202Sp10Probs65-72[1] - EE202 DUE WEDNESDAY APRIL 14...

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EE202 HOMEWORK PROBLEMS SPRING 10 D UE W EDNESDAY A PRIL 14 65. Solve each of the indicated questions. (a) In the circuit below, L 1 = 0.8 H, L 2 = 0.45 H, M = 0.175 H, R s = R = 12 ! . If v s ( t ) = 30cos(10 t ) V, find the maximum instantaneous steady state power delivered to R when (i) a dot is in position A, and (ii) a dot is in position B. (b) For the circuit shown below with i L (0 ! ) = 0 and v C (0 ! ) = 2V , the current, i L ( t ) , in amps for t ! 0 . (c) Find the input impedance Z in ( s ) for the circuit below. 66. In the circuit below, the coupling coefficient k has been adjusted so that the exact resonant frequency is ! = 200 rad/sec given that C = 0.35 mF, R = 2 , L 1 = L 2 = 0.1 H.
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page 2 Spring 10 2 (a) Find the equivalent inductance, L eq , of the coupled inductors, the mutual inductance M , and the coupling coefficient k . (i) Step 1: replace the coupled coils by an inductor labeled L eq . Find the value of L eq that meets the resonance condition specified in the problem statement. Are there two values? If so pick the largest. (ii) Step 2: For circuit (aa) below, L eq = L 1 L 2 ! M 2 L 1 + L 2 ! 2 M and for circuit (bb) below L eq = L 1 L 2 ! M 2 L 1 + L 2 + 2 M . Nice trick formulas. Determine M using your answer from step 1.
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