8.022pset9 - the capacitor in the circuit(a[5 pts Derive a...

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Massachusetts Institute of Technology Department of Physics 8.022 Spring 2004 Assignment 9: AC Circuits Post date: Thursday, April 22nd Due date: Thursday, April 29th Be sure to write your name and section number on your pset Please staple multiple pages together 1. Purcell 8.3: Parallel RLC (10 pts). 2. Purcell 8.7: Resonant cavity (15 pts). 3. Purcell 8.9: Efect oF resistance on RLC Frequency (10 pts). Note, Q = corresponds to R = 0. Also, the percentage change is just the Fractional change, Fractional change = ω Q = - ω Q =1000 ω Q = times 100. 4. Purcell 8.10: RL in parallel in C (15 pts). 5. Purcell 8.13: Bridge For determining unknown inductance (15 pts). 6. Charge in series RLC (15 pts). We have examined in detail a series RLC circuit driven by a periodic EM± E = E 0 cos( ωt ), Focusing on the current in the circuit and the voltage drop across circuit elements. We will now look at the behavior oF q ( t ), the charge on
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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 2-R 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 1-ω 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.

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