A capacitor of capacitance C is given a charge Q. At `t=0`,it is connected to an uncharged of equal capacitance through a resistance R. Find the charge on the second capacitor as a function of time.

Explanation

Let charge on the second
capacitor at any time t be q, then
the remainig charge on first
capacitor will be Q - q. the current in the cirucit at any time
is `I = dq//dt.` Applying Kirchhoff's
law, we get

`(Q - q)/(C ) = (q)/(C ) + IR or(Q-2q)/(C ) =(dq)/(dt) R or int_0^q (dq)/(Q-2q) = int_0^t (dt)/(RC)`
Solving we get `q =(Q)/(2)(1^(-2t//RC))`