Bad alternator or battery?
Drove my Jeep to and from work on Friday, drove fine. I went out Saturday morning and my battery was dead. Jumped it, and it started right up. Let it run for a little and then started giving it little revs to get the alt to charge the battery faster. I then had to stay on the gas, because I could tell if I let off it would shut off. When it did shut off, it wouldn't start again because the battery was dead. I figured the alternator was bad and it was only running off what little charge the battery had. I went out tonight and was going to take the alternator off a while but I figured I better check to make sure that's what it was before buying one. I jumped it but it didn't want to stay running at first, even while the jumper cables were still hooked up. I let it charge a little and then it started. I turned all all the lights on, wipers, etc. The battery gauge was right on 14. It ran for a little and then when I gave it some gas it shut off again, and the battery was dead. Now I'm not sure if the alternator isn't charging the battery or if the battery is just refusing to take much of a charge. I've had alternators go bad before, while driving, and know the symptoms, and my Jeep had none. Just a dead batt. one morning. What does it seem like it is? What is a sure fire way to check? Thanks.
2001 Grand Cherokee Limited. 4.7 V8, Quadradrive, Tow Package