Let a series RLC network be connected to a source voltage \(V\), drawing a current \(I\).

(a) In terms of the load impedance \(Z=Z ot Z\), find expressions for \(\mathrm{P}\) and \(\mathrm{Q}\), from complex power considerations.

(b) Express \(p(t)\) in terms of \(\mathrm{P}\) and \(\mathrm{Q}\), by choosing \(i(t)=\sqrt{2} \mathrm{I} \cos \omega t\).

(c) For the case of \(Z=R+j \omega L+1 / j \omega C\), interpret the result of part

(b) in terms of \(\mathrm{P}, \mathrm{Q} L\), and \(\mathrm{Q}_{C}\). In particular, if \(\omega^{2} \mathrm{LC}=1\), when the inductive and capacitive reactances cancel, comment on what happens.