Definitely should be worried. The minimum voltage you should have is in the high 13's. When a battery is flat the alternator has to work a lot harder, so voltage will be a bit lower.
When the battery is charged, the alternator is not working hard so can supply a higher voltage. You should always have a higher voltage on a charged battery.
Regardless of what accessories are running, when the engine is running you should always have a minimum voltage of high 13's.(with the exception of a winch or anything that is pulling 100+ amps)


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