An unchanged capacitor with a solid dielectric is connected to a similar air capacitor charged to a potential of `V_(0).`. If the common potential after sharing of charges becomes V, then the dielectric constant of the dielectric must be

Options

A. `(V_(0)-V)/V`
B. `(V_(0)+V)/V`
C. `V_(0)/V`
D. `V_(0)/(2V)`

Answer

A

Explanation

`V=(C_(1)V_(1)+C_(2)V_(2))/(C_(1)+C_(2))`
`=(CKxx0+CV_(0))/(CK+C)=(CV_(0))/(C(K+1))=V_(0)/(K+1)`
`K=(V_(0)-V)/V`