Question

The instantaneous values of current (in ampere) and potential (in volt) in an A.C. circuit are $i=4\sin \omega t$ and $V=100\cos (\omega t-\frac{\pi }{3})$ respectively. The power factor of the circuit is

• A. $\frac{1}{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. $1$
• D. $\frac{\sqrt{3}}{2}$

Answer 1

The correct option is A $\frac{1}{2}$

$i=4\sin \omega t$

$v=100\cos (\omega t-\frac{\pi }{3})=100\cos (\frac{\pi }{3}-\omega t)$

$=100\sin \{\frac{\pi }{2}-(\frac{\pi }{2}-\omega t)\}$

$=100\sin \{\frac{\pi }{2}-\frac{\pi }{3}+\omega t\}$

$v=100\sin \{\omega t+\frac{\pi }{6}\}$

phase difference $\varphi =\pi /6$

power factor $=\cos \varphi =\cos \pi /6$

$=\frac{\sqrt{3}}{2}$

power factor $=\cos \varphi$

$\varphi =$ phase

Close property

$\cos (-\theta )=\cos \theta$