Exam 3 Review Session

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1 Exam 3 Review Session I will hold a review for Exam 3 which covers Chapters 27, 28, 29 and 30, on Wednesday November 7 th at 7:15pm in MPHY 205. Exam 3 will be given in class on Thursday, November 8 th. November 6, 2012 Physics 208 1

2 Inductance Chapter 30 November 6, 2012 November 6, 2012 Physics 208 2

3 Learning goals for Chapter on Inductance How a time varying current in one coil can induce an EMF in a second coil. How to relate the induced EMF in a circuit to the rate of change of the current in that circuit. How to calculate the energy stored in a magnetic field. How to analyze circuits that include both a resistor and an inductor. Why electrical oscillations occur in circuits that include both an inductor and a capacitor. Why oscillations decay in circuits with an inductor, resistor and capacitor. November 6, 2012 Physics 208 3

4 A new circuit element based on Faraday s Law November 6, 2012 Physics 208 4

5 A new circuit element based on Faraday s Law November 6, 2012 Physics 208 5

6 Two kinds of inductance. Circuit 1 Circuit 2 November 6, 2012 Physics 208 6

7 The EMF induced in circuit 2 due to circuit 1 November 6, 2012 Physics 208 7

8 Units of Inductance. November 6, 2012 Physics 208 8

9 Example. Suppose we see an EMF of 5.0 volts in circuit 2 due to a changing current in circuit 1. Suppose the current in circuit 1 is changing at 4.0 Amps/sec. What is the Mutual inductance of these circuits?? M = EMF 2 / (di 1 /dt) November 6, 2012 Physics 208 9

10 Now for the EMF induced in circuit 1 due to circuit 2 November 6, 2012 Physics

11 The symmetry between the two circuits. November 6, 2012 Physics

12 Another example of Mutual Inductance. November 6, 2012 Physics

13 Finding the Mutual Inductance.. November 6, 2012 Physics

14 Filling some numbers to get a feeling for the size of this effect NOTE: Typical values of inductances range from a few Henries down to microhenries.. November 6, 2012 Physics

15 Let s try another example with a more complicated field November 6, 2012 Physics

16 Finding the flux inside the toroid November 6, 2012 Physics

17 Doing the integral over the flux B-field for a Toroid November 6, 2012 Physics

18 Inductive effects in a single loop November 6, 2012 Physics

19 Defining self-inductance November 6, 2012 Physics

20 November 6, 2012 Physics

21 Doing the calculation November 6, 2012 Physics

22 Energy stored in B-fields November 6, 2012 Physics

23 Work done in establishing the B-field in the inductor November 6, 2012 Physics

24 Work done = Energy Stored November 6, 2012 Physics

25 Finding the energy stored in a Solenoid using this relationship 0 field solenoid B - N L N I B T = μ Solenoid using this relationship. ( ) ( ) R N I N R L N I da B T T loop one = = Φ π μ r r Can also use this relationship to find the Self-Inductance when you know ( ) 2 0 I R L N I N I N L T T loop one T = Φ = π μ y the energy stored I L R N LI U T = = π μ November 6, 2012 Physics

26 The relationship U = between the 2 energy stored and the B-field NT μ0 I LπR 2 L μ B LπR 2 μ ( )( ) in the system. U = 0 2 Note: similarities between the energy density stored in Electric and magnetic fields!! u u B field E field = = 1 2 2μ ε E ( B ) energy density in a magnetic field ( ) energy density in an electric field November 6, 2012 Physics

27 November 6, 2012 Physics

28 November 6, 2012 Physics

29 November 6, 2012 Physics

30 November 6, 2012 Physics

31 November 6, 2012 Physics

32 November 6, 2012 Physics

33 November 6, 2012 Physics

34 November 6, 2012 Physics

35 November 6, 2012 Physics

36 November 6, 2012 Physics

37 Novembe6 1, 2012 Physics

38 November 6, 2012 Physics

39 November 6, 2012 Physics

40 November 6, 2012 Physics

41 November 6, 2012 Physics

42 November 6, 2012 Physics

43 Transformers.. Voltage transfer based on Faraday s Law Because of the properties of the transformer iron, the magnetic field reside inside the iron and is nearly uniform throughout the iron. November 6, 2012 Physics

44 in Φ = Φ out = N in N Φ out 1turn Φ 1turn in dφ dφ1 turn EMFin = = Nin dt dt out d Φ d Φ1 turn EMFout = = Nout dt dt since the flux through a single turn is the same for the input side and the output side then, EMF in EMF out = N N in out November 6, 2012 Physics

45 Chapter 27 November 6, 2012 Physics

46 November 6, 2012 Physics

47 Chapter 28 November 6, 2012 Physics

48 November 6, 2012 Physics

49 November 6, 2012 Physics

50 Chapter 29 November 6, 2012 Physics

51 November 6, 2012 Physics

52 Chapter 30 November 6, 2012 Physics

53 November 6, 2012 Physics

54 November 6, 2012 Physics

PHYS 1441 Section 001 Lecture #22 Wednesday, Nov. 29, 2017

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