A network of four `10 muF` capacitors is connected to a 500V supply as shown in Fig. Determine the (a) equivalent capacitance of the network and (b) charge on each capacitor.

Explanation

(a) In fig. `C_(1) , C_(2), C_(3)` are connected in series
`:. (1)/(C_(s)) = (1)/(C_(1)) + (1)/(C_(2)) +(1)/(C_(3)) = (3)/(10)`
`C_(s) = (10)/(3) muF`
This combination is in parallel with `C_(4)`
`:.` Equivalent capacitanace, `C = C_(s) + C_(4)`
`= (10)/(3) + 10 = 13.3 muF`
(b) charge on `C_(1), C_(2). C_(3)` is same = Q say
Let charge on `C_(4)` be Q'.
`:. (Q)/(C_(1)) + (Q)/(C_(2)) + (Q)/(C_(3)) = 500`
`Q((1)/(C_(s))) = 500`
or `Q = 500 C_(s) = 500xx(10)/(3) muC = 1.7xx10^(-3) C`
Also , `(Q)/(C_(4)) = 500, Q = C_(4)xx500 = 10xx500 mu C`
`= 5xx10^(-3)C`