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 ε r ​ = 4. (i) Calculate capacitance of each capacitor if equivalent capacitance of the combination is 4 μF. (ii) Calculate the potential difference between the plates of X and Y. (iii) Estimate the ratio of electrostatic energy stored in X and Y.

Answer

(March 2014)

Explanation

i. Let V be the p.d. across X. Then p.d. across Y will be `V/5`.
`therefore V+V/5="12 volt "rArr (6V)/(5)="12 volt or V=10volt"`
p.d. across X=10 volt
p.d. across `Y=(10)/(5)="2 volt"`
ii. `("Energy stored in X")/("Energy stored in Y")=(1/2 C(10)^(2))/(1/2 5C(2)^(2))=(100)/(20) 5:1 [therefore E=1/2 CV^(2)]`