Two parallel palate capacitors `X` and `Y` have the same area of plates and same separation between then. `X` has air between the plates and `Y` contains a dielectric medium of `in_(r) = 4,`

Calculate (i) capacitance of `X` and `Y` if equivalent capacitance fo combination is `4 mu F`. (ii) pot diff between the plates of `X` and `Y`. (iii) What is the ratio of electrostatic energy stored in `X` and `Y` ?

Answer

`5 mu F, 20 mu F, 9.6 V, 2.4 V ; 4 : 1`

Explanation

`C_(1)` is capacity of `X , C_(2)` is capacity of `Y` fig.
`C_(2) = 4 C_(1)`.
As `(1)/(C_(s)) = (1)/(C_(1)) + (1)/(C_(2)) :. (1)/(4) = (1)/(C_(1)) + (1)/(4 C_(1)) = (5)/(4 C_(1))`
`C_(1) = 5 mu F , C_(2) = 20 mu F`
`q_(1) = q_(2) = C_(s) V = 4xx12 = 48 mu C`
`V_(1) = (q_(1))/(C_(1)) = (48)/(5) = 9.6 V, V_(2) = (q_(2))/(C_(2)) = (48)/(20) = 2.4 V`
`(U_(1))/(U_(2)) = (C_(2))/(C_(1)) = 4`