An uncharged parallel plate capacitor having a dielectric of dielectric constant `K` is connected to a similar air core parallel plate capacitor charged to a potential `V_(0)`. The two share the charge, and the common potential becomes `V`. The dielectric constant `K` is`

Options

A. `(V-V_(1))/(V_(1))`
B. `(V_(1)-V)/(V_(1))`
C. `(V_(1)-V)/(V_(1)+V)`
D. `(V_(1)-V)/(V)`

Answer

A

Explanation

Common potential`=V_(1)=(C_(1)(0)+C_(2)(V))/(C_(1)+C_(2))`
`C_(1)=(Kepsi_(0)A)/(d), C_(2)=(epsi_(0)A)/(d)" , "V_(1)=(((Kepsi_(0)A)/(d))(0)+((epsi_(0)A)/(d))(V))/((Kepsi_(0)A)/(d)+(epsi_(0)A)/(d))`
`V_(1)=(V)/(K+1) implies K+1=(V)/(V_(1)) " "therefore K=(V-V_(1))/V_(1)`.