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")`
`thereforeV=(C_(1)V_(1)+C_(2)V_(2))/(C_(1)+C_(2))=(0+CV_(0))/(KC+C)`
`=(CV_(0))/(C(1+K))` or `V=(V_(0))/(1+K)`
`impliesK+1=(V_(0))/(V) impliesK=(V_(0))/(V)-1=(V_(0)-V)/(V)`