Q. A coil of inductive reactance $1 / \sqrt{3 \, } \Omega \, \, $ and resistance $1 \, \Omega $ is connected to a 200 V, 50 Hz AC supply. The time lag between maximum voltage and current is

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A

$\frac{1}{200} \, s$

0%

B

$\frac{1}{300}s$

50%

C

$\frac{1}{500}s$

0%

D

$\frac{1}{600} s$

50%

Solution:

Given,
Inductive reactance of coil $\left(X_{L}\right)=\frac{1}{\sqrt{3 \, }}\Omega $
Resistance $\left(R\right)=1 \, \Omega $
We know that,
$tan \phi = \frac{\omega L}{R}$
$tan \phi = \frac{X_{L}}{R}$
$tan \phi = \frac{1 / \sqrt{3}}{1}$
$\phi=\left(tan\right)^{- 1} \left(\frac{1}{\sqrt{3}}\right)$
$\phi=30^{o}$
$\therefore \, \, \omega t=\frac{\pi }{6}$
$t=\frac{\pi }{6 \omega }$
$t=\frac{\pi }{6 \times \left(2 \pi f\right)}$
$t=\frac{1}{12 f}$
Here, $f=50 \, Hz$
$t=\frac{1}{12 \times 50}=\frac{1}{600}s$

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