Phys2212_35.1+to+35.5+and+33.9

Phys2212_35.1 to 35. - Physics 2212 Electricity and Magnetism Lecture 24(Knight 33.9 34.1-5 LC and AC Circuits LC Circuits A charged capacitor

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Physics 2212 Electricity and Magnetism Lecture 24 (Knight: 33.9, 34.1-5) LC and AC Circuits
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March 7, 2007 Physics 2212 - Lecture 23 LC Circuits A charged capacitor bears a certain resemblance to a stretched spring (remember the rubber diaphragm), storing energy even when the charge is not moving. An inductor similarly resembles a moving mass (remember the flywheel), storing energy only when charge is in motion. We know that a mass and spring can make an oscillator. What about a capacitor and inductor. Consider the circuit shown in the diagram. What happens when the switch is closed? The capacitor discharges by creating a current in the inductor. But where does the energy go that had been stored in the inductor? There are no dissipative elements in the system. Therefore, when the charge of the capacitor goes to zero, all of its previous energy must reside in the inductor. The current in the inductor falls while charging the capacitor in the opposite direction. And so on …
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March 7, 2007 Physics 2212 - Lecture 23 The Oscillation Cycle
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March 7, 2007 Physics 2212 - Lecture 23 LC circuits (2) Q L dI dt + C 1 = 0 d 2 Q dt 2 Q + LC 1 = 0 Q = α Sin( ϖ t + φ ) 1 L C ϖ 2 =
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March 7, 2007 Physics 2212 - Lecture 23 Example : An AM Radio Oscillator You have a 10mH inductor. What capacitor should you use with it to make an oscillator with a frequency of 920 kHz? (This frequency is near the center of the AM radio band. 5 -1 6 -1 2 2 (9.20 10 s ) 5.78 10 s f ϖ π = = × = × 11 2 6 -1 2 2 1 1 3.0 10 F 30 pF (5.78 10 s ) (1.0 10 H) C L - - = = = × = × ×
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March 7, 2007 Physics 2212 - Lecture 23 Plumber’s LC Analogy P 1 Valve = Switch Rubber Diaphragm = Capacitor Flywheel = Inductor Pressure = Potential Water Flow = Current Valve Rubber Diaphragm The “plumber’s analogy” of an LC circuit is a rubber diaphragm that has been stretched by pressure on the top (P 1 ) side. When the valve starts the flow, the diaphragm forces water past the flywheel, which begins to spin. After the diaphragm has become flat, the momentum of the flywheel forces the diaphragm to be stretched in the other direction, and the cycle repeats. P 2 P 3 Flywheel V 1 V 3 V 2
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March 7, 2007 Physics 2212 - Lecture 23 Chapter 33 - Summary (1)
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March 7, 2007 Physics 2212 - Lecture 23 Chapter 33 - Summary (2)
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March 7, 2007 Physics 2212 - Lecture 23 Chapter 33 - Summary (3)
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March 7, 2007 Physics 2212 - Lecture 23 AC Sources and Phasors You can think of an AC generator as a battery-like object with an emf that varies sinusoidally as E (t) = E 0 cos ϖ t , where E 0 is the maximum emf and ϖ is the angular frequency, with ϖ =2 π f , where f is the frequency in Hz. Alternatively, the emf and other oscillatory quantities can be represented by a phasor diagram . The phasor is a vector of length E 0 that rotates counterclockwise around the origin with angular frequency ϖ , so that the angle it makes with the horizontal axis at any time is ϖ t . The projection of the phasor on the horizontal axis at any time gives the emf.
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This note was uploaded on 06/07/2009 for the course PHYSICS 2212 taught by Professor Geist during the Fall '09 term at Georgia Perimeter.

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Phys2212_35.1 to 35. - Physics 2212 Electricity and Magnetism Lecture 24(Knight 33.9 34.1-5 LC and AC Circuits LC Circuits A charged capacitor

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