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Unformatted text preview: Physics 21 Fall, 2004 Solution, Hour Exam #2 The graders for the problems were: 1 Shaffer, 2 Hickman, 3 Pagan, 4 Wentzel, 5 Lowe For questions about the grading, see the grader by Nov. 12. Problem 1. For the following circuit: R L C V rms ( frequency ) L I rms 1/ 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) Draw a phasor diagram for this circuit, and use it to find an expression for the phase angle in terms of R , L , and C , and . From the phasor diagram, we have tan = L 1 C R , or sin = L 1 C q ( L 1 C ) 2 + R 2 . This expression is valid for either L > 1 /C or L < 1 /C ; in the latter case the angle will be negative. (c) If R = 3 . 00 , L = 5 . 00 mH, and C = 1 . 25 mF, what angular frequency gives the maximum rms current for a fixed V rms ? What is the value of at this frequency? The length of the vector V rms in the diagram is V rms = p ( L 1 /C ) 2 + R 2 I rms , so that I rms = V rms / p ( L 1 /C ) 2 + R 2 will be largest when L = 1 /C . Then = 0 and = 1 LC 1 p (0 . 005 H)(0 . 00125 ) = 400 rad / s (d) If the ac power source is turned off, how long does it take the oscillating current to diminish to 25% of its steady state value? Use the values of R , L , and C given in part (c). The exponential decay obeys exp( Rt/ 2 L ), so . 25 = exp( Rt/ 2 L ) t = 2 L ln 4 R = 4 . 6 ms Problem 2. An electron with velocity v passes unde- ected through a region where there are uniform electric and magnetic fields. The components of v are v...
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