How do I pinpoint a problem when the Charging Light stays on while driving?

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My dash board charging light just started staying on, while driving. After Autozone tested the battery they said it was bad. I replaced the battery and the light still stays on. The Autozone tech said I need to drive it for a couple days and come back so they can run diagnostics. After 1 1/25 hours of driving the new battery failed. They tested it and said it had a bad cell,so they gave me another. The light still stays on and they want me to drive for a couple days before they run diagnostics. I noticed that every time I accelerate and the RPMs hit 2500 or higher, the charging light turns off. The charging light remains off for a few seconds, but it comes back on when the RPMs drop to the normal range (1500 - 2000). I also noticed that the dashboard voltage indicator remains around 10 (there is actually no number on that mark).