An inductor of inductance L=400\: mH and resistors of resistances R_{1}=2\, \Omega \; and\; R_{2}=2\, \Omega are connected to a battery of emf 12 V as shown in the figure. The internal resistance of the battery is negligible. The switch S is closed at t=0 . The potential drop across L as a function of time is

  • Option 1)

    6e^{-5t}V\; \;

  • Option 2)

    \; \frac{12}{t}e^{-3t}V\;

  • Option 3)

    \; \; 6(1-e^{-t/0.2})V\;

  • Option 4)

    \; 12e^{-5t}V

 

Answers (1)

As we learnt in 

Self Inductance -

An emf is induced in the coil or the circuit which oppose the change that causes it. Which is also known back  emf.

- wherein

 

 time constant of the given circuit isT=\frac{\mathrm{L} }{\mathrm{R} _{2}}=\frac{400mh}{2}=0.2 sec

\therefore potential drop is

\xi =\varepsilon _{0}\cdot e^{-}\frac{\mathrm{t} }{\mathrm{T} } \\\xi =12\cdot e^{-5t}


Option 1)

6e^{-5t}V\; \;

This is incorrect

Option 2)

\; \frac{12}{t}e^{-3t}V\;

This option is incorrect

Option 3)

\; \; 6(1-e^{-t/0.2})V\;

This option is incorrect

Option 4)

\; 12e^{-5t}V

This option is correct

Most Viewed Questions

Preparation Products

Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series JEE Main May 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 2999/-
Buy Now
Knockout JEE Main May 2022

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 34999/- ₹ 24999/-
Buy Now
JEE Main Rank Booster 2021

Booster and Kadha Video Lectures, Unlimited Full Mock Test, Adaptive Time Table, 24x7 Doubt Chat Support,.

₹ 13999/- ₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions