Two parallel plate capacitors X and Y have the same area of plates and same separation between them.
X has air between the plates while Y contains a dielectric medium of `e_(r ) = 4`

(i) Calculate capacitance of aech capacitor if equivalent capacitance of the combination is `4mu_(F)`
(ii) Calculate the potential difference between the plates of X and Y
(iii) Estimate the ratio of electrostatic energy stored in X and Y .

Explanation

`"(i) Let "" "X =C`
`"then "" " Y= Er C =4C`
Let C be the equivalent capacitance.
`(1)/(C ) = (1)/(C )+(1)/(4C) " " rArr " "C '=(4C)/(5)`
`" but " C '= 4 mu F " so " , (4C)/(5)=4 " "rArr " "C =5 mu F`
`rArr X =5 mu F " ", " "Y=20 mu F`
(ii) In series `q= CV " so " V prop .(1)/(C )`
`rArr V_(x) : V_(y) = C_(y): C_(x) =20 : 5 = 4:1`
So, `V_(x) =(4)/(5) xx 15 =12 V " ", " " V_(y) =(1)/(5) xx 15 =3 V`
(iii) In series Q is constant
So `, U_(x): U_(y) = (1)/(2) .(Q^(2))/(C_(x)) : (1)/(2),(Q^(2))/(C^(y)) =C_(y) : C_(x) =4:1`