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  • The current in a coil of self inductance is increasing according to <img alt="I=2 \sin \lef

The current in a coil of self inductance 2.0 \mathrm{H} is increasing according to I=2 \sin \left(t^{2}\right) A. The amount of energy spent during the period when current changes from 0 \: to \: 2 \mathrm{~A} is__________ J.

Option: 1

4


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\mathrm{e= \left | L\left ( \frac{di}{dt} \right ) \right |= 2\times 2\left [ \cos \left ( t^{2} \right ) \right ]2t}
\mathrm{e= 8\left [ \cos \left ( t^{2} \right ) \right ]t}

\mathrm{dH= ei\, dt}
\mathrm{dH= 16t\, \sin \left ( t^{2} \right )\cos \left ( t^{2} \right )dt}
\mathrm{dH= 8t\, \sin \left ( 2t^{2} \right )dt}

\mathrm{\left.\begin{matrix} Put,2t^{2}= x\\ 4t\: dt= dx \\ \int dH= \int_{0}^{\pi}2\, \sin \left ( x \right )dx \end{matrix}\right|\begin{matrix} When\\I= 0,t^{2} = 0 \\x= 0 \\ I= 2,t^{2}= \frac{\pi}{2} \\x= \pi \end{matrix}}

\mathrm{H= 2\left [ -\cos x \right ]_{0}^{\pi}}
      \mathrm{= 2\left ( -\cos \pi -\left ( -\cos 0^{\circ} \right ) \right )}
\mathrm{H= 4\, J}

Posted by

Rishabh

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