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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 ϵLR2eFor series connection of a resistor and inductor, time variation of current is I=I0(1−e−t/tc)=ϵR(1−e−t/tc) Here, tC=LR q=Tc∫0Idt ⇒ ∫dq=∫ϵR(1−e−t/tc)dt ⇒q=ϵR[t+tCe−t/tc]tc0 ⇒q=ϵR[tC+tCe−tC] ⇒q=ϵRLRe ∴q=ϵLR2 e

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