Question

An inductive coil has a resistance of $100\Omega$. When an A.C. signal of frequency $1000\text{Hz}$ is fed to the coil, the applied voltage leads the current by ${45}^{\circ }$. What is the approximate inductance of the coil (in $\text{mH}$) ?

Answer 1

We know that
$\tan \varphi =\frac{X_L}{R}$
Further, $X_L=\omega L$
Hence $L=\frac{R\tan \varphi }{\omega }=\frac{100\times 1}{2\pi f}=\frac{100}{2\times 3.14\times 1000}$
$L=15.9\times {10}^{-3}\text{H}$
$L=16\text{mH}$