A parallel-plate capacitor is filled with two dielectrics as shown in the figure. We have to show that its capacitance is given by

Solution:             Click For PDF Version

Let the area of the plates of the capacitor be A and separation of its plates be d. Let it be filled with materials having dielectric constants and as shown in the figure.

For calculating the capacitance of this capacitor we will consider that it is equivalent to two capacitances each of area and containing materials of dielectric constants and , respectively, which are connected in parallel. Therefore, the capacitance of the combination will be