The figure shows a circuit containing an electromotive force, a capacitor with a capacitance of $ C $ farads $ (F), $ and a resistor with resistance of $ R $ ohms $ (\Omega). $ The voltage drop across is $ Q/C, $ where $ Q $ is the charge (in coulombs), so in this case Kirchhoff's Law gives

$ RI + \frac {Q}{C} = E(t) $

But $ I = dQ/dt $ (see Examples 3.7.3), so we have

$ R \frac {dQ}{dt} + \frac {1}{C}Q = E(t) $

Suppose the resistance is $ 5 \Omega, $ the capacitance is 0.05 F, a battery gives a constant voltage of 60 V, and the initial charge is $ Q(0) = 0 C. $ Find the charge and the current at time $ t. $