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)

$\frac{1}{20\pi }$

Answer 2

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