The instantaneous values of alternating current and voltages in a circuit are given as
i = 1/√2 sin (100πt) amper
e = 1/√2 sin (100πt + π/3) Volt
The average power in Watts consumed in the circuit is:

Options

(a) 1/4
(b) √3 / 4
(c) 1/2
(d) 1/8

Correct Answer:

1/8

Explanation:

The average power in the circuit where cos ? = power factory

= Vᵣₘₛ x Iᵣₘₛ cos ?
? = π/3 = phase difference = 180/3 = 60
Vᵣₘₛ = 1/√2 / √2 = 1/2 volt
Iᵣₘₛ = 1/√2 / √2 = (1/2) A
cos ? = cos π/3 = 1/2

= 1/2 x 1/2 x 1/2 = 1/8 W