Question

The r.m.s. current in an ac circuit is 2 A. If the watt less current be $\sqrt{3}$ A , what is the power factor

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

Answer 1

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

$i_{wL}=i_{rms}sin\varphi \Rightarrow \sqrt{3}=2sin\varphi \Rightarrow sin\varphi =\frac{\sqrt{3}}{2}$
$\Rightarrow \varphi ={60}^{\circ }$ so p.f $=cos\varphi =cos{60}^{\circ }=\frac{1}{2}.$