Question

When $100$ volt $DC$ source is applied across a coil, a current of $1A$ flows through it. When $100V$ $AC$ source of $50Hz$ is applied to the same coil, only $0.5A$ current flows. Calculate the inductance of the coil.

• A. $\left(\pi /\sqrt{3}\right)H$
• B. $\left(\sqrt{3}/\pi \right)H$
• C. $\left(2/\pi \right)H$
• D. None of these

Answer 1

The correct option is B $\left(\sqrt{3}/\pi \right)H$

$I_{dc}=\frac{V_{dc}}{R}$

$I=\frac{100}{R}\Rightarrow R=100\Omega$

$I_{ac}=\frac{V_{ac}}{\sqrt{R^2+X_L^2}}$

$0.5=\frac{100}{\sqrt{(100{)}^2+X_L^2}}$

or $X_L=100\sqrt{3}\Omega =\left(2\pi fL\right)$

$\therefore L=\frac{100\sqrt{3}}{2\pi f}$

$=\frac{100\sqrt{3}}{2\pi \left(50\right)}$

$=\left(\frac{\sqrt{3}}{\pi }\right)H$