A parallel plate capacitor has plate area A and plate separation d. The space between the plates is filled up to a thickness x (ltd) with a dielectric constant K. Calculate the capacitance of the system.

Explanation

The situation is shown in . The given system is equivalent to the series combinaton of two capacitors, one between a and c and the other between c and b. Here c represents the upper surface of the dielectric. This is because the potential at the upper surface of the dielectric is constant and we can imagine a thin metal plate being placed there. The capacitance of the capacitor between a and c is `
`C_1 = (Kepsilon_o A)/(x)`
` and the between c and b is `
`C_2 = (epsilon_0A)/(d-x)`
`. The equivalent capacitance is `
`C=(C_1C_2)/(C_1 +C_2) = (Kepsilion_A)/(Kd - x(K-1)`
`.