Question

The rms current in an AC circuit is $2A$. If the wattless current be $\sqrt{3}A$, what is the power factor of the circuit?

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

Answer 1

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

We know that, $i_{wL}=i_{rms}\sin \varphi$
$\Rightarrow \sqrt{3}=2\sin \varphi \Rightarrow \varphi ={60}^o$
so, power factor $=\cos \varphi =\cos {60}^o=\frac{1}{2}$