1. Electromagnetic Oscillations and Alternating Current
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)
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2. LR Circuit i
Steady Source
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3. Max Current Rate of increase = max emf VR=iR ~current
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4. Solve the loop equation.
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5. Time Dependent Result:
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6. We also showed that
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7. At t=0, the charged capacitor is now connected to the inductor
At t=0, the charged capacitor is now connected to the inductor. What would you expect to happen??
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8. L C
(31 - 2)
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9. L C
(31 - 3)
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10. L C
(31 - 4)
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11. The Graph of that LC (no emf) circuit ..
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12. Induction - Spring 2006

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

15. LC Circuit
High
Q/C
Low
Low
High
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16. The Math Solution (R=0):
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17. 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.
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18. Variable Emf Applied
emf DC
Sinusoidal
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19. Sinusoidal Stuff
“Angle”
Phase Angle
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20. Same Frequency
with
PHASE SHIFT f
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21. Different Frequencies
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22. Induction - Spring 2006
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23. Induction - Spring 2006
(31 - 7)

24. Note – Power is delivered to our homes as an oscillating source (AC)
This makes AC Important!
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25. 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
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26. The Real World
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27. A
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28. Induction - Spring 2006

29. The Flux:
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30. Source Voltage:
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31. ( )
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32. ( )
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33. O
( )
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34. ( )
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35. O
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36. ( )
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37. SUMMARY Circuit element Average Power Reactance Phase of current
Voltage 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
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38. ( )
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39. O A B
( )
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40. O A B
( )
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41. ( )
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42. ( )
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43. ( )
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44. ( )
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45. Induction - Spring 2006
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46. Induction - Spring 2006
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