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} $
