# In a a.c circuit the e.m.f (e) and the current (i) at any instant are given respectively by :

$e= E_0\: \sin\: \omega t$

$i = I_0\: \sin ( \omega t - \phi )$

The average power in the circuit over one cycle of a.c. is

$\begin {array} {1 1} (1)\;E_0I_0 & \quad (2)\;\large\frac{E_0I_0}{2} \\ (3)\;\large\frac{E_0I_0}{2}\sin \phi & \quad (4)\;\large\frac{E_0I_0}{2} \cos \phi \end {array}$