RLC Series Circuit. In the study of an electric circuit consisting of a resistor, capacitor, inductor, and an electromotive force, we are led to an initial value problem of the form
L dI/dt+RI+q/C=E(t),q(0)=q_0,I(0)=I_0
where L is the inductance in henrys, R is the resistance in ohms, C is the capacitance in farads, E(t), is the electromotive force in volts, q(t) is the charge in coulombs on the capacitor as time t, and I=dq/dt is the current in amperes. Find the current at time t if the charge on the capacitor is initially zero, the initial current is zero;
L=10 H,R=20 ?,C=(6260)^(-1) F,and E(t)=100 V.
[Hint: Differentiate both sides of the differential equation in (20) to obtain a homogenous linear second-order equation for I(t). Then use (20) to determine dI/dt at t=0