How much current can a power generator produce and how does that current vary as you introduce more load onto the generator?
There is no fundamental limit to how much current a generator can handle, however, the characteristics of the generator’s wiring, its magnetic fields, and the machinery turning it all tend to limit its current capacity. A generator’s wires aren’t perfect and, as the current passing through the generator increases, its wires waste more and more power. Like any wiring, a generator’s wires convert electric power into thermal power in proportion to the square of the current. Thus if you double the current in the generator, you quadruple the power loss. While this power loss and the resulting heat are trivial at low currents, they become serious problems at high currents.
Increasing the current in the generator also affects its magnetic fields because currents are magnetic. At a low current, the current’s magnetism can be ignored. But when a generator is handling a very large current, the magnetic fields associated with that current are no longer small perturbations on the generator’s normal magnetic fields and the generator may not perform properly any more.
Finally, a generator’s job is to transfer energy from a mechanical system to the electric current passing through it. As the amount of current in the generator increases, the amount of work that the mechanical system provides must also increase—the generator becomes harder to turn. There will always be a limit to how much torque an engine or crank can exert on the generator to keep it spinning and thus there will be a limit to how much current the generator can handle.
As for how the current varies with load: the more current the load permits to pass through it, the more current will pass through the generator. Assuming that the generator is well built and has very little electric resistance, the load will serve to limit the current. The generator will then deliver just as much current as the load will permit. If the load permits more current, the generator will deliver more. As a result, the wires in the generator will waste more power as heat, the magnetic fields in the generator will become more complicated, and the device powering the generator will have to work harder to keep the generator turning.