lecture_22 (dragged) 4

# lecture_22 (dragged) 4 - What if there is no resistance...

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MA 36600 LECTURE NOTES: MONDAY, MARCH 9 5 How does the charge Q ( t ) change over time t ? If there is no outside electromotive force i.e., E ( t )isthezero function, then the solution depends on the discriminant R 2 4 L/C : If R 2 4 L/C > 0, then we expect exponential decay. The resistance R is so large that all of the charge Q gets discharged within the resistor. If R 2 4 L/C < 0, then we expect oscillations. The capacitor loses its charge to the resistor and inductor, but the inductor works to keep the charge within the circuit by giving some back to the capacitor. Hence the capacitor and inductor exchange charges over time.
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Unformatted text preview: What if there is no resistance i.e., R = 0? Then we have the diFerential equation Q + 1 LC Q = E ( t ) L . Hence there is a transient charge Q c ( t ) = A cos t + B sin t in terms of = 1 LC . If we have an electromotive force E ( t ) = E cos t at the same frequency as the natural frequency of the circuit, then we expect resonance within the circuit. That is, the amplitude of the charge | Q ( t ) | as t . This would cause a meltdown in the circuit!...
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## This note was uploaded on 11/30/2011 for the course MATH 366 taught by Professor Edraygoins during the Spring '09 term at Purdue University-West Lafayette.

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