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).

(a) Find the charge Q(t) and current I(t) in the RC circuit if E(t) = E0(a constant voltage supplied by a battery) and the switch is closed at time t = 0, so that Q(0) = 0. (b) Show that