(a) Find the equivalent capacitance of the combination between A and B in the figure

If the points A and B are maintained at 15 V and 0 V respectively then
(b) Find the charges on `3mu F, 4 mu F "and " 5 muF ` capacitors
(c ) What are the potentials of the points C and D ?

Explanation

The simplified form of the given combination has been shown in the figure (b )
Here `(C_(1))/(C_(2))= (2muF)/(4mu F) = (1)/(2)`
`(C_(3))/(C_(4))=(3muF)/(6 muF) =(1)/(2)`

Thus `(C_(1))/(C_(2))=(C_(3))/(C_(4))`
Hence (a) `C_(eq)= (C_(1)C_(2))/(C_(1)+C_(2))+(C_(3)C_(4))/(C_(3)+C_(4))`
`=((2xx4)/(2+4)+(3xx6)/(3+6))muF=((4)/(3)+2)muF=(10)/(3)muF`
(b ) `V_(A)-V_(B)= 15 V `
`:.` The charge on `(4)/(3)muF` capacitor is
`q_(1)=((4)/(3)muF)(15V) = 20 muC `

Hence the charge on `4muF` capacitor in figure ( c) is also `q_(1) = 20 muC `
The charge on 2`muF` capacitor in figure (d) is
`q_(2) = (2muF) (15 V) =30 muC`
So the charge on the `3mu F` capacitor in figure ( c) is also
`q_(2) = 30 muC `
The charge on `5 muF ` capacitor is zero .
Hence our answer are `30mu C ` on `3 mu F` capacitor `20 mu C` on 4 `muF` capacitor and zero on `5muF` capacitor .
(c ) The potential difference across `3mu F ` capacitor of figure ( c) is

`V_(A)-V_(C) =(30muC)/(3 muF) = 10 V`
or `15 V- V_(C) = 10 V `
`implies V_(C) = 5 V`