An uncharged parallel plate capacitor filled with a dielectric of dielectric constant `K` is connected to an air filled identical parallel capacitor charged to potential `V_1`. If the common potential is `V_2`, the value of `K` is

Options

A. a)`(V_1 - V_2)/( V_1)`
B. b)`(V_1)/( V_1 - V_2)`
C. c)`(V_2)/( V_1 - V_2)`
D. d)`(V_1 - V_2)/(V_2)`

Answer

D

Explanation

Here,
`V_2 = ((CV_1 + 0))/( (C + KC))`
`V_2 = (V_1)/( 1+ K)`
`(V_2)/(V_1) = (1)/( 1+K)`
`1+ K = (V_1)/( V_2)`
`K= (V_1)/(V_2) -1`
`k= (V_1-V_2)/(V_2)`