Question

In an AC circuit voltage $V=V_{0}sinwt$ and inductor L is connected across the circuit. Then the instentaneous power will be

• A. $\frac{V_0^2}{2wl}sinwt$
• B. $\frac{{-V}_0^2}{2wl}sinwt$
• C. $\frac{V_0^2}{2wl}sin2wt$
• D. $\frac{V_0^2}{wl}sinwt$

Answer 1

The correct option is C $\frac{V_0^2}{2wl}sin2wt$

Instantaneous power is given by: $P=V\left(t\right)i\left(t\right)$

For the given circuit, $-L\frac{di}{dt}=V_0\sin \omega t\Rightarrow i=\frac{-V_0}{L}\int \sin \omega tdt=\frac{V_0}{\omega L}\cos \omega t$.

Thus, instantaneous power, $P=\frac{V_0^2}{2\omega L}\sin 2\omega t$