Question

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

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

Answer 1

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


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