how can capacitor being so small function properly when in the deivation of capactance we used the formulas of electric field due to infinite sheets or rods

For this u need to kow abt the basic concepts of capicatance. How it works and on which principle?

approve!

Imagine 2 walls of height 1 metre. They are extremely close, almost touching each other hardly a few micrometers apart. You are very very tiny smaller much smaller than the seperation between the walls. You stand between the walls and look above. What would you see?

You will definitely see that the walls almost go to an infinite distance. That''s how the capacitor works, the dist. btw the plates is so small that at a point so close to the wall, the plates would seem infinitely large.

So, the results we derived are very much right.