Problems Through deal with the RC circuit in Fig., containing a resistor (R ohms), a capac...

Problems Through deal with the RC circuit in Fig., containing a resistor (R ohms), a capacitor (C farads), a switch, a source of emf but no inductor. Substitution of L = 0 in Eq. gives the linear first-order differential equation

for the charge Q = Q(t) on the capacitor at time t. Note that I(t) = Q′(t).

Suppose that in the circuit of Fig., we have R = 10, C = 0.02, Q(0) = 0, and E(t) = 100e−5t (volts). (a) Find Q(t) and I(t). (b) What is the maximum charge on the capacitor for t ≥ 0 and when does it occur?