Two condensers `C_(1)` and `C_(2)` in a circuit are joined as shown in figure. The potential of point `A` is ` V_1` and that of `B` is ` V_2` . The potential of point `D` will be `

Options

A. `(1)/(2) (V_(1) + V_(2))`
B. `(C_(2)V_(1) + C_(1)V_(2))/(C_(1) + C_(2))`
C. `(C_(1)V_(1) + C_(2)V_(2))/(C_(1) + C_(2))`
D. `(C_(2)V_(1) - C_(1)V_(2))/(C_(1) + C_(2))`

Answer

C

Explanation

Charge on `C_(1) =` charge on `C_(2)`
`rArr C_(1) (V_(A - V_(D)) = C_(2) (V_(D) - V_(B))`
`rArr C_(1) (V_(1) - V_(D)) = C_(2) (V_(D) - V_(2)) rArr V_(D) = (C_(1)V_(1) + C_(2)V_(2))/(C_(1) + C_(2))`