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In an a.c. circuit the e.m.f. (e) and the current (i) at any instant are given respectively by e = E₀ sin ωt and i = I₀ sin (ωt − ϕ). The average power in the circuit over one cycle of a.c. is:

1. E₀I₀/2
2. E₀I₀/2 sin ϕ
3. E₀I₀/2 cos ϕ
4. E₀I₀

Correct answer: E₀I₀/2 cos ϕ

Solution

The average power in an AC circuit is given by P_avg = (E₀I₀/2) cos ϕ, where ϕ is the phase difference between the voltage and current. This formula accounts for the power factor (cos ϕ), which represents the fraction of power effectively used in the circuit.

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