Question

In an ac circuit, V and I are given by V = 150 sin (150t) V and I = 150 sin $\left( 150 + \frac{\pi}{3} \right)A$The power dissipated in the circuit is

• A. 106 W
• B. 150 W
• C. 5625 W
• D. Zero

Answer 1

Answer: (C)

5625 W

Answer 2

: Compare V = 150sin (150t) with

$V = V_{0}\sin\omega t,$ we get $V_{0} = 150V$

Compare I = 150 sin$\left( 150t + \frac{\pi}{3} \right)$ with

$I = I_{0}\sin g(\omega t + \varphi),$ we get

$I_{0} = 150A,\varphi = \frac{\pi}{3} = 60^{o}$

The power dissipated in ac circuit is

$P = \frac{1}{2}V_{0}I_{0}\cos\varphi = \frac{1}{2} \times 150 \times 150 \times \cos 60^{o} = \frac{1}{2} \times 150 \times 150 \times \frac{1}{2} = 5625W$