Ask & Answer Question

Physics NCERT Exemplar Solutions Class 11th Chapter Eleven Physics Class 12th Electromagnetic Induction

A $10 Ω$ 20 mH coil carrying constant current is connected to a battery of 20 V through a switch. Now after switch is opened current becomes zero in 100 $μ s .$ The average e.m.f. induced in the coil is__________V.

2 Views | Posted 2 weeks ago

Asked by Shiksha User

1 Answer

Answered by

Raj Pandey | Contributor-Level 9

2 weeks ago

Decay of current in Inductor is given by,

$i = i_{0} e^{- t / τ} [W h e r e τ = \frac{L}{R}; i_{0} = \frac{v}{R} = \frac{20}{10} = 2]$

At t = 100 $μ s$

i = 0

i.e. i = i₀ $e^{- 100 / τ} = 0$ -(1)

e.m.f induced

$e = \frac{- L d i}{d t} = - L \frac{d}{d t} [i_{0} e^{- t / τ}]$

...more

Decay of current in Inductor is given by,

$i = i_{0} e^{- t / τ} [W h e r e τ = \frac{L}{R}; i_{0} = \frac{v}{R} = \frac{20}{10} = 2]$

At t = 100 $μ s$

i = 0

i.e. i = i₀ $e^{- 100 / τ} = 0$ -(1)

e.m.f induced

$e = \frac{- L d i}{d t} = - L \frac{d}{d t} [i_{0} e^{- t / τ}]$

= $= - L i_{0} \frac{- 1}{2} e^{- t / τ}$

$e = \frac{L i_{0}}{τ} e^{- t / τ}$

$e_{a v g} = \frac{\int_{0}^{200 μ s} e d t}{\int_{0}^{200 μ s} d t} = \frac{\int_{0}^{200 μ s} \frac{L i_{0}}{τ} e^{- t / τ} d t}{\int_{0}^{200 μ s} d t}$

$= \frac{L i_{0}}{200 \times 1 0^{- 6} s e c} = \frac{20 \times 1 0^{- 3} \times 2}{200 \times 1 0^{- 6}} = 400$

less

Decay of current in Inductor is given by,              <math> <mrow> <mi>i</mi> <mo>=</mo> <msub> <mrow> <mi>i</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <msup> <mrow> <mi>e</mi> </mrow> <mrow> <mo>−</mo> <mi>t</mi> <mo>/</mo> <mi>τ</mi> </mrow> </msup> <mtext> </mtext> <mrow> <mo>[</mo> <mrow> <mi>W</mi> <mi>h</mi> <mi>e</mi> <mi>r</mi> <mi>e</mi> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mi>τ</mi> <mo>=</mo> <mfrac bevelled="true"> <mrow> <mi>L</mi> </mrow> <mrow> <mi>R</mi> </mrow> </mfrac> <mo>;</mo> <msub> <mrow> <mi>i</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mi>v</mi> </mrow> <mrow> <mi>R</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mn>0</mn> </mrow> <mrow> <mn>1</mn> <mn>0</mn> </mrow> </mfrac> <mo>=</mo> <mn>2</mn> </mrow> <mo>]</mo> </mrow> </mrow> </math>                At t = 100 <math> <mrow> <mi>μ</mi> <mi>s</mi> </mrow> </math>                i = 0              i.e. i = i0 <math> <mrow> <msup> <mrow> <mi>e</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> <mn>0</mn> <mn>0</mn> <mo>/</mo> <mi>τ</mi> </mrow> </msup> <mo>=</mo> <mn>0</mn> </mrow> </math>           -(1)              e.m.f   induced              <math> <mrow> <mi>e</mi> <mo>=</mo> <mfrac> <mrow> <mo>−</mo> <mi>L</mi> <mi>d</mi> <mi>i</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mo>−</mo> <mi>L</mi> <mfrac> <mrow> <mi>d</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mrow> <mo>[</mo> <mrow> <msub> <mrow> <mi>i</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <msup> <mrow> <mi>e</mi> </mrow> <mrow> <mo>−</mo> <mi>t</mi> <mo>/</mo> <mi>τ</mi> </mrow> </msup> </mrow> <mo>]</mo> </mrow> </mrow> </math>                = <math> <mrow> <mo>=</mo> <mo>−</mo> <mi>L</mi> <msub> <mrow> <mi>i</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mfrac> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <msup> <mrow> <mi>e</mi> </mrow> <mrow> <mo>−</mo> <mi>t</mi> <mo>/</mo> <mi>τ</mi> </mrow> </msup> </mrow> </math>               <math> <mrow> <mi>e</mi> <mo>=</mo> <mfrac> <mrow> <mi>L</mi> <msub> <mrow> <mi>i</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <mi>τ</mi> </mrow> </mfrac> <msup> <mrow> <mi>e</mi> </mrow> <mrow> <mo>−</mo> <mi>t</mi> <mo>/</mo> <mi>τ</mi> </mrow> </msup> </mrow> </math> <math> <mrow> <msub> <mrow> <mi>e</mi> </mrow> <mrow> <mi>a</mi> <mi>v</mi> <mi>g</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mstyle displaystyle="true"> <mrow> <munderover> <mo>∫</mo> <mrow> <mn>0</mn> </mrow> <mrow> <mn>2</mn> <mn>0</mn> <mn>0</mn> <mi>μ</mi> <mi>s</mi> </mrow> </munderover> <mrow> <mi>e</mi> <mi>d</mi> <mi>t</mi> </mrow> </mrow> </mstyle> </mrow> <mrow> <mstyle displaystyle="true"> <mrow> <munderover> <mo>∫</mo> <mrow> <mn>0</mn> </mrow> <mrow> <mn>2</mn> <mn>0</mn> <mn>0</mn> <mi>μ</mi> <mi>s</mi> </mrow> </munderover> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mrow> </mstyle> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mstyle displaystyle="true"> <mrow> <munderover> <mo>∫</mo> <mrow> <mn>0</mn> </mrow> <mrow> <mn>2</mn> <mn>0</mn> <mn>0</mn> <mi>μ</mi> <mi>s</mi> </mrow> </munderover> <mrow> <mfrac> <mrow> <mi>L</mi> <mtext> </mtext> <mtext> </mtext> <msub> <mrow> <mi>i</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <mi>τ</mi> </mrow> </mfrac> <msup> <mrow> <mi>e</mi> </mrow> <mrow> <mo>−</mo> <mi>t</mi> <mo>/</mo> <mi>τ</mi> </mrow> </msup> <mi>d</mi> <mi>t</mi> </mrow> </mrow> </mstyle> </mrow> <mrow> <mstyle displaystyle="true"> <mrow> <munderover> <mo>∫</mo> <mrow> <mn>0</mn> </mrow> <mrow> <mn>2</mn> <mn>0</mn> <mn>0</mn> <mi>μ</mi> <mi>s</mi> </mrow> </munderover> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mrow> </mstyle> </mrow> </mfrac> </mrow> </math> <math> <mrow> <mo>=</mo> <mfrac> <mrow> <mi>L</mi> <msub> <mrow> <mi>i</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <mn>2</mn> <mn>0</mn> <mn>0</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>6</mn> </mrow> </msup> <mi>s</mi> <mi>e</mi> <mi>c</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mn>0</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> <mo>×</mo> <mn>2</mn> </mrow> <mrow> <mn>2</mn> <mn>0</mn> <mn>0</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>6</mn> </mrow> </msup> </mrow> </mfrac> <mo>=</mo> <mn>4</mn> <mn>0</mn> <mn>0</mn> </mrow> </math>

0 Upvotes 0 Downvotes

Get authentic answers from experts, students and alumni that you won't find anywhere else

On Shiksha, get access to

65k Colleges
1.2k Exams
688k Reviews
1800k Answers

Community GuidelinesUser Points System

QuestionsDiscussionsTags

A $10 Ω$ 20 mH coil carrying constant current is connected to a battery of 20 V through a switch. Now after switch is opened current becomes zero in 100 $μ s .$ The average e.m.f. induced in the coil is__________V.

1 Answer

Learn more about...

Most viewed information

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question

A 1 0 Ω 20 mH coil carrying constant current is connected to a battery of 20 V through a switch. Now after switch is opened current becomes zero in 100 μ s . The average e.m.f. induced in the coil is__________V.

1 Answer

Learn more about...

Most viewed information

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question

A $10 Ω$ 20 mH coil carrying constant current is connected to a battery of 20 V through a switch. Now after switch is opened current becomes zero in 100 $μ s .$ The average e.m.f. induced in the coil is__________V.