Question

The potential difference $V$ and the current $I$ flowing an instrument in an ac circuit of frequency f are given by $V=5cos\omega t$ volts and$I=2sin\omega t$ amperes (where $\omega =2\pi f$). The power dissipated in the instrument is :-

• A. Zero
• B. 10 W
• C. 5 W
• D. 2.5 W

Answer 1

Answer: (A)

Zero

$V=5cos\omega t=5sin(\omega t+\frac{\pi }{2})$ and $I=2sin\omega t$

$Power=V_{rms}\times I_{rms}\times cos\varphi =0$

(Since $\varphi =\frac{\pi }{2}$, therefore $cos\varphi =cos\frac{\pi }{2}=0$)