Wouldn't the wire thickness not limit the current output of the alternator, rather wouldn't increasing the wire resistance increase the voltage and do nothing to the current, according to Ohm's Law?

Since V=IR, increasing the resistance increases the voltage if the current is constant.

A creek that has been redirected to flow through a garden hose has much more potential energy in the garden hose at an instant of time compared to if the creek had been redirected to flow throw a 6 foot diameter pipe, but the same amount of water will flow through the garden hose, just it will take more time to flow through and the potential energy at an instant of time will be greatly increased.

So voltage is potential energy.

So a car battery of 12 volts with 4 ohms of internal resistance so with 3 amps of current, when it is connected to resistance wire, the 3 amps of current will still flow through, just it will take more time for the 3 amps of current to flow through, and the voltage will be greatly increased (and the resistance wire will glow red hot before lighting your house on fire, unless it is in a vacuum tube so that it doesn't burn).

So if it takes more time for the 3 amps of current to flow through the resistance wire, wouldn't that keep the current constant but the power is what is effected because current has no time domain component but power is equal to potential energy divided by time, so that for more work in less time the power is greater, and for the same work in less time the power is greater?

P=W/T

So then for electricity the equation would be P=V/T

but that doesn't make any sense because Ohm's Law for power is P=IV

wait, so does that mean that current has a time component, and ampere is not a base unit?

If we had P=V/T, in order to get to P=IV, that would mean that current is equal to 1/T, so increasing the time for the current to flow decreases the current, so greater resistance decreases the current, but that would contradict Ohm's Law of V=IR which says that voltage increases as resistance increases?

oh wait, I think I get it now: Ohm's Law of V=IR says that if EITHER the current OR the resistance increases, then the voltage increases, and if both current AND resistance increase, then the voltage increases. So since V/R = I, that means that as resistance increases and voltage is constant, current decreases, which makes sense from the time component in current.

So not only does it take more time for the 3 amps of current to flow through the resistance wire, but also the current output is decreased, even though the current of 3 amps will still flow through EVENTUALLY.

So if you connect a 3 amp 36 watt guitar amp (P=IV, V= 12 volts, I = 3 amps, P=36 watts) to a 3 amp car battery, then the battery will drain MUCH FASTER than if you connect a 500mAmp 6 watt cell phone charger (P=IV, V=12 volts, 0.001 amps are in a milliamp, I=0.5 amps, P= 6 watt).

So the conclusion is that yes, the resistance of wire will limit the current output of an alternator, as well as determine the voltage output using Ohm's Law.

but still, wouldn't the frequency of the alternator determine the current output of the alternator IN AN IDEALIZED WIRE WITH NO RESISTANCE?