapter 36. Reading Quizzes

4. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley The analysis of AC circuits uses a rotating vector called a A.rotor. B.wiggler. C.phasor. D.motor. E.variator.

5. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley The analysis of AC circuits uses a rotating vector called a A.rotor. B.wiggler. C.phasor. D.motor. E.variator.

6. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley In a capacitor, the peak current and peak voltage are related by the A.capacitive resistance. B.capacitive reactance. C.capacitive impedance. D.capacitive inductance.

7. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley In a capacitor, the peak current and peak voltage are related by the A.capacitive resistance. B.capacitive reactance. C.capacitive impedance. D.capacitive inductance.

8. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley In a series RLC circuit, what quantity is maximum at resonance? A.The voltage B.The current C.The impedance D.The phase

9. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley In a series RLC circuit, what quantity is maximum at resonance? A.The voltage B.The current C.The impedance D.The phase

10. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Chapter 36. Basic Content and Examples

11. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley AC Sources and Phasors

12. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley AC Sources and Phasors

13. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley AC Circuits In an AC resistor circuit, Ohm’s law applies to both the instantaneous and peak currents and voltages.

14. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley AC Circuits The resistor voltage v R is given by where V R is the peak or maximum voltage. The current through the resistor is where I R = V R /R is the peak current.

15. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.1 Finding resistor voltages QUESTION:

16. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.1 Finding resistor voltages

17. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.1 Finding resistor voltages

18. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.1 Finding resistor voltages

19. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.1 Finding resistor voltages

20. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley

21. Capacitor Circuits The instantaneous voltage across a single capacitor in a basic capacitor circuit is equal to the instantaneous emf: Where V C is the maximum voltage across the capacitor, also equal to the maximum emf. The instantaneous current in the circuit is The AC current to and from a capacitor leads the capacitor voltage by π/2 rad, or 90°.

22. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Capacitive Reactance The capacitive reactance X C is defined as The units of reactance, like those of resistance, are ohms. Reactance relates the peak voltage V C and current I C : NOTE: Reactance differs from resistance in that it does not relate the instantaneous capacitor voltage and current because they are out of phase. That is, v C ≠ i C X C.

23. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.3 Capacitor current QUESTION:

24. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.3 Capacitor current

25. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.3 Capacitor current

26. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.3 Capacitor current

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28. Inductor Circuits The instantaneous voltage across a single inductor in a basic inductive circuit is equal to the instantaneous emf: Where V L is the maximum voltage across the inductor, also equal to the maximum emf. The instantaneous inductor current is The AC current through an inductor lags the inductor voltage by π/2 rad, or 90°.

29. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Inductive Reactance The inductive reactance X L is defined as Reactance relates the peak voltage V L and current I L : NOTE: Reactance differs from resistance in that it does not relate the instantaneous inductor voltage and current because they are out of phase. That is, v L ≠ i L X L.

30. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley

31. EXAMPLE 36.5 Current and voltage of an inductor QUESTION:

32. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.5 Current and voltage of an inductor

33. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.5 Current and voltage of an inductor

34. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.5 Current and voltage of an inductor

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36. The Series RLC Circuit The impedance Z of a series RLC circuit is defined as Impedance, like resistance and reactance, is measured in ohms. The circuit’s peak current is related to the source emf and the circuit impedance by Z is at a minimum, making I a maximum, when X L = X C, at the circuit’s resonance frequency:

37. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley

38. Power in AC Circuits The root-mean-square current I rms is related to the peak current I R by Similarly, the root-mean-square voltage and emf are The average power supplied by the emf is

39. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.7 Lighting a bulb QUESTION:

40. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.7 Lighting a bulb

41. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.7 Lighting a bulb

42. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.7 Lighting a bulb

43. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.7 Lighting a bulb

44. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Chapter 36. Summary Slides

45. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Important Concepts

46. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Important Concepts

47. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Key Skills

48. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Key Skills

49. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Applications

50. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Applications

51. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Chapter 36. Clicker Questions

52. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley The magnitude of the instantaneous value of the emf represented by this phasor is A.constant. B.increasing. C.decreasing. D.It’s not possible to tell without knowing t.

53. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley A.constant. B.increasing. C.decreasing. D.It’s not possible to tell without knowing t. The magnitude of the instantaneous value of the emf represented by this phasor is

54. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley The resistor whose voltage and current phasors are shown here has resistance R A.> 1 Ω. B.< 1 Ω. C.It’s not possible to tell.

55. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley A.> 1 Ω. B.< 1 Ω. C.It’s not possible to tell. The resistor whose voltage and current phasors are shown here has resistance R

56. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley What is the capacitive reactance of “no capacitor,” just a continuous wire? A.0 B.∞ C.Undefined

57. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley A.0 B.∞ C.Undefined What is the capacitive reactance of “no capacitor,” just a continuous wire?

58. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Rank in order, from largest to smallest, the cross-over frequencies of these four circuits.

59. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Rank in order, from largest to smallest, the cross-over frequencies of these four circuits.

60. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley A series RLC circuit has V C = 5.0 V, V R = 7.0 V, and V L = 9.0 V. Is the frequency above, below or equal to the resonance frequency? A.Above the resonance frequency B.Below the resonance frequency C.Equal to the resonance frequency

61. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley A.Above the resonance frequency B.Below the resonance frequency C.Equal to the resonance frequency A series RLC circuit has V C = 5.0 V, V R = 7.0 V, and V L = 9.0 V. Is the frequency above, below or equal to the resonance frequency?

62. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley The emf and the current in a series RLC circuit oscillate as shown. Which of the following would increase the rate at which energy is supplied to the circuit? A.Decrease ε 0 B.Increase C C.Increase L D.Decrease L

63. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley A.Decrease ε 0 B.Increase C C.Increase L D.Decrease L The emf and the current in a series RLC circuit oscillate as shown. Which of the following would increase the rate at which energy is supplied to the circuit?