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In the circuit shown in figure switch S ...

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

Text Solution

Verified by Experts

The correct Answer is:
`(EL)/(eR^(2))`
`I=E/R(1-e^(-t//tau))` and `Deltaq=int_(0)^(tau)Idt`
so `Deltaq=int_(0)^(tau)E/R(1-e^(-t//tau))dt=E/Rint_(0)^(tau)(1-e^(-t//tau))dt`
`=E/R[(t)_(0)^(t)+tau(e^(-t//tau))_(0)^(tau)]`
`=E/R[tau+tau(e^(-1)-1)]=E/Rtau/e put tau=L/R`
so `Deltaq=(EL)/(R^(2)e)`
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