Age old question...Bad Battery or Bad Alternator???
Start the car and then remove the negative battery cable. If the car dies, then the alternator is not putting out enough charge. ..
PLEASE can we bury this old wives tale. NEVER unhook a battery cable on a running car. Yes, yes, YES you might get by with this 10, 100, 1000 times Hell you might even get by with it 10000 times without damaging something.
It is a flawed test and proves nothing, here's why
IF the system is working OK, but the engine and loads (headlights or even just ignition) is below the otuput of the low speed idle, it might die and be working perfectly fine
On the other hand, the alternator might have all but two diodes blown clear out of the housing, and still put out enough to run the ignition. In this case, you would pull the cable, it would keep running, and you would (incorrectly) think it's fine
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To the OP. The voltages you got while running indicate one thing. It is not charging
Battery readings "stopped" at this point are meaningless because the battery is likely somewhat discharged.
So you need a couple of "quick checks" to separate the problem
1.......Is it the alternator?
(What are we working on?????????? year, make, model??? What type of alternator? is this the pre---70 Mopar charging system?)
Remove the green field wire, and use a clip lead to jumper from the battery (starting relay large stud) over to the now exposed alternator field terminal. If you are in subdued light, you should see a small spark
Start the car and watch the voltmeter / ammeter. Bring up RPM, it should show some increase.
If not hook your multimeter directly to the alternator output stud. Repeat the test. If the voltage stays below 13V it is not charging. The alternator is bad
If the voltage goes way high, 16V or higher at the alternator, but stays low at the battery depending on RPM, then you have an open in the alternator charge line
If the meter does show a charge, showing the alternator is OK, hook the field wire back up
2.....Disconnect the two regulator wires and jumper them together. Repeat the above test If it again shows a charge, this shows the field wiring as well as the alternator is OK. -------
3......If the above test is OK, first try cleaning and re-grounding the regulator. If no improvement, replace the regulator. MAKE CERTAIN the regulator is grounded.
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Once you get the problem "fixed," post back. You are NOT done. You need to do at least two other things
1........Once you get the charging system operational, and the battery back up, you need to find someone to properly load test the battery. A battery that old is likely on it's last rodeo
2........Post back here, and do a search. You want to look for how to check for voltage drop in the harness which actually causes OVER charging (over voltage) on an otherwise working system