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Q.

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

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a

100 W

b

50 W

c

87 W

d

71 W

answer is B.

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Detailed Solution

$\begin{array}{l} E_{rms} = \frac{E_{peak}}{\sqrt{2}} = \frac{200}{\sqrt{2}} v o l t \\ I_{rms} = \frac{I_{peak}}{\sqrt{2}} = \frac{1}{\sqrt{2}} A m p \\ ϕ = \frac{π}{3} \\ ∴ P_{average} = E_{rms} I_{rms} cosϕ = \frac{200}{\sqrt{2}} \times \frac{1}{\sqrt{2}} \times \cos \frac{π}{3} = 50 W \end{array}$

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