Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

A sinusoidal voltage $\mathrm{V(t)=210\sin3000\: t\: volt}$ is applied to a series $\mathrm{LCR}$ circuit in which $\mathrm{L=10mH,C=25\mu F\: and\: R=100\Omega }$ . The phase difference $\mathrm{\left ( \phi \right )}$ between the applied voltage and resultant current will be :
Option: 1
$\mathrm{\tan^{-1}\left ( 0.17 \right )}$

Option: 2
$\mathrm{\tan^{-1}\left ( 9.46 \right )}$

Option: 3
$\mathrm{\tan^{-1}\left ( 0.30 \right )}$

Option: 4
$\mathrm{\tan^{-1}\left ( 13.33 \right )}$

Answers (1)

$\mathrm{V(t)=210 \sin (3000 t)} \\$

$\mathrm{L=10 \times 10^{-3} \mathrm{H}} \\$

$\mathrm{C=25 \times 10^{-6} \mathrm{~F}} \\$

$\mathrm{R=100 \Omega}$

$\mathrm{\tan \phi= \frac{\left|X_{L}-X_{C}\right|}{R}} \\$

$\mathrm{X_{L}=\omega L =2 \pi f L} \\$

$\mathrm{=3000 \times 10 \times 10^{-3}} \\$

$\mathrm{X_{L} =30 \Omega}$

$\mathrm{X_{c}=\frac{1}{\omega c}=\frac{1}{3000 \times 25 \times 10^{-6}}} \\$

$\mathrm{X_{C}=\frac{40 \Omega}{3} }\\$

$\mathrm{\tan \phi=\frac{\left|30-\frac{40}{3}\right|}{100}=\frac{1}{6}} \\$

$\mathrm{\phi=\tan ^{-1}\left(\frac{1}{6}\right)=\tan ^{-1}(0.166)}$

Hence the correct answer is option 1.

Posted by

Kshitij

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

5 g of Na₂SO₄ was dissolved in x g of H₂O. The change in freezing point was found to be 3.82⁰C. If Na₂SO₄ is 81.5% ionised, the value of x (K

A capacitor is made of two square plates each of side 'a' making a very small angle $\alpha$

A solution of m-chloroaniline, m-chlorophenol and m-chlorobenzoic acid in ethyl acetate was extracted initially with a saturated solution of NaHCO₃ to give fraction A. The leftover organic phase was extracted with d

Trending Articles/News

anam-khan

JEE Main 2025 Session 2 City Slip (OUT) Live: NTA exam city intimation slip link available; admit card date

anam-khan

AESL expands Aakash Digital 2.0 to offer AI-powered coaching for NEET, JEE, Olympiads

anam-khan

Bihar Board extends BSEB Super 50 free coaching application last date to March 26

Latest Question