The diodes in the alternator are blown open if there is a surge from the battery or a dead spot on the starter motor causes a spike in voltage to the system, destroying the alternator. Either way, when the alternator goes, the car will start and run on battery. It can take up to 150 miles before you realize that you're on battery power. The battery will die, the car will stop and jumping it will not keep the car running long. This occurs because the alternator is not charging the battery like it is suppose to. A check can be made by turning on the bright lights and watching to see if they stay dim or get dimmer. If the alternator is working the bright lights always get brighter.
When your car won't start..lol..or when it won't stay running
Problems starting the car is usually a good sign. Problems with battery charging too.
If you have trouble starting your car or if your lights(inside and out) are dimmer. If your battery keeps dying. Any Autozone store will check your battery and alternator for free