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

Concepts/Formulas used:


Kirchhoff’s loop rule:


The sum of potential differences around a closed loop is zero.


Capacitance:


If two conductors have a potential difference V between the them and have charges Q and -Q respectively on them, then their capacitance is defined as




Note that



and



By conservation of charge,



       ………………..(1)


Now, applying Kirchhoff’s loop rule, we get




Using (1), we get





where A is a constant.




Let



Substituting , we get B = -Q


Hence,



1