In an a.c circuit the e.m.f. (e) and the current (i) at any instant are given

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

Options

(a) E₀I₀ / 2
(b) E₀I₀ / 2 sin ?
(c) E₀I₀ / 2 cos ?
(d) E₀I₀

Correct Answer:

E₀I₀ / 2 cos ?

Explanation:

The average power in the circuit over one cycle of a.c. is given by
Pₐᵥ = eᵣₘₛ x iᵣₘₛ x cos ?
= E₀ / √2 x I₀ / √2 x cos ? = E₀I₀ / 2 cos ?

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