Consider the circuit shown in Figure P10-15.

(a) Find \(V_{\mathrm{T}}(s)\) and \(Z_{\mathrm{T}}(s)\).

(b) Plot the poles and zeros of \(Z_{\mathrm{T}}(s)\).

(c) Let \(V_{1}(s)=V_{\mathrm{A}} / s\) and plot the poles and zeros of \(V_{\mathrm{T}}(\) \(s\) ).

(d) Select values of \(R\) and \(L\) so that \(V_{\mathrm{T}}(s)\) has a pole at -50 \(\mathrm{krad} / \mathrm{s}\). What are the poles and zeros of \(Z_{\mathrm{T}}(s)\) with your choice of \(R\) and \(L\) ?