A capacitor of `20 muF` is charged to `500` volts and connected in parallel ith another capacitor of `10 muF` and charged to `200` volts. The common potential is

Options

A. 400 V
B. 200 V
C. 100 V
D. 50 V

Answer

A

Explanation

Suppose `C_(1) and C_(2)` are capacities of two condensers charged to potentials `V_(1) and V_(2)`. Respectively. Total charge before sharing `=C_(1)V_(1)+C_(2)V_(2)`
If V is the common poetnial on sharing charges, then total charge after sharing `=C_(1)V+C_(2)V=(C_(1)+C_(2))V`
As mo charge is lost in the process of sharing, therefore
`(C_(1)+C_(2))V=C_(1)V_(1)+C_(1)V_(1)+C_(2)V_(2)`
`therefore" "V=(C_(1)V_(1)+C_(2)V_(2))/(C_(1)+C_(2))`
`=((20xx10^(-6)xx500)+(10xx10^(-6)xx200))/((20xx10^(-6))+(10xx10^(-6)))`
= 400 V