Two parallel plate capacitors X and Y, have the same area of plates and same separation between plates. X has air and Y with dielectric of constant 2 , between its plates. They are connected in series to a battery of 12 V. The ratio of electrostatic energy stored in X and Y is-

Options

A. `4:1`
B. `1:4`
C. `2:1`
D. `1:2`

Answer

C

Explanation

Given

`V=12V`
`C_(1)=epsi_(0)(A)/(d).C_(2)=K epsi_(0)(A)/(d)=2C_(1)`
In series charge **q** is constant.
`U_(1)=(Q^(2))/(2C)=(Q^(2))/(2C_(1))`
`U_(2)=(Q^(2))/(2C)=(Q^(2))/(4C_(1))`
`:. (U_(1))/(U_(2))=(Q^(2))/(2C_(1))xx(4C_(1))/(Q^(2))xx(4C_(1))/(Q^(2))=2:1`