Consider the RLC circuit in Problem 11.

a. Write the governing equation in terms of the electric charge \(q\).

b. Assuming initial conditions are \(q(0)=0, \dot{q}(0)=1\), plot \(q\) and \(i\) versus \(t\) (same figure) when the applied voltage \(v_{a}\) is a unit impulse.

Data From Problem 11:

The governing equation for an RLC circuit driven by the applied voltage \(v_{a}(t)\) is derived as

\[L \frac{d i}{d t}+R i+\frac{1}{C} \int i d t=v_{a}(t)\]

where \(L=4 \mathrm{H}, R=4 \Omega\), and \(C=\frac{1}{2} \mathrm{~F}\).