Question

Consider an initially passive RC circuit (no inductance) with a battery supplying e_0 volts. If the switch is closed at time t = a and opened at
time t = b > a (and left open thereafter), the current in the circuit satisfies the initial value problem:

Ri′ + (1/C)i = e_0δ(t–a) – e_0δ(t-b); i(0) = 0

Solve this problem if R = 100 Ω, C = 10^(-4) F, e_0 = 100 V, a = 1(s) and b = 2(s). Show that i(t) > 0, if 1 < t < 2 and that i(t) < 0 if t > 2