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

Explanation

(a) In the given network, `C_1, C_2` and `C_3` are connected in series. The effective capacitance C. of these three capacitors is given by
`(1)/(C.) = (1)/(C_1) + (1)/(C_2) + (1)/(C_3)`
For `C_1 = C_2 = C_3 10 muF, C. = (10//3) muF` . The network has C. and `C_4` connected in parallel. Thus, the equivalent capacitance C of the network is
`C = C. +C_4 = (10/3 + 10)mu F = 13.3 mu F`
(b) Clearly, from the figure, the charge on each of the capacitor, `C_1, C_2` and `C_3` is the same, say Q. Let the charge on `C_4` be Q.. Now, since the potential difference across AB is Q/C, across BC is `Q//C_2` across CD is `Q//C_3`, we have
`(Q)/(C_1) + (Q)/(C_2 ) + (Q)/(C_3) = 500V`
Also `Q.//C_4 = 500V`
This gives for the given value of the capacitances.
`Q = 500 V xx 10/3 muF = 1.7 xx 10^(-3) C`
`Q. = 500 V xx 10 muF = 5.0 xx 10^(-3) C`