question: while A is using his central air-condition,the water produced in his pipes,leaks ,and seeps through the ceiling of B is A responsible?

Yes. see BK 6a those who open their gutter (to dispose of accumulated filth ) are responsible if it damages while in motion.

we must note that in BM end of Bayis & Aliya we find somewhat different:whereby one may wash his hands on the floor of the attic and let the water drip on the downstairs' head,provided the water drips after he finished washing--not while he is still washing.

We assume that in our case , it drips on sheet rock while air-condition in use.More important,the reasoning given על הניזק להרחיק can only make sense when the object in question (i.e. the head of B )can "move away" while the water is dripping ,but does not apply when A , visibly damages B's property /object.

please comment for objection.