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
Inductance Chapter 30 November 6, 2012 November 6, 2012 Physics 208 2
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
A new circuit element based on Faraday s Law November 6, 2012 Physics 208 4
A new circuit element based on Faraday s Law November 6, 2012 Physics 208 5
Two kinds of inductance. Circuit 1 Circuit 2 November 6, 2012 Physics 208 6
The EMF induced in circuit 2 due to circuit 1 November 6, 2012 Physics 208 7
Units of Inductance. November 6, 2012 Physics 208 8
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
Now for the EMF induced in circuit 1 due to circuit 2 November 6, 2012 Physics 208 10
The symmetry between the two circuits. November 6, 2012 Physics 208 11
Another example of Mutual Inductance. November 6, 2012 Physics 208 12
Finding the Mutual Inductance.. November 6, 2012 Physics 208 13
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 208 14
Let s try another example with a more complicated field November 6, 2012 Physics 208 15
Finding the flux inside the toroid November 6, 2012 Physics 208 16
Doing the integral over the flux B-field for a Toroid November 6, 2012 Physics 208 17
Inductive effects in a single loop November 6, 2012 Physics 208 18
Defining self-inductance November 6, 2012 Physics 208 19
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Doing the calculation November 6, 2012 Physics 208 21
Energy stored in B-fields November 6, 2012 Physics 208 22
Work done in establishing the B-field in the inductor November 6, 2012 Physics 208 23
Work done = Energy Stored November 6, 2012 Physics 208 24
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. ( ) ( ) 2 2 0 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 2 2 0 2 2 2 1 2 1 I L R N LI U T = = π μ November 6, 2012 Physics 208 25
The relationship U = between the 2 energy stored and the B-field 2 2 2 1 NT μ0 I LπR 2 L μ0 1 2 2 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 2 0 1 2 0 E ( B ) energy density in a magnetic field ( ) energy density in an electric field November 6, 2012 Physics 208 26
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Novembe6 1, 2012 Physics 208 37
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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 208 43
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 208 44
Chapter 27 November 6, 2012 Physics 208 45
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Chapter 28 November 6, 2012 Physics 208 47
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Chapter 29 November 6, 2012 Physics 208 50
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Chapter 30 November 6, 2012 Physics 208 52
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