In an a.c. circuit the voltage applied is $E=E_0\sin \omega t$. The resulting current in the circuit is $I=I_0\sin \left(\omega t-\frac{\pi }{2}\right)$. The power consumption in the circuit is given by:

The average power consumption in an AC circuit is given by:
$$P_{avg}=V_{rms}{I}_{rms}\cos \varphi$$
where $\varphi$ is the phase difference between voltage and current.From the given equations, the phase of voltage is $\omega t$ and the phase of current is $\omega t-\frac{\pi }{2}$.The phase difference $\varphi =\frac{\pi }{2}$.The power factor is $\cos \varphi =\cos \left(\frac{\pi }{2}\right)=0$.Therefore, $P_{avg}=V_{rms}{I}_{rms}\times 0=0$.