Question

When $100V$ dc is applied across a coil, a current of $1A$ flows through it and when $100V$ ac of $50Hz$ is applied to the same coil, only $0.5A$ flows. The inductance of coil is

• A. $5.5H$
• B. $3/\pi H$
• C. $\sqrt{3}/\pi H$
• D. $2.5H$

Answer 1

The correct option is C $\sqrt{3}/\pi H$

$R=\frac{V_{DC}}{I_{DC}}=\frac{100}{1}=100\Omega$
$\frac{V_{AC}^2}{I_{AC}^2}=R^2+X_L^2\Rightarrow \frac{{100}^2}{{0.5}^2}={100}^2+X_L^2\Rightarrow X_L=\sqrt{30000}=100\sqrt{3}\Omega$
$X_L=L2\pi f\Rightarrow 100\sqrt{3}=L2\pi 50\Rightarrow L=\frac{\sqrt{3}}{\pi }H$