Chapter 30, Problem 81GP

An ac voltage source $V=V_0\sin \left(\omega t+90°\right)$ is connected across an inductor L and current $I=I_0\sin \left(\omega t\right)$ flows in this circuit. Note that the current and source voltage are 90º out of phase. (a) Directly calculate the average power delivered by the source over one period T of its sinusoidal cycle via the integral $\bar{P}={\displaystyle {\int }_0^{T}VI}dt/T$. (b) Apply the relation $\bar{P}=I_{rms}{V}_{rms}\cos \varphi$ this circuit and show that the answer you obtain is consistent with that found in part (a). Comment on your results.