bad alternator?

[j dubb240]

i have a 91 240sx ka24de. i rebuilt the engine about a year ago, and it has good power but it stumbles sometimes. i thought it might have been out of time, or fuel injectors stopped up. but that wasnt the problem. so i went to autozone and had the alternator tested and it would stay at 14 volts for a while then drop down to 9 and 10 volts and then go back up.he sayed that it was bad. what caused it to do that? i use my battery to start my jeep too and when i put my battery back in my car it runs great for about 5 mins. so im about 99.9% sure its my alternator what do you guys think? thanks, justin