Consider the circuits shown in figure. Find
(a)
(b)
(c )
(d)
(i) currents through resistances immediately after closing the switch
(ii) Currents through resistaces after a long time ie., steady state.

Explanation

`(x)` at `t=0` capacitor offers zero resistance ie., repalce it by a wire and solve
`(y)` at `t=oo` i.e., steady state, capacitor offers inifinite resistance or no current flows in the branch containing capacitor. (a)
(i) `t=0`

`i_(1) = E/(3R)`
`i_(2)=E/(6R)`
(ii) `t=oo`

`i_(1) = E/(3R)` ltbr .`i_(2) = 0`
(b)
(i) `t = 0`

`i_(1)=E/(9R)`
`i_(2) = E/(18R)`
(ii) `t = oo`

`i_(1)=0`
`i_(2) = E/(18R)`
(c)
(i)`t=0`

`i = (E)/(R+2R) = E/(3R)`

`i_(1) = (6R)/(3R+6R) i = (2E)/(9R)`
`i_(2) = i - i_(1) = E/(9R)`
`(ii)t = oo`

`i_(0)`
`i_(2) = E/(R+6R) = E/(7R)=i_(2)`
(i)` t=0`

`i_(1)=0`
`i_(2) = 0`
`i =E/R`
(ii) `t=oo`
`i_(1)=0`
`i_(2) =0`
`i=E/(R+2R) = E/(3R)`.