Unformatted text preview: the capacitor in the circuit. (a) [5 pts] Derive a diferential equation showing the time evolution oF the charge on the capacitor. Don’t solve it! (b) [5 pts] Use the known solution For I ( t ) and the de²nition I = dq/dt to ²nd an expression For q ( t ). Give the complex charge, ˜ q ( t ), as well as the physical charge on the capacitor. What is the amplitude q oF q ( t )? (c) [5 pts] Show that the maximum charge amplitude is at ω = q ω 2R 2 / 2 L 2 . 7. Quality Factor details (20 pts). (a) [12 pts] ±or the series RLC circuit, show that the Frequencies ω 1 and ω 2 at which the average power provided by the source is halF the maximum are given by ω 1 , 2 = s ω 2 + R 2 4 L 2 ± R 2 L (b) [8 pts] Show that the AC quality Factor Q = ω ω 1ω 2 is the same as the quality Factor obtained For the damped RLC circuit....
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This homework help was uploaded on 04/11/2008 for the course PHYSICS 8.022 taught by Professor Hughes during the Spring '08 term at MIT.
 Spring '08
 Hughes
 Mass

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