Find the charges on the three capacitors shown in figure

Explanation

Let a charge `q_(1)` flows through cell of voltage V and a charge `q_(2)` flows through cel of voltage 2V.
From circuit diagram
Applying Kirchhoff's first law at point B
`q_(3) = q_(1)+ q_(2)` ....(i)
Applying Kirchhoff's 2nd law in loop ABEFA
`-(q_(1))/(C ) - ( q_(3))/( 3C) + V = 0`
or `3q_(1) + q_(3) = 3CV ` ....(ii)
From equation (i)
`3q_(1) ( q_(1) +q_(2))= 3CV`
or ` 4 q_(1) + q_(2) = 3CV ` ....(iii)
Applying Kirchhoff's 2nd law in loop DEBCD
`-2 V + ( q_(3))/( 3C)+ ( q_(2))/( 2C) = 0`
or `3q_(3) + 2q_(3) = 12 CV` ....(iv)

From equation (ii) and (iv)
`{:(,4q_(1),+,q_(2),=,3CV),(,"-"4q_(1),"_"+,10q_(2),=,"_"24CV):}`
`bar(-9q_(2) = -21 CV )impliesq_(2) = (7)/(3) CV`
From equation (iii)
`4 q_(1) +(7)/(3) CV = 3CV`
` 4q_(1) = 3CV - ( 7)/( 3) CV = ( CV - 7CV)/(3) = (2)/(3) CV`
`q_(1) = ( CV)/( 6) ` and ` q_(3) = q_(1)+q_(2) = (CV)/(6)+ ( 7)/( 3) CV= ( CV)/( 6) + ( 14)/( 6) CV =( 15)/( 6) CV = ( 5)/( 2) CV`