examPS - Physics 21 Fall, 2004 Solution, Practice Exam #2...

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Physics 21 Fall, 2004 Solution, Practice Exam #2 Problem 1. For the following circuit: R L C V rms ( frequency ω ) φ ω L I rms 1/ ω C I rms R I rms V rms (a) Write the loop equation for this circuit. V IR L dI dt Q C =0 (b) If R =20Ω, L =0 . 025 H, and C =50 µ F (50 × 10 6 F), ±nd the frequency ω for which the current lags the volt- age across the inductor by 30 . Hint: Make sure ω> 0 . OOPS, the question SHOULD HAVE SAID, ±nd the frequency ω for which the applied voltage lags the volt- age across the inductor by 30 . From the diagram, the phase angle φ can be written tan φ = ωL 1 ωC R . If the applied voltage V sin( ωt + φ ) lags the voltage across the inductor by 30 , then φ =60 and tan φ = 3= ωL 1 ωC R We transform this into a quadratic equation for ω 2 3 1 /C =0 , whose solution is ω = 3 R ± p 3 R 2 +4 L/C 2 L . We must take the plus sign so that ω> 0; the result is ω =1 . 82 kH. A negative value of ω would reverse the directions of the vertical vectors on the phasor diagram, and change the phase relations. (c) If
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This note was uploaded on 08/06/2008 for the course PHYS 21 taught by Professor Hickman during the Fall '07 term at Lehigh University .

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examPS - Physics 21 Fall, 2004 Solution, Practice Exam #2...

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