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will the car start after sitting for a short while (like less than 4 hrs.)? If it drains the battery, or you notice the interior lights are dim when entering the car, good chances that the alternator is going bad.....also if you put the air conditioner on and the car starts missing and eventually dies, with a low voltage reading (like the one you are describing), it more than likely is an alternator......just been through that myself.....
You have a defective alternator. Good alternators will maintain 14.7 volts across the battery (14.3 v on dash voltmeter) when cold and as the alternator reaches its operating temperature its output voltage will be 13.3 volts across the battery. Also, batteries are considered discharged at 12.0 volts or lower, charge your battery up with a battery charger. Never expect your alternator to charge a dead battery up because dead batteries draw large current at first and this heats the alternator and shortens its life. Batteries can't be charged up in 15 minutes either, so thinking that if you run the engine for 15 minutes your battery will be charged is incorrect. Get a battery tender and keep your battery charged if you don't drive your C4 often. Batteries kept charged will have a normal life.