  Question

# A parallel plate capacitor of area A, plate separation d and capacitance C is filled with three different dielectric materials having dielectric constants as shown. If a single dielectric material is to be used to have the same capacitance C in this capacitor then its dielectric constant K is given by  A

B

C

D

## K =

Medium
Solution Verified by Toppr
Correct option is D)

## 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   0 0