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,