Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard
  1. Home
  2. Engineering
  3. Stuck here, help me understand: A 20 Henry inductor coil is connected to a 10 ohm resistance in series as shown in figure. The time at which rate of dissipation of energy (Joule's heat) across resistance is equal to the rate at which magnetic ene
# Engineering

A 20 Henry inductor coil is connected to a 10 ohm resistance in series as shown in figure. The time at which rate of dissipation of energy (Joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor, is :


 

  • Option 1)

    ln\; 2

  • Option 2)

    2\; ln\; 2

  • Option 3)

    \frac{1}{2}\; ln\; 2

     

  • Option 4)

    \frac{2}{ ln\; 2}\;

Answers (1)
S solutionqc

For L-R circuit

i=\frac{E}{R}(I-e^{-t/t}) where L = \frac{L}{R}

and rate of magnetic energy stored in inductor =i\times L\times \frac{di}{dt}.......\; \; \; \; (1)

and rate of dissipiation of energy across Resistance =i^{2}R\; \; \; \; \; ......(2)

from question (1)=(2)

So i^{2}R=i\; L\; \frac{di}{dt}

R\times\frac{E}{R}(I-e^{-\frac{Rt}{L}})=\left ( L\times\frac{E}{R}\times\frac{R}{L}e^{-\frac{Rt}{L}} \right )

\Rightarrow 2\; e^{-\frac{Rt}{L}}=1

      \frac{R}{L}t=ln\; 2

t=\frac{L}{R}ln\; 2

t=\frac{20}{10}ln\; 2

t=2\; ln\; 2


Option 1)

ln\; 2

Option 2)

2\; ln\; 2

Option 3)

\frac{1}{2}\; ln\; 2

 

Option 4)

\frac{2}{ ln\; 2}\;

Similar Questions

Latest Asked Questions

Most Viewed Questions

Preparation Products

Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
Buy Now
Test Series JEE Main 2024

Chapter/Subject/Full Mock Tests for JEE Main, Personalized Performance Report, Weakness Sheet, Complete Answer Key,.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout JEE Main (One Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout JEE Main (Twelve Months Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 19999/- ₹ 14499/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
Start Now
 
Exams
Articles
Questions