A parallel plate capacitor is of area 6 `cm^(2)` and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constant `K_(1)=10`, `K_(2)=12 and K_(3) = 14`. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be :

Explanation

`C = 7 xx (A/3 epsi_0)/(d) + 15 xx A/3 (epsi_0)/(d) + 5 xx A/3 (epsi_0)/(d) = 27 xx A/3 (epsi_0)/(d) = (9A epsi_0)/(d)`