>> I am no expert, and perhaps quite wrong, but I believe that it is nothing
>> to do with EMF and all those other clever things. It is simply that wire
>> has a natural resistance which results in heat generation. If it is coiled up, then
>> it cannot dissipate that heat.
>>
>> Don't forget, there are two current carrying wire and essentially it's going in opposite directions.
>> Surely they would disrupt/cancel each others' fields?
Technically, the resistance of the wire itself doesn't change due to bends in a wire. But the wire is much more than just a resistive component. With enough turns/loops you can make the wire exhibit inductive properties.
Every current carrying conductor produces a magnetic field in the plane perpendicular to the flow of current, and revolving around the conductor.
Each loop of the inductor exhibits a capacitance effect with the next loop. That is, a looped wire will exhibit all three properties: inductance, resistance and capacitance.
So, explicitly, the resistance of the wire doesn't change when you bend it. However, the potential drop across it can change enormously by the way you bend the wire and make it interact with itself.
All valid for AC
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