Three identical capacitors `C_(1) , C_(2)` and `C_(3)` of capacitance `6 mu F` each are connected to a `12 V` battery as shown in Fig. Find

(i) charge on each capacitor
(ii) equivalent capacitance of the network.
(iii) energy stored in the network of capacitors.

Answer

`q_(1) = q_(2) = 36 mu C`; `q_(3) = 72 mu C ; 9 mu F ; E_(1) = E_(2) = 108 mu J, E_(3) = 432 mu J`

Explanation

As is clear from Fig `C_(1), C_(2)` are in series.
`:. (1)/(C_(s)) = (1)/(C_(1)) + (1)/(C_(2)) = (1)/(6) + (1)/(6) = (1)/(3), C_(s) = 3 muF`
`q_(1) = q_(2) = C_(s) xx V = 3xx12 = 36 mu C`,
`q_(3) = C_(3) V = 6xx12 = 72 mu C`
(ii) `C_(3)` is parallel combination of `C_(1)` and `C_(2)`.
`:. C_(p) = C_(3) + C_(s) = 3 + 6 = 9 mu F`
(iii) `U_(1) = U_(2) = (1)/(2) q_(1) V = (1)/(2) q_(2) V`
`= (1)/(2) xx36xx3 = 108 mu J` ,
`U_(3) = (1)/(2) C_(3) V^(2) = (1)/(2)xx6xx12^(2) = 432 mu J`