Average energy stored in a pure inductance L | vedclass

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(D) The energy stored in an inductor is derived from the work done against the induced back electromotive force $(e.m.f.)$.The induced $e.m.f.$ in an

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$\frac{1}{2}L{i^2}$

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(D) The energy stored in an inductor is derived from the work done against the induced back electromotive force $(e.m.f.)$.The induced $e.m.f.$ in an inductor is given by $e = -L \frac{di}{dt}$.The work done $dW$ to increase the current by $di$ in time $dt$ against this back $e.m.f.$ is $dW = -e \cdot i \cdot dt$.Substituting the expression for $e$,we get $dW = -(-L \frac{di}{dt}) \cdot i \cdot dt = L \cdot i \cdot di$.To find the total energy $U$,we integrate from current $0$ to $i$:$U = \int_0^i L \cdot i \cdot di = L \left[ \frac{i^2}{2} \right]_0^i = \frac{1}{2} L i^2$.

Average energy stored in a pure inductance $L$ when a current $i$ flows through it,is

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