A capacitor or capacitance `C_(1)` is charge to a potential V and then connected in parallel to an uncharged capacitor of capacitance `C_(2)`. The fianl potential difference across each capacitor will be

Options

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

Answer

A

Explanation

The charge remains constant in the first and second case.
`therefore Q=C_(1)V=C'V'` where `C'=C_(1)+C_(2)`
`therefore (C_(1)+C_(2))V'=C_(1)V`
`therefore V'=(C_(1)V)/(C_(1)+C_(2))`