Question

If power factor is $1/2$ in a series $RL$ circuit $R=100\Omega.$ If $AC$ mains of $50Hz$ is used then $L$ is :-

• A. $\frac{\sqrt{3}}{\pi }$ Henry
• B. $\pi $ Henry
• C. $\frac{\pi }{\sqrt{3}}$ Henry
• D. $\text{ None of these }$

Answer 1

Answer: (A)

$cos\phi=\frac{R}{Z}=\frac{100}{Z}=\frac{1}{2}$
$Z=200=\sqrt{R^{2} + X_{L}^{2}}$
$\Rightarrow X_{L}=\sqrt{3}\times 100\Omega=\omega L=100\pi L$
$L=\frac{\sqrt{3}}{\pi }H$