IIT JEE , AIEEE Forum - Physics , Electricity

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At any time t the charge is given by :

q = A + Be^-t/T
where A and B are some constants to be found out and T is the time-constant of the circuit which is RC.

At t=0, q = Q
A + Be^-0/T = Q
A + B = Q ...................(1)

When t tends to infinity, potential difference across capacitor is E.
So q = EC
q = A + Be^-infinity/T = A = EC.............(2)

From (1) and (2) :
A = EC and B = Q - EC

Hence, q = A + Be^-t/T
q = EC + (Q-EC)e^-t/T

q = EC(1 - e^-t/RC) + Qe^-t/RC

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