Question

An inductor $ L,\,\,a $ capacitor of $ 20\mu F $ and a resistor of $ 10\Omega $ are connected in series with an $AC$ source of frequency $ 50\,Hz $ . If the current is in phase with the voltage, then the inductance of the inductor is

• A. 2.00 H
• B. 0.51 H
• C. 1.5 H
• D. 0.99 H

Answer 1

Answer: (B)

In an L - C - R circuit, the current and the voltage are in phase
$ ( \phi = 0 ), $ when
$ \tan \, \phi = \frac{ \omega L - \frac{ 1}{ \omega C } }{ R } = 0 $
or $ \omega L = \frac{ 1}{ \omega C} $
or $ L = \frac{ 1}{ \omega^2 C} $
Here, $ \omega = 2 \pi f $
$= 2 \times 3.14 \times 50 \, s^{ - 1} = 31.4 \, s^{ - 1} $
and $C = 20 \,\mu F = 20 \times 10^{ - 6 } $ F
L = $ \frac{ 1}{ ( 314 \, s^{ - 1} )^2 \times ( 20 \times 10^{ - 6} \, F ) } $
$= 0.51\,H $