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To see if a generator or alternator is charging, check the battery voltage after it has been setting over night. A good battery will be 12.6 volts fully charged.
Use a hand held volt meter or the car's guage if it has one.
Whatever the voltage is, start the engine and recheck the voltage. On a alternator it should start charging at idle and bring the voltage up to its setting. Many alternators increase the battery to 13.4-14.5 volts.
Generators may show a dim GENERATOR light at idle but the light should go out as soon as you raise the rpm up. Raising the idle rpm slightly may cure this. It should also show above 12.6 volts after it has topped off the battery.
If the car continues to start normally, then the charging system is working.
Sometimes turning on the head lites will change the charging voltage.