An inductor for which \(L=10 \mathrm{mH}\) is connected to an \(\mathrm{AC}\) source. The source emf is given by \(\mathscr{E}=\mathscr{E}_{\max } \sin \omega t\), with \(\mathscr{E}_{\max }=5.0 \mathrm{~V}\) and \(\omega=200 \mathrm{~s}^{-1}\).

(a) What is the amplitude of the current through the inductor? 

\((b)\) How does the current amplitude change as you lower the source angular frequency? As you lower the inductance?