I've looked several of these "DIY spot welder" videos on Youtube, such as this:
We have a much larger number of turns on the primary than on the secondary. Then we connect the primary to an AC voltage, say 240V and a small resistance load on the secondary (or we short it).
I have found several explanations for what happens and they all say that as the voltage is stepped down on the secondary, the current is stepped up accordingly. The voltage on the secondary is now only a few volts, but the current can be up to kiloamps. This high current generates high heat which melts the metal (the secondary load).
But shouldn't the power be the same? The power is the product of current and voltage. Because of conservation of energy, as the current is stepped up, the voltage is stepped down as the product stays the same.
In the opposite case where we step up voltage I can understand what's going on by looking at the transformer model:
If the secondary coil number gets higher, the current to the R_s branch gets higher. So even though the current is stepped down, the power used becomes higher as we are "pulling" more current from the supply.
But what happens when the current is stepped up? If the primary has more turns, it would seem that the ratio N_p / N_s is higher and the current to the R_s branch is lower.
Could somebody explain to me what is it that I'm misunderstanding? Why is it better to step up the amperage, rather than just use the input AC voltage or step up the voltage instead of the current?
EDIT: A lot of the answers state the relation between current, resistance and power:
$$P = i^2R$$
But we also know that the voltage across a load is also a function of the current, by Ohm's law:
$$V = iR$$
So if we have a high current, we should have a high voltage as well. Now Ohm's law and transformer seem to disagree!