First slide

Power in a.c. circuit

Question

In an A.C. circuit V and I are given by
$V = 100 \sin (1000 t) volt and I = 1000 \sin (1000 t + π / 3) mA$
The power dissipated in the circuit is

Easy

A

10⁴ W
B

25 W
C

10 W
D

250 W

Solution

Power dissipated
$\begin{array}{l} = V_{r . m . s .} \times I_{r . m . s .} \times \cos ϕ \\ P = \frac{V_{0}}{\sqrt{2}} \times \frac{I_{0}}{\sqrt{2}} \times \cos ϕ \\ = \frac{100}{\sqrt{2}} \times \frac{1000 \times 10^{- 3}}{\sqrt{2}} \cos \frac{π}{3} = 25 W \end{array}$

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