How can a fuse have a constant current rating regardless of the voltage of the circuit?

I came across a simple question recently that bugged me because Google didn't seem to have any answers. The best I could come across is people saying "resistance is near 0" and other wrong/irrelevant answers.

The answer is actually quite simple, it's because you can assume the power a fuse fails at is constant and that a fuse has a constant resistance. This is because a fuse is usually just a wire that will melt at a certain temperature. Below is the math to prove it.

• ConstantPower = Voltage x Current
• ConstantPower = (Resistance x Current) x Current (using Ohm's law)
• ConstantPower = Resistance x Current^2
• ConstantPower = ConstantResistance x Current^2
• squareroot(ConstantPower/ConstantResistance) = Current
• Constant = Current

As a reminder, this is true even if the fuse had a very high resistance, as long as the resistance is constant.