The switch in Figure P10-53 has been in position A for a long time and is moved to position B at \(t=0\).

(a) Write an appropriate set of node-voltage or mesh current equations in the \(s\) domain.

(b) Use MATLAB to solve for \(V_{\mathrm{C}}(s)\) and \(v_{\mathrm{C}}(t)\) for \(V_{\mathrm{S}}(t\) ) \(=15 e^{-10,000 t} \mathrm{~V}\).

(c) Repeat (a) and (b) for \(V_{\mathrm{S}}(t)=15 e^{-2000 t} \mathrm{~V}\).

(d) Use MATLAB to plot both results on the same graph. What case is each?