A.C. Cooling fan

Does my ac compressor have anything to do with my small fan coming on? I run a hot wire to my fan connector and both fans run. Only my large fan comes on at operating temperature. My a.c. Blows cold when the large fan kicks on.

The cooling fans have a known issue of the armature brushes sticking, causing fan failure. Try whacking it with a small hammer to loosen the stuck brushes.