under normal operation the voltage should be around 13.7 which is target charging voltage. A very quick thing to do is to put a volt meter on the battery before the motor is running. if the voltage is less the 12 you have charging/battery issues which leads to believe the alternator is the suspect but could be grounding issues. A lot of times batteries fail because the alternator is not doing its proper job. After the motor is running put volt meter on battery to see if you have over 13 volts. If you don't, I would suspect the alternator again. But it could be likely you are having a grounding/other electrical issue.
