In an AC circuit, the emf (e) and the current (i) at any instant are given respectively by

$\mathrm{e}={\mathrm{E}}_0\mathrm{sin\omega t}$

$\mathrm{i}={\mathrm{I}}_0\sin (\mathrm{\omega t}-\mathrm{\varphi })$

The average power in the circuit over one cycle of AC is

• A

  $\frac{{\mathrm{E}}_0{\mathrm{I}}_0}{2}$

• B

  $\frac{{\mathrm{E}}_0{\mathrm{I}}_0}{2}\mathrm{sin\varphi }$

• C

  $\frac{{\mathrm{E}}_0{\mathrm{I}}_0}{2}\mathrm{cos\varphi }$

• D

  ${\mathrm{E}}_0{\mathrm{I}}_0$