In the figure shown below, find out the current as function of time and charge on capacitor `C_1 `and also plot the graph of charge on plate A and B of capacitor `C_2` as a function of time.

Explanation

Let at any time charge on `C_(1)=q`
Now apply, K.V.L. `-I R -q/c -((q-2epsiC))/(C)+epsi=0`
`3e=(2q)/(c)+iR rArr 3eC=2q+iRC`

` 3eC=2q+iRC raRR underset(0)overset(q)int (dq)/(3eC-2q)= underset(0)overset(t)int (dt)/(RC)`
`=(ln(3eC-2q))/(2) underset(0)overset(q)int =t/(RC)`
`3eC-2q=3eCe^(-2t//RC)`
`rArr q=(3eC)/(2) (1-e^(-2t//RC)`
`i=(dq)/(dt)=(3e)/(R) e^(-2tt/RC)`
At plate A, Charge `q_(A)=q-2eC=3/2 eC(1-e^(-2t//RC)-2eC`

`=-(ec)/(2)-(3ec)/(2) e^(-2t//RC)`
`q_(A)=-(ec)/(2)(1+3e^(-2t//RC))`
`q_(B)=(ec)/(2)(1+3e^(-2t//RC)`