Electrical problem
1992 Nissan Sunny 6 cyl Front Wheel Drive Automatic 130000 miles

I would like to ask what could be wrong with my Nissan Sunny. It's enging would not crank up. I was able to start it up and drive it initially, but when i turned it off and restarted, it would not start. When i took the battery voltage while my engine was running, i noticed that it was going down by increments of .01V down to 10V. My battery is just a few months old and when i checked its voltage with the engine off, its voltage was slowly increasing by .01V increments up to 11.9V. I tried to restart but still, the engine would not crank up. I also noticed, that my headlights start dimming when i try to crank up the engine. Could i have a defective alternator? or something else? really need your help. thanks.