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EP 229 Assignment 10 (due Tuesday April 5) 1. In capacitor discharging through an RL series circuit, the energy decreases by 1 % in each oscillation when R = 2 : If the resistance is removed, the LC circuit oscillates at f = 1 kHz. Find the values of L and C: The circuit is weakly damped and the capacitor charge may be approximated by 0s 1 q (t) = q0 exp Ans. L = 0:199 H, C = 127 nF. R t cos @ 2L 2. Find the current when the voltage across a 50 1 LC R 2L 2 tA inductive reactance is given as follows: (a) 50 sin !t (b) 30 sin (!t + 20 ) (c) 80 sin (377t + 40 ) 3. Repeat 2 for a 30 capacitive reactance. 4. Problem 33.25. 5. Problem 33.39. 6. A series LCR circuit is driven by an oscillating voltage source v (t) = 6 sin (314t + 60 ) : The resistance of the circuit is 3 k ; the inductive reactance is 2 k and capacitive reactance is 1 k :Find (a) the total impedance (b) the RMS current (c) the average power dissipated in the resistor Ans. Z = 3:166 18:4 ; iRM S = 1:34 mA, Pave = 5.4 mW. 7. Find the total impedance seen by the 15 V (RMS) voltage source, the RMS current driven and the average power delivered by the voltage source. 3.5 µF 15 V 500 Hz Ans. Z = 99:86 10 µF 20 Ohms 30 mH 15 mH 60:6 ; 1.1 W. 1 30 Ohms