Question

When $100$ volt dc is applied across a coil, a current of $1amp$ flows through it, when $100volt$ ac of $50Hz$ is applied to the same coild only $0.5amp$ flows. Calculate the resistance and inductance of the coil.

Answer 1

In case of a coil L-R circuit
$I=\frac{V}{Z},Z=\sqrt{R^2+{\left(\omega L\right)}^2}$
So when dc is applied, $\omega =0,Z=R$
And hence $R=100\Omega$
And when ac of $50Hz$ is applied
$I=\frac{V}{Z},Z=\frac{V}{I}=\frac{100}{0.5}200\Omega$
But $Z=\sqrt{R^2+{\left(\omega L\right)}^2}$
$2\pi f{L}^2={200}^2-{100}^2=3\times {10}^{-4}$
$L=\frac{\sqrt{3}\times {10}^2}{2\pi \times 50}=\frac{\sqrt{3}}{\pi }H=0.55H$