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

Answer

C

Explanation

`"Common potential, V"=("Total charge")/("Total capacitance")`
`V=(C_(1)V_(1)+C_(2)V_(2))/(C_(1)+C_(2))=(0+CV_(0))/(KC+C)`
`K=(V_(0))/(V)-1=(V_(0)-V)/(V)`