In a L−R decay circuit, the initial current at t = 0 is I. The total charge that has flown through the resistor till the energy in the inductor has reduced to one−fourth of its initial value, is
Physics · Electromagnetic Induction
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Question

In a L−R decay circuit, the initial current at t = 0 is I. The total charge that has flown through the resistor till the energy in the inductor has reduced to one−fourth of its initial value, is

G1 Physics · Accepted Answer

During LR decay, i=I e^(−Rt/L). When inductor energy becomes one-fourth, current becomes I/2. Therefore q=∫i dt=(LI/R)(1−1/2)=LI/(2R). Hence option B.