1992 Plymouth Acclaim Check engine light comes on and check

If your going to troubleshoot this yourself? I'd check trouble codes first. On some of these systems, if there is a problem with the charging system, it should set a code. It won't tell you what part is faulty just where to start testing.

If your using alternators from the discount autostores, I've seen some of them that were faulty, straight out of the box.

Make sure the battery has a full charge and the cables/wires from the battery posts are all clean and tight. Don't use the alternator to charge a low battery, use a charger.