Question

An inductive coil has a resistance of $100\Omega ,$ when an $\text{a.c.}$ signal of frequency $1\text{kHz}$ is fed to the coil, the applied voltage leads the current by ${45}^{\circ }.$ What is the approximate inductance of the coil ?

• A. $4\text{mH}$
• B. $8\text{mH}$
• C. $12\text{mH}$
• D. $16\text{mH}$

Answer 1

The correct option is D $16\text{mH}$

Given,
$R=100\Omega ;f=1\text{kHz};\varphi ={45}^{\circ }$

For $\text{LR}$ circuit, the phase angle is given by

$\tan \varphi =\frac{X_L}{R}=\frac{\omega L}{R}$

$\tan {45}^{\circ }=\frac{X_L}{R}=\frac{\omega L}{R}$

$\omega L=R$

$\therefore L=\frac{R}{\omega }=\frac{R}{2\pi f}$

$=\frac{100}{2\pi \times 1000}$

$L\approx 16\text{mH}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.