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 ${45}^o$. The inductance of the coil is

• A. $\frac{1}{100\pi }$H
  
• B. $\frac{1}{20\pi }$H
• C. $\frac{1}{40\pi }$H
• D. $\frac{1}{60\pi }$H

Answer 1

Answer: (B)

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

$X_L=\omega L$

$L=\frac{X_L}{\omega }$ $=\frac{100}{2\pi f}$ $=\frac{100}{2\pi 1000}$ $=\frac{1}{20\pi }H$