I am planning to build a foam cutter by heating up a piece of nichrome wire. I found that nichrome has a relatively high resistance compared to other conductors and it is the reason why it is used as a heating element. That is what confuses me because I think it only applies for constant voltage sources, but I've seen DIYers online using a battery directly with the wire. If I use a constant voltage source , then P=V^2/R and the smaller the resistance the higher the output power and the wire will heat up faster. A high resistance wire like nichrome doesn't seem to be the ideal type to be used for a constant voltage supply. I've seen diy foam cutters online powered directly by 9V batteries. How does it work? If a nichrome wire works for a battery, then a lower resitance copper wire should work too, as long as it isn't lower than the battery's internal resistance. A constant current source is more suited for a high resistance wire, since P=I^2R.