There is a video on youtube with a device for melting metal (video below). It's a step-down transformer that transforms 120VAC in primary coil to ~3VAC in secondary coil, therefore stepping up the current 40x.
Initially I assumed this device is good at melting due to the Power=Current²*Resistance formula. But I got confused when author of that video melted some rocks, which do not conduct electricity. I think that formula can only be applied to materials that conduct electricity, like metal nails etc, but that is not the case with rocks. What I think should happen (which is wrong apparently) - copper wires in secondary should heat up and melt themselves.
Question nr. 1 - if formula I mentioned is not in play here, then what other formula can be used to describe amount of heat dissipated?
Question nr. 2 - In case of melting steel nails, steel has greater resistance than copper wires, therefore majority of heat is concentrated in the nail only and it leaves secondary transformer coil intact. But in case of melting rocks, why is the heat still concentrated on rocks? Since they don't conduct electricity, I think secondary winding should melt before the rock can melt.