Question

An alternating potential $V=V_0\sin \omega t$ is applied across a circuit. As a result the current $I=I_0\sin (\omega t-\frac{\pi }{3})$ flows through it. The average power consumed in the circuit is

• A. $0.5V_0{I}_0$
• B. $0.707V_0{I}_0$
• C. $0.25V_0{I}_0$
• D. $1.414V_0{I}_0$

Answer 1

The correct option is C $0.25V_0{I}_0$

Average power consumed in AC circuit is given by
$P=I_{r.m.s}.V_{r.m.s}\cos \varphi$
$=\frac{I_0}{\sqrt{2}}\frac{V_0}{\sqrt{2}}\cos \frac{\pi }{3}$
$=\frac{V_0{I}_0}{4}$
$=0.25V_0{I}_0$