Find currents through resistors
(i) immediately after closing the switch
(ii) after a long time.

Explanation

(a) At `t=0` capacitor offers zero resistance i.e. it can be replaced by wire.

`I = E/(R+2R) = E/(3R)`
`V = I xx 2R = (2E)/(3)`

`i_(1) = (2E//3)/(3R) = (2E)/(9R)` ltbr. `i_(2) = (2E//3)/(6R) = E/(9R)`
(b) After a long time i.e., `t = oo`, capacitor, offers infinte resistance. No current flows through the resistance in series with capacitor

`i = (E)/(R+3R) = E/(4R)` gt