If an electrolyzer is installed in a car powered by gasoline, where does the energy required for splitting the water ultimately come from?

Answer

The existing gasoline engine, forcing it to burn more fuel to power the overloaded alternator.

The alternator draws mechanical energy from the engine to produce electricity. Supplying a large electrical load like electrolysis forces the engine to consume more gasoline to overcome the resulting resistance, leading to a net loss due to inefficiency.

If an electrolyzer is installed in a car powered by gasoline, where does the energy required for splitting the water ultimately come from?
Chemistrywaterenergyfuelreaction