Power is the rate of doing work. In A.C. current and voltage change at every moment. Since power is the product of instantaneous voltage and current, therefore it changes at every moment.
To determine average power in a circuit containing pure resistor, determine total energy spent in one cycle and divide it by the time period.
Instantaneous power
= EI = [E0 sin ωt] [ I0 sin ωt]
Instantaneous work done in small interval dt is
dW = EI dt = E0I0 sin2 ωt dt
∴ Average power over a complete cycle of a.c. through a resistor is the product of virtual voltage and virtual current.
