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Question

A simple LR circuit is connected to a battery at time t=0. The energy stored in the inductor reaches half its maximum value at time

A
RLln[221]
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B
LRln[212]
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C
LRln[221]
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D
RLln[212]
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Solution

The correct option is A LRln[221]
RL circuit analysis :-
Kirchhoff's Volatage Law;
ViRLdidt=0;
ViR=Ldidt
1Ldt=1ViRdi
t01Ldt=i01ViRdi
tLR=ln(ViRV)
eRtL=ViRV
iR=V(1eRtL);
i=VR(1eRtL);
When t,iVR
Energy stored in an inductor =Li2/2
Energy stored reaches half ita maximum value when i becomes V2R.
thus,
VR2=VR(1eRtL).
1eRtL=12
112=eRtL
ln(112)=RtL
t=LRln(221)

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