Find out current `I_1 , I_2, I_3, ` charge on capacitor and ` (dQ)/(dt) ` of capacitor in the current when it is initially uncharged in the following situations.

(a) Just after the switch is closed
(b) After a long time when switch is closed.

Explanation

Initially the capacitor is uncharged so its behaviour is like a conductor.
Let potential at A is zero so at B and C also zero and at F it is `epsi`. Let potential at E is x so at D also x.
`(x-e)/(R)+(x-0)/(R)+(x-0)/(R)=0`
`(3x)/(R)=(e)/(R)`
`x=e/3, Q_(c)=0`
`therefore I_(1)=(-e//3+e)/(R)=(2e)/(3R)`
`I_(2)=(dQ)/(dt)=(e)/(3R), I_(3)=(e)/(3R)`