Electro Magnetic Induction And Alternating Currents Question 523

Question: Average energy stored in a pure inductance L when a current i flows through it, is [MP PET/PMT 1988]

Options:

A) $ Li^{2} $

B) $ 2Li^{2} $

C) $ \frac{Li^{2}}{4} $

D) $ \frac{Li^{2}}{2} $

Show Answer

Answer:

Correct Answer: D

Solution:

As we know $ e=-\frac{d\varphi }{dt}=-L\frac{di}{dt} $

Work done against back e.m.f. e in time dt and current i is
$ dW=-eidt=L\frac{di}{dt}idt=Li\ di $
$ \Rightarrow \ W=L\int_{0}^{i}{i\ di}=\frac{1}{2}Li^{2} $



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