Question

You are given an air filled parallel plate capacitor C1. The space between its plates is now filled with slabs of dielectric constants K1 and K2 as shown in C2 . Find the capacitances of the capacitor C2 if area of the plates is A and distance between the plates is d.

Answer 1

The space between the parallel plates of capacitor is air: 
   capacitance = C₁

Now the space is filled by two slabs of equal width (d/2) and of same area A as that of the parallel plates.

$C_2=\frac{\epsilon_0 A}{\frac{d}{2K_1}+\frac{d}{2K_2}}\\\\=\frac{2 \epsilon_0 A}{d}*(\frac{K_1 K_2}{K_1+K_2})$

If the dielectric slabs are occupying an area of A/2 and the entire width d, that means the dielectric slabs are side by side.  Then it is like two half-capacitors are connected in parallel.  So their capacitances add.

$C_2=\frac{\epsilon_0 A/2}{\frac{d}{K_1}}+\frac{\epsilon_0(A/2)}{\frac{d}{K_2}}\\\\=\frac{\epsilon_0 A}{2d}*(K_1+K_2)$

Answer 2

Explanation:

this is your answer best of luck