Question

When an $AC$ signal of frequency $1kHz$ is applied across a coil of resistance $100\Omega$, then the applied voltage leads the current by ${45}^o$. The inductance of the coil is:

• A. $16mH$
• B. $12mH$
• C. $8mH$
• D. $4mH$

Answer 1

The correct option is A $16mH$

$\therefore {45}^o$ phase angle means,
$X_L=R$
$\therefore \left(2\pi fL\right)=R$
$\therefore L=\frac{R}{2\pi f}$
$=\frac{100}{\left(2\pi \right)\left({10}^3\right)}$
$=0.0159H$
$=16mH$