Solved: Consider an initially passive LC circuit (no

Chapter 4, Problem 4.6.18

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Consider an initially passive LC circuit (no resistance) with a battery supplying eo volts. (a) If the switch is closed at time t = 0 and opened at time t = a > 0, show that the current in the circuit satisfies the initial value problem 1 Li" + C i = eoo(t) -eoo(t -a); i(O) = i'(O) = O. (b) If L = 1 H, C = 10-2 F, eo = 10 V, and a = n (s), show that ' ( { Sin lOt I t) = o if t < n, if t > n. Thus the current oscillates through five cycles and then stops abruptly when the switch is opened (Fig. 4.6.6).