A coil of inductance 2H and negligible resistance is connected to a source of supply whose voltage, in volt, is given by V=4t. If the voltage is applied when t=0 then the energy stored in the coil in 4s is ___ joule.

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answer is 256.

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Detailed Solution

$V_{L} = L \frac{dI}{dt}$
$4 t = 2 \frac{dI}{dt} \Rightarrow dI = 2 tdt \Rightarrow I = \int dI \Rightarrow I = 2 \int_{0}^{4} tdt$
$\begin{array}{l} = \frac{2 (16)}{2} = 16 A \\ U = \frac{1}{2} {LI}^{2} = \frac{1}{2} (2) (16)^{2} = 256 J \end{array}$

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