I know that **coefficient of friction=f/N** , and I also know that it depends on that surface area of contact and the material.

But my doubt is ,from this formula if N is halved then coefficient of friction should increase but that does not happen, it remains unchanged, why?

If it's because **f** might adjust itself accordingly to keep it constant ,then what about in case of know *kinetic friction*? 

*Only static friction is self adjusting, right*!