'68 Barracuda - charging system questions

To return to the voltage regulator. If the voltage regulator is seeing anything less than the set point, say 14 Volts, its going to try to increase the alternator's output voltage. If the regulator is seeing voltage above set point, its going to decrease the alternator's output voltage. Resistance to flow between the alternator output and the regulator's measurement point causes the regulator to do the wrong thing.

The more current, the more resistance and the more the voltage drops.
So if the electromagnet is a big current user, there's a going to be a big voltage drop across the first poor connection.
There will be less drop across the second poor connection because there's only a small current going through the lamp.
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Batteries have a lot of stored power, but under big loads voltage does drop.
So in reality we see something like this when a heavy load is placed on the battery.

A battery's stored energy can only be guestimated from its voltage. An ammeter on a charger will show when its full but not condition. To test the condition either a hydrometer or a load test is needed.