Does the power of the muscels depends on the size of it?

Yes: The maximum force that a muscle can exert is directly proportional to its lean mass. This is a common-sense idea that is scientifically accurate.

Actually no: The power comes from good cellular energy. Of course, if you want tro be a weight lifter you need more muscle fibers that grow with proper exercises. Look at the legs of runners. Mostly they are relatively thin and gracile.