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Question



As shown in the figure, a battery of emf ϵ is connected to an inductor L and resistance R in series. The switch is closed at t=0. The total charge that flows from the battery, between t=0 and t=tc (tc is the time constant of the circuit) is

A
ϵLR2e
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B
ϵLR2(11e)
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C
ϵLR2
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D
ϵReL2
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Solution

The correct option is A ϵLR2e
For series connection of a resistor and inductor, time variation of current is I=I0(1et/tc)=ϵR(1et/tc)

Here, tC=LR

q=Tc0Idt

dq=ϵR(1et/tc)dt

q=ϵR[t+tCet/tc]tc0

q=ϵR[tC+tCetC]

q=ϵRLRe

q=ϵLR2 e

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