BMW Repair Questions? Ask a Mechanic for Answers ASAP
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13V while running is too low, as is 11V at the battery.
you definitely have an alternator and/or battery problem which should be addressed as voltage issues are very common to cause electrical problems
as far as other causes, a failed ignition switch, bad ground or failed control module somewhere on the car can also cause similar issues, but I would first resolve the obvious voltage issue which exists based on the readings you have provided.
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