The common mistake students do in this problem is that they assume and in parallel and their combination in series with . Which is completely wrong method. [Refer Fig. 1]
For two capacitors to be taken in parallel, their both ends should be at same potential.
Here, the upper ends of and are at same potential as they are connected to A through a metal plate.
But their lower ends being connected to a dielectric are not at same potential. As Electric field will be different in both dielectrics and , since .
Hence, To solve this problem, we divide dielectric in two equal parts as shown in figure 2. So,
Now, From figure, Clearly, we can assume and in series and and , further their combinations will be in parallel.
Combining series combinations in figure 3, we get:
Putting values of and from Step
Hence equivalent dielectric constant will be as given in Option