Suppose an RLC circuit, with a resistor of resistance \(R=100\) ohms, an inductor of inductance \(L=0.5\) henries, and a capacitor with a capacitance of
\(C=2\times 10^{-4}\) farads, has (at time \(t=0\)) an initial current of \(25\) amps that is initially decreasing at \(1\) amp per second, and is attached to a 9-volt battery.

(a)
Let’s derive an IVP satisfied by the current \(I(t)\) at \(t\geq 0\) seconds.
(b)
Let’s solve this IVP.
(c)
What happens to the current in the long run? And what happens to the (positive) charge on one of plates of the capacitor in the long run?