You would think that the alternator would be able to charge a battery up and IF you did in fact think that, you'd be????
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WRONG! ANNNKKK!!
I'm sorry. Jay what do we have for our parting contestants today?
Well Art, some of our contestants will receive the new edition of "rebuiling to maximize profits by using substandard parts" written by a group of chain store auto parts houses. And, for other lucky contestants, we have the home edition of "Can OEM parts REALLY be that much better?" written by Ford and Mitsubishi..
So.. Here's the skinny of it.. it takes a long time for the alternator to actually fully recharge a drained battery. Were talking many hours at engine running speeds. While thats happening, the alterntor is working hard and making heat. The problem is that it isn't getting rid of this heat as it would from a normal external electrical load. Remember, the mitsu is rated a 110A, but thats a short term peak, not a sustained rating, hence the substandard parts, IMO.
So, if you don't want to risk messing the new alt up, then you need to fully charge the battery. You can, but after going through 2 remans, I wouldn't take the chance.
Note also, if you ever fully kill the battery by leaving your lights on or something like that, jump it just enough to get it started, run it as little as possible, and then have it recharged. I'm talking about a deep discharge event, not just leaving the headlights on for an hour or 2. A shallow discharge isn't usually to hard on the alt.
OK, so where to get a charger.. most autoparts places sell a cheap 2A trickle charger which should work fine. Every car owner should have one, IMO.
You could use the cables, but you'd have to leave them on and the car idling for quite a while to get to a full charge. I wouldn't overwork it by revving the engine. That alt is generating heat too.
Hope this helps, and I wan't trying to pick on anyone, just making a little satire to weave a story.