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Hi,
Ive got an 04 F250 and when I accelerate the battery light comes on. I tested the voltage on the battery while idle and all is fine exactly 14.4 volts. However when I accelerate to about 2500 or 3000 rpm the voltage drops to 12.6 - 13.0 and then the light comes on. Water levels in the battery is fine too. Is this a battery problem or a failing alternator?
Sounds to me like a failing alternator. You should be able to have that tested at just about any decent local auto parts store. You could have a slipping belt too but I think you'd get other issues with that situation.
You have a diode issue in the alternator. Once thing you can check for (although the battery shouldn't allow it) is AC voltage. There should ne next to none at idle and then more as you reach where the alt has failed.