First slide

Power in a.c. circuit

Question

In an AC circuit, V and I are given by $V = 100 \sin (100 t) volts, I = 100 \sin (100 t + \frac{π}{3}) mA .$ The power dissipated in the circuit is

Easy

A

10⁴ watt
B

10 watt
C

2.5 watt
D

5 watt

Solution

$P = V_{r.m.s.} \times i_{r.m.s.} \times cosϕ = \frac{100}{\sqrt{2}} \times \frac{100 \times 10^{- 3}}{\sqrt{2}} \times \cos \frac{π}{3}$
$= \frac{10^{4} \times 10^{- 3}}{2} \times \frac{1}{2} = \frac{10}{4} = 2 .5 watt$

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