Here's wikipedia
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This is why I call it an exciter coil, though I keep spelling exciter wrong.
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I guess you refer to it as a field coil. I think the alternator in the car looks something like this.
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with the addition of a rectifier/regulator between the M and the plus and minus outputs.
I think in old cars the 'f' field coil went directly to the battery light and the ignition, but when I unplugged the exciter wire, the exciter stayed stuck on. Now that short has burned out and the exciter is stuck off but the battery light is on so something is there grounding the light bulb.
So my question is: Does the exciter wire directly power the field coil or does the exciter wire go to a transistor or something that turns the field coil on? Is there a transistor or diode I can replace?
Yes there are schematics on the internet but I have not found any that go beyond black boxes for the regulator and the alternator. Basically they're just wiring diagrams for the car and not circuit diagrams.
It's an old car, A 1997 VW GTI VR6. If it was a new car I would buy a new alternator. But in an old car, you have to consider how much money to put in to it before the next thing breaks and when do you give up?