Calculating capacitance of capacitor filled with 2 dielectrics

[darkv0id]

Homework Statement

A capacitor is formed by 2 square metal plates of edge a and separated by distance d. Dielectrics of dielectrics constants K₁ and K₂ are filled in the gap as shown.

2. The attempt at a solution

This was my initial approach:

I integrated the parallel combination of elemental capacitors dC₁ and dC₂, but I didnt get the correct answer.

Next, I tried taking the elemental capacitors in series instead of parallel:

This time my answer turned out to be correct.

Can someone help me identify the flaw in my initial approach? I suspect I was wrong in assuming that the elemental capacitors were in parallel in the first place.

Opinions?

 

[darkv0id]

Anyone ?

 

[darkv0id]

No one?

Please, can anyone help me out?