Question

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

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

Answer 1

Answer: (C)

5625 W

Compare V = 150 sin (150 t) with $V=V_{0}sin\omega t$, we get $V_0$ = 150 V

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

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

$I_0=150A,\varphi =\frac{\pi }{3}=60$

The power dissipated in ac circuit is

$P=\frac{1}{2}{V}_0{I}_{0}cos\varphi =\frac{1}{2}\times 150\times 150\times cos60$

$=\frac{1}{2}\times 150\times 150\times \frac{1}{2}=5625W$