Chapter 2, Problem 2.18P

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

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

(b) Express $p\left(t\right)$ in terms of P and Q, by choosing $i\left(t\right)=\sqrt{2}\text{I}\cos \omega t$. (c) For the case of $Z=R+j\omega L+1/j\omega C$, interpret the result of part (b) in terms of $\text{P,}{\text{Q}}_L$, and ${\text{Q}}_c$. In particular, if ${\omega }^2\text{LC}=1$, when the inductive and capacitive reactances cancel, comment on what happens.