You're missing half of the electrical equation: AMPS. Any idea how many amps a car battery can output? 350-800, depending on the battery. That's a HUGE amount of energy. You can't get something for nothing; physics doesn't work that way. The more draw you put on the charging system, the more work your engine has to do. Let's look at an example:
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120 amp alternator, outputting 14 volts
120x14= 1,680 watts
1 horsepower = 746 watts.
1680/746 = 2.25 hp
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Electrolysis, under ideal conditions, requires 143 kJ of energy per mole of water. Ideal conditions include supplying 1.48V to the water. So, your other 12.52V are just heating up the water.
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Hydrogen atomic mass: 1.00794
Oxygen atomic mass: 15.9994
2(1.00794)+15.9994= 18.01528
Mass of 1 mole of water: 18.01528g
One ounce of water weighs 29.574g
29.574/18.01528= 1.64160 moles per ounce
1.64160x143= 234.74972 kJ per ounce
Now, Joule is a measure of energy, while Watt is a measure of power. Watt= Joule/second
177.6 x S =234.74972 kJ
S = 1.32178
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Assuming my math is correct, you're drawing 177.6W in order to break apart 1 ounce of water every 1.32178 seconds. Don't think you're going to be producing a whole lot of gas at that rate. Buuut, why don't we figure out just how much?