2. Induction - Spring 2006 1 What is going on? There are only 2 more weeks after spring break. Spring break is next week (3/31-4/4), have a good one and be safe. Projects are due the last class before the final week Final exam.

3. Induction - Spring 2006 2 Chapter 31 Electromagnetic Oscillations and Alternating Current In this chapter we will cover the following topics: -Electromagnetic oscillations in an LC circuit -Alternating current (AC) circuits with capacitors -Resonance in RCL circuits -Power in AC-circuits -Transformers, AC power transmission (31 - 1)

4. Induction - Spring 2006 3 LR Circuit i Steady Source

5. Induction - Spring 2006 4 Max Current Rate of increase = max emf V R =iR ~current

6. Induction - Spring 2006 5 Solve the loop equation.

7. Induction - Spring 2006 6 Time Dependent Result:

8. Induction - Spring 2006 7 We also showed that

9. Induction - Spring 2006 8 At t=0, the charged capacitor is now connected to the inductor. What would you expect to happen??

10. Induction - Spring 2006 9 L C (31 - 2)

11. Induction - Spring 2006 10 L C (31 - 3)

12. Induction - Spring 2006 11 L C (31 - 4)

13. Induction - Spring 2006 12 The Graph of that LC (no emf) circuit..

14. Induction - Spring 2006 13

15. Induction - Spring 2006 14 Mass on a Spring Result Energy will swap back and forth. Add friction  Oscillation will slow down  Not a perfect analogy

16. Induction - Spring 2006 15

17. Induction - Spring 2006 16 LC Circuit High Q/C Low High

18. Induction - Spring 2006 17 The Math Solution (R=0):

19. Induction - Spring 2006 18 New Feature of Circuits with L and C These circuits produce oscillations in the currents and voltages Without a resistance, the oscillations would continue in an un-driven circuit. With resistance, the current would eventually die out.

20. Induction - Spring 2006 19 Variable Emf Applied emf Sinusoidal DC

21. Induction - Spring 2006 20 Sinusoidal Stuff “Angle” Phase Angle

22. Induction - Spring 2006 21 Same Frequency with PHASE SHIFT 

23. Induction - Spring 2006 22 Different Frequencies

24. Induction - Spring 2006 23 (31 - 6)

25. Induction - Spring 2006 24 (31 - 7)

26. Induction - Spring 2006 25 Note – Power is delivered to our homes as an oscillating source (AC)

27. Induction - Spring 2006 26 Producing AC Generator x x x x x x x x x x x x x x x x x x x x x x x

28. Induction - Spring 2006 27 The Real World

29. Induction - Spring 2006 28 A

30. Induction - Spring 2006 29

31. Induction - Spring 2006 30 The Flux:

32. Induction - Spring 2006 31 Source Voltage:

33. Induction - Spring 2006 32 (31 - 10)

34. Induction - Spring 2006 33 (31 - 12)

35. Induction - Spring 2006 34 O (31 - 13)

36. Induction - Spring 2006 35 (31 - 14)

37. Induction - Spring 2006 36 O (31 - 15)

38. Induction - Spring 2006 37 (31 - 16)

39. Induction - Spring 2006 38 Circuit element Average Power Reactanc e Phase of currentVoltage amplitude Resistor R Current is in phase with the voltage Capacitor C Current leads voltage by a quarter of a period Inductor L Current lags behind voltage by a quarter of a period SUMMARY (31 - 17)

40. Induction - Spring 2006 39 (31 - 18)

41. Induction - Spring 2006 40 O A B (31 - 19)

42. Induction - Spring 2006 41 O A B (31 - 20)

43. Induction - Spring 2006 42 (31 - 21)

44. Induction - Spring 2006 43 (31 - 22)

45. Induction - Spring 2006 44 (31 - 23)

46. Induction - Spring 2006 45 (31 - 25)

47. Induction - Spring 2006 46 (31 - 26)

48. Induction - Spring 2006 47 (31 - 27)