A circuit has in series an electromotive force given by $E(t)=100 \sin 200 t \mathrm{~V}$, a resistor of $40 \Omega$, an inductor of $0.25 \mathrm{H}$, and a capacitor of $4 \times 10^{-4}$ farads. If the initial current is zero, and the initial charge on the capacitor is $0.01$ coulombs, find the current at any time $t>0$.