The instantaneous values of alternating current and voltages in a...

Given equations $$i=\frac{1}{\sqrt{2}} \sin (100 \pi t)$$ and $e=\frac{1}{\sqrt{2}} \sin (100 \pi t+\pi / 3) \therefore \quad i_o=\frac{1}{\sqrt{2}}$ and $V_o=\frac{1}{\sqrt{2}}$ We know that average power \begin{aligned} & P_{\mathrm{av}}=V_{\mathrm{rms}} \times i_{\mathrm{rms}} \cos \phi \\ &=\frac{1}{2} \times \frac{1}{2} \times \cos 60^{\circ} \\ & \qquad\left[\because i_{\mathrm{rms}}=\frac{i_o}{\sqrt{2}} \text{ and } V_{\mathrm{rms}}=\frac{V_o}{\sqrt{2}}\right] \\ &=\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \\ &=\frac{1}{8} \mathrm{~W} \end{aligned}