Question

An inductive coil has a resistance of $100 \, \Omega $ When an AC signal of frequency $1000\, Hz$ is applied to the coil, the voltage leads the current by $ 45^{\circ} $ . The inductance of the coil is

• A. $ \frac{1}{10\pi } $
• B. $ \frac{1}{20\pi } $
• C. $ \frac{1}{40\pi } $
• D. $ \frac{1}{60\pi } $

Answer 1

Answer: (B)

$\tan \phi=\frac{X_{L}}{R}$
$\therefore \tan 45^{o}=\frac{L \omega}{R}$
$L=\frac{R}{\omega}=\frac{100}{2 \pi \times 1000}$
$\left(\because \tan 45^{\circ}=1\right)$
$L=\frac{1}{20 \pi}$