The current in a coil of self… - JEE Main 2022 Physics PYQ

JEE Main 2022 — Physics Electromagnetism

2022integerhard

The current in a coil of self inductance $L=2.0H$ is increasing according to the law $i=2\mathrm{sin}({t}^{2})$ . Find the amount of energy spent (in $J$ ) during the period when the current changes from $0$ to $2A$ .

Official previous-year question

Held on 25 Jun 2022 · Verified 6 Jul 2026.

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Solution

Let the current be $2A$ at $t=\tau$

Then $2=2sin{\tau }^{2}\Rightarrow \tau =\sqrt{\pi /2}$

when the instantaneous current is $i$ , the

self-induced emf is $L\frac{di}{dt}.$ If $dq$ amount of

charge is displaced in time $dt$ , then elementary work done

$=(L\frac{di}{dt})dq=L\frac{di}{dt}idt=$ $Lidi$

$\displaystyle \therefore W={\int }_{0}^{t}Lidi$ $\displaystyle ={\int }_{0}^{t}L2sin{t}^{2}d(2sin{t}^{2})$

$\Rightarrow W={\int }_{0}^{t}8Lsin{t}^{2}cos{t}^{2}tdt=4L{\int }_{0}^{t}sin2{t}^{2}dt$

Let $\theta =2{t}^{2}\Rightarrow d\theta =4tdt$

$\therefore$ the integral

$=4L\int sin\theta dt/4L(-cos\theta )=-Lcos2{t}^{2}$

$\therefore W=-{[cos2{t}^{2}]}_{0}^{\sqrt{\pi /2}}=2L=4J$

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JEE Main 2022 — Physics Electromagnetism

2022integerhard

Official previous-year question

Held on 25 Jun 2022 · Verified 6 Jul 2026.

Did you get this right?

Solution

Let the current be $2A$ at $t=\tau$

Then $2=2sin{\tau }^{2}\Rightarrow \tau =\sqrt{\pi /2}$

when the instantaneous current is $i$ , the

self-induced emf is $L\frac{di}{dt}.$ If $dq$ amount of

charge is displaced in time $dt$ , then elementary work done

$=(L\frac{di}{dt})dq=L\frac{di}{dt}idt=$ $Lidi$

$\displaystyle \therefore W={\int }_{0}^{t}Lidi$ $\displaystyle ={\int }_{0}^{t}L2sin{t}^{2}d(2sin{t}^{2})$

$\Rightarrow W={\int }_{0}^{t}8Lsin{t}^{2}cos{t}^{2}tdt=4L{\int }_{0}^{t}sin2{t}^{2}dt$

Let $\theta =2{t}^{2}\Rightarrow d\theta =4tdt$

$\therefore$ the integral

$=4L\int sin\theta dt/4L(-cos\theta )=-Lcos2{t}^{2}$

$\therefore W=-{[cos2{t}^{2}]}_{0}^{\sqrt{\pi /2}}=2L=4J$

Your note

JEE Main Electromagnetism in other years

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Solution

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Solution

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JEE Main Electromagnetism in other years

More JEE Main Electromagnetism questions

Other Physics topics for JEE Main

Mechanics

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

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