First slide

Power in a.c. circuit

Question

In an AC circuit, the instantaneous values of e.m.f. and current are e = 200 sin (314t) volt and $i = \sin (314 t + \frac{π}{3})$ amperes. The average power consumed in watt is

Easy

A

200
B

100
C

50
D

25

Solution

$V_{rms} = \frac{200}{\sqrt{2}}, i_{rms} = \frac{1}{\sqrt{2}}$
$∴ P = V_{rms} i_{ms} cosϕ = \frac{200}{\sqrt{2}} \times \frac{1}{\sqrt{2}} \cos \frac{π}{3} = 50 watt$

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