98 Mazda 626 Altenator Question

When I turn on anything electrical, like the AC or headlamps, it seems like it really puts a strain on the engine. In fact, I can't even start the car with the AC on or the belt squeals like a stuck pig. With lights on every time the AC kicks on they flash and dim a bit. I checked the tension and it seems very tight, less than a half inch of play when pushing on the middle. Other than the squealing of the belt, there are no noises associated with this problem.

Could this be a symptom of my alternator going bad? Any ideas?