The first concept to understand is that a battery is made up of cells. If a cell or two begins to short out, the battery will still have 12.5 volts--it just won't have as much amperage as it did to start with. When a battery has shorted cells, the battery will take a charge in most cases, but it will not hold that charge long. It can be charged during the day to a full charge and die overnight. The way to check a battery for a bad cell if no major equipment is available except a voltmeter is as follows: Put the voltmeter on 20 volts and place the red line on the battery positive and the black on the battery negative. Have a helper try to start the car. The battery must be charged to do this test. A dead battery cannot be tested. If the battery shows close to 12 volts when the car is started, it should not drop below 10.5 volts while the starter is engaged. If it does, the battery is bad.
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If it does not drop low when starting, the battery is probably good. Test the alternator next. Leave the voltmeter attached to the battery and start the car. With all the accessories off and the engine running, the voltage across the battery should be 13.8 volts or higher. A good alternator will put out 14.5 volts to charge. A voltage of 13.8 is acceptable.
Turn on the lights, air conditioning and radio. Check the voltage to see if the regulator is working. The voltage should not drop more than half a volt. If it does, replace the alternator. It is good to know that not many alternators fail completely all at once. What happens is one of the three diode packs goes out first. This reduces the amperage and voltage it is capable of putting out. If just one diode is out, the alternator will still charge the car with the air conditioning and lights off, but when they are on, it puts out just barely over battery voltage, so it would take a long time to recharge the battery. Each day the car is used the alternator with one bad diode will put half the charge into the battery that was just taken out. In a couple days the battery will be dead again.
If the battery and alternator are good, then there is a good likelihood that there is a drain from a circuit in the car, such as a light left on or shorted. Somewhere there is a short that is draining the battery. Take the negative lead off the battery. Place the voltmeter in between the negative wire and the negative terminal (one lead should be on the negative wire, one should be on the battery negative post). Note the voltage. It should be very low in millivolts. There will always be a small drain due to the circuits in the computers.
Turn the voltmeter to amps. Even if the voltmeter shows 12 volts, the battery won't die easily as long as the amperage drain is less than a quarter amp. If it is more than a quarter amp, there is a drain. Leave the ampmeter installed. Take one fuse out at a time (from the fuse block under the bonnet and inside the car). Once the fuse is pulled check the ampmeter and see if the drain has gone away. If so, the circuit the drain is in has been located. If the ampmeter stays the same when the fuse is pulled, reinstall it and go on to the next until you find the circuit that is causing the drain.