In uk.d-i-y, Colin Wilson wrote:

If the 2 way extension lead was on a reel, it may be that the load and
inductive resistance (the magnetic field caused by the load can
affect the way the cable copes with the load*) caused the heat - if
you`re going to use a heavy load on an extension reel it`s wise to fully
unwind it first.

The heating in a coiled extension cable has nothing to do with
induction. Nothing. The live and neutral cores run right next to
each other, and carry the identical current (barring L-to-E leaks!)
in opposite directions; thus the magnetic fields cancel (almost)
completely. The heating of coiled extension cables is *all* about
the boring *resistive* losses warming up the copper, and having a
hard time escaping through radiation, conduction, or convection,
because the cable's all bunched up together. You'd get just as much
heating if you folded the cable there, back, there, back, side-by-side,
tightly bunched, as you get by having it coiled. Unwinding an extension
reel before passing a heftier load through it *is* essential, but it's
done to allow air to circulate between the loosely-looping spillage of
cable you leave behind (where it won't create a tripping hazard, of
course; can you tell we've got an EHS audit in the Labs this week? All
our sharp blades locked away in the tool cupboard, and I might even bother
to put the side panel back on my PC before the day is out, *and* try
to remember to keep my shoes and socks on...)

The shape of a coiled extension lead powerfully suggests "transformer",
"solenoid", "speaker coil", "motor winding", and similar constructions
to all of us: but you'll notice all of those - and the 'reactors' Colin
mentions on the 33kV network - are wound with a *single* conductor, not
with a flow and return right next to each other!

Avoiding inductive effects is the main reason for good wiring practice
requiring phase and neutral to be carried either in the same multicore
cable, or on single conductors running in the same conduit. Separating
them can cause increased radio-frequency interference (some of the
schemes for wiring two-way light switching play hell with induction-loop
hearing aid pickup, f'r example!). And those who separate phase
conductors as they enter machinery - especially if there's a nice thick
iron panel between the entry points - lose power and may encounter
embarassing heating from the eddy currents created; you're supposed to
cut slots between the entry points to reduce this effect if you can't
feed the conductors in through the one hole.

Stefek 'slayer of urban myths' Z