A) \[L{{i}^{2}}\]
B) \[2L{{i}^{2}}\]
C) \[\frac{L{{i}^{2}}}{4}\]
D) \[\frac{L{{i}^{2}}}{2}\]
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 \[dW=-eidt=L\frac{di}{dt}idt=Li\ di\] \[\Rightarrow \ W=L\int_{0}^{i}{i\ di}=\frac{1}{2}L{{i}^{2}}\]
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