In an AC circuit, the emf (e) and the current (i) at any instant are given respectively bye=E0sinωti=I0sin(ωt−ϕ)The average power in the circuit over one cycle of AC is

The power is defined as the rate at which work is being done in the circuit.Power = Rate of work done in one complete cycle.or      Pav=WTor     Pav=E0I0cosϕT/2Tor    Pav=E0I0cosϕ2Where cos ϕ is called the power factor of an AC circuit.