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)

0.51 H

Answer 2

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 = $\frac{ 1}{ ( 314 \, s^{ - 1} )^2 \times ( 20 \times 10^{ - 6} \, F ) }$ $= 0.51\,H$