Question

The reactance of a coil when used in the $AC$ power supply ($220 \,V, 50$ cycle/s) is $ 50\,\Omega $ . The inductance of the coil is nearly

• A. 0.16 H
• B. 0.22 H
• C. 2.2 H
• D. 1.6 H

Answer 1

Answer: (A)

In a coil the product of angular frequency $(\omega)$ and inductance $(L)$ is known as the reactance of the coil or inductive reactance and is denoted by $X_{L}$.
Thus, $X_{L}=\omega L=2 \pi f L$
where $f$ is frequency.
Putting the numerical values from the question, we have
$X_{L} =50\, \Omega, f=50\, cps$
$\therefore L =\frac{X_{L}}{\omega}=\frac{X_{L}}{2 \pi f}=\frac{50}{2 \pi \times 50} $
$=\frac{1}{2 \times 3.14}=0.16\, H$