In an a.c circuit the current and emf vary continuously with time. Therefore power at a given instant of time is calculated and then its mean is taken over a complete cycle. Thus, we define instantaneous power of an a.c. circuit as the product of the instantaneous emf and the instantaneous current flowing through it.
The instantaneous value of emf and current is given by
e = E0 sin ωt
i = I0 sin (ωt + φ)
where φ is the phase difference between the emf and current in an a.c circuit
The average power consumed over one complete cycle is
On simplification, we obtain
Pav = (E0 I0) /2 cos φ
Pav = E0/√2 . I0√2 cos φ= Erms . Irms φ
Pav = apparent power × power factor
where Apparent power = Erms Irms and power factor = cos φ
The average power of an ac circuit is also called the true power of the circuit.