(Solved): RLC Series Circuit. In the study of an electrical circuit consisting of a resistor, capacitor, indu ...

RLC Series Circuit. In the study of an electrical circuit consisting of a resistor, capacitor, inductor, and an electromotive force (see Figure 1), we are led to an initial value problem of the form $$L\frac{d^{2}q}{d{t}^2}+R\frac{dq}{dt}+\frac{q}{C}=E(t);q\left(t_0\right)=q_0,I\left(t_0\right)=I_0$$ 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 at time $$t$$, and $$I=\frac{dq}{dt}$$ 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, $$L=10\mathrm{H},R=20?,C=(40{)}^{?1}\mathrm{F}$$, and $$\mathrm{E}(\mathrm{t})=100\mathrm{V}$$. Figure 1 RLC Series Circuit