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Questions  

In the circuit shown, switch S is closed at time t = 0. The charge which passes through the battery in one time constant is

a
eR2EL
b
ELR
c
ELeR2
d
eLER

detailed solution

Correct option is C

The current at time t is given byi=i01-e-t/τ Where i0=ER and τ=LR So dQ=idt=i01-e-t/τdtQ=∫dQ=∫0τi01-et/τdt=i0∫0τdt-∫0τe-t/τdt⇒Q=ER·LRe=ELeR2⇒Q=ELeR2

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