Consider a load impedance of \(Z=j \omega L\) connected to a voltage and \(V\) let the current drawn be \(I\).

(a) Develop an expression for the reactive power \(\mathrm{Q}\) in terms of \(\omega, L\), and I, from complex power considerations.

(b) Let the instantaneous current be \(i(t)=\sqrt{2} \mathrm{I} \cos (\omega t+\theta)\). Obtain an expression for the instantaneous power \(p(t)\) into \(L\), and then express it in terms of \(\mathrm{Q}\).

(c) Comment on the average real power \(\mathrm{P}\) supplied to the inductor and the instantaneous power supplied.