Question

The potential difference across an instrument in an a.c. circuit of frequency f is $V$ and the current flowing through it is $I$ such that $V=5\cos \left(2\pi ft\right)\text{volts}$ and $I=2\sin \left(2\pi ft\right)\text{amp}$. The power dissipate in the instrument is :

• A. $10\text{watt}$
• B. $5\text{watt}$
• C. $2.5\text{watt}$
• D. zero

Answer 1

The correct option is D zero

Given,
$V=5\cos 2\pi ft$ and $I=2\sin 2\pi ft$

Average power dissipated is an $AC$ circuit is given by , $P=VI\cos \theta$

Using $\sin ({90}^o+\theta )=\cos \theta$

We have $V=5\sin (2\pi ft+\frac{\pi }{2})$

Phase difference between $V$ and $I$ is $\theta =\frac{\pi }{2}$

Therefore the power dissipated is $0$.

Hence, option (a) is the correct answer.