Question

If in a $L-R$ series circuit the power factor is $\frac{1}{2}$ and $R=100\Omega$, then the value of $L$ is, when $AC$ mains is used

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

Answer 1

The correct option is B $\frac{\sqrt{3}}{\pi }H$

Power factor, $\cos \varphi =\frac{1}{2}$
$\varphi ={60}^{\circ }$
$\therefore \tan {60}^{\circ }=\frac{wL}{R}$
$\sqrt{3}=\frac{2\pi \times L}{100}$
$L=\frac{\sqrt{3}\times 100}{2\pi \times 50}$
$=\frac{\sqrt{3}}{\pi }H$.