In a water heater stove or arc welder, the most basic electric circuit is formed when one has a source (AC or DC) and 2 wires going to and from the heating element, in the case of the heater and stove, or to the gap where the arc is formed, in case of the welder.
When the arc forms it creates a very low resistance path in air, for example, allowing for relatively large current. The same thing, just without the arc, is happening in the heating element. Heating element has a relatively low resistance allowing for large currents through the element and the element itself giving out large amounts of heat.
The question is why doesn't the whole circuit go hot as the arc or the heating element, why does this temperature increase happen only at the specific places in the circuit, since the same current is flowing through the whole circuit? is it because the wires need to be of much less resistance then the described elements or is there another explanation? Thanks.