Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Figure shows a series LCR circuit with <img alt="\mathrm{\mathrm{R}=200 \Omega, \mathrm{C}=15.0 \mu \mathrm{F} \, \, and \, \, \mathrm{L}=230 \mathrm{mH}. }" src="https://entrancecorner.oncodecogs.

Figure shows a series LCR circuit with \mathrm{\mathrm{R}=200 \Omega, \mathrm{C}=15.0 \mu \mathrm{F} \, \, and \, \, \mathrm{L}=230 \mathrm{mH}. }If \mathrm{\varepsilon=36.0 \sin 120 \pi, } the amplitude \mathrm{I_0 } of the current i in the circuit is close to:
                                                         

Option: 1

109 mA


Option: 2

126 mA


Option: 3

150 mA


Option: 4

164 mA


Answers (1)

best_answer

Given \mathrm{ \mathrm{R}=200 \Omega, \mathrm{C}=15.0 \mu \mathrm{F}=15 \times 10^{-6} \mathrm{~F} }
\mathrm{\mathrm{L}=230 \mathrm{mH}=230 \times 10^{-3} \mathrm{H}, \varepsilon=36.0 \sin 120 \pi \mathrm{t} }
Compare it with standard equation
\mathrm{\varepsilon=\varepsilon_0 \sin \omega \mathrm{t} }
We get
\mathrm{\varepsilon_0=36.0, \omega=120 \pi }
The capacitive reactance is
\mathrm{\mathrm{X}_{\mathrm{C}}=\frac{1}{\omega \mathrm{C}}=\frac{1}{120 \pi \times 15 \times 10^{-6}}=177 \Omega }
The inductive reactance is
\mathrm{X_L=\omega L=120 \pi \times 230 \times 10^{-3}=87 \Omega }
Impedance of the series LCR circuit is
\mathrm{ \begin{aligned} & \mathrm{Z}=\sqrt{\mathrm{R}^2+\left(\mathrm{X}_{\mathrm{C}}-\mathrm{X}_{\mathrm{L}}\right)^2}=\sqrt{(200)^2+(177-87)^2}=219 \Omega \\ & \therefore \quad \mathrm{I}_0=\frac{\varepsilon_0}{\mathrm{Z}}=\frac{36 \mathrm{~V}}{219 \Omega}=164 \mathrm{~mA} \end{aligned} }

Posted by

Sanket Gandhi

View full answer

JEE Main high-scoring chapters and topics

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

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026 application correction begins on jeemain.nta.nic.in; edit details by December 2
anam-khan

JEE Mains 2026 LIVE: NTA to conduct session 1 from January 21 to 30; exam pattern, syllabus
anam-khan

JEE Main 2026 correction window opens tomorrow; NTA allows exam city change

Latest Question