A coil of inductance 2, H having negligible r | vedclass

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(A) The induced electromotive force $(EMF)$ in an inductor is given by $\varepsilon = L \frac{dI}{dt}$.Since the resistance is negligible,the applied

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$144$

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(A) The induced electromotive force $(EMF)$ in an inductor is given by $\varepsilon = L \frac{dI}{dt}$.Since the resistance is negligible,the applied voltage $V$ is equal to the induced $EMF$ $\varepsilon$,so $V = L \frac{dI}{dt}$.Given $V = 3t$ and $L = 2\, H$,we have $3t = 2 \frac{dI}{dt}$.Rearranging the terms,we get $dI = \frac{3}{2} t \, dt$.Integrating both sides from $t = 0$ to $t = 4\, s$ and $I = 0$ to $I = I_f$:$\int_{0}^{I_f} dI = \int_{0}^{4} \frac{3}{2} t \, dt$$I_f = \frac{3}{2} \left[ \frac{t^2}{2} ight]_{0}^{4} = \frac{3}{4} (16) = 12\, A$.The energy stored in the coil is given by $U = \frac{1}{2} L I_f^2$.$U = \frac{1}{2} 	imes 2 	imes (12)^2 = 144\, J$.

$A$ coil of inductance $2\, H$ having negligible resistance is connected to a source of supply whose voltage is given by $V = 3t$ volt (where $t$ is in seconds). If the voltage is applied when $t = 0$,then the energy stored in the coil after $4\, s$ is ............ $J$.

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