What happens in a tightly wound up cable reel under AC power? This question came up when I used our vacuum cleaner (230 V, 50 Hz AC, 1 kW) without pulling out most of the cable, i.e. about 8 meters were still wrapped around a small cable reel (maybe 5-10 cm diameter) inside the device. I got told this should be avoided because the cable might produce an electromagnetic field or heat up strongly when it's wound up like that.
Is this true? Would it be dangerous to operate a device consuming much AC power with a tightly wound up cable? What could happen worst-case and how high power consumption would be needed to expect any effect? Or is that just a myth?
 A: A typical (cheap) extension reel (10 metres, 10 amps) has the following specifications:
Uncoiled 2400W (10 A) 240 V
Coiled 720 W (3 A) 240 V
The reel had 4 sockets and a 13 A fuse in the mains plug.
Measuring the lead resistances I found them to be approximately $0.3 \; \Omega$ and $0.4 \; \Omega$ so a total of $0.7 \Omega$.
Suppose that the maximum current $13$ A hen the power dissipated in the whole cable would be $13^2 \times 0.7 \approx 120$ W.  
If the reel is tightly wound and assuming that the electrical insulation on the cables is also a good insulator of heat you have the potential for quite a rise in the temperature of the cable even if some of the $120$ watts is lost through the outer surfaces of the reel.  
In the past I have certainly noticed a wound up reel getting hot (rather than just warm) so unless I am using small power devices have always at least partially unwound a reel.

Update
A quick sum shows that the radius of the copper conductor has to be a rather low 0.4 mm to give a resistance of 0.35 $\Omega$ for a 10 m extension reel so I am undertaking a deconstruction job on the extension reel.   
Even if the resistance of the copper cable is a factor of $10$ were and the power dissipated is of the order of $10$ watts this still has the possibility of raising the temperature of the reel to a dangerous, melting insulation, level.

Update 2 
The cable used had a copper conductor cross sectional area of 2.5 mm$^2$ and PVC insulation rated up to a maximum working temperature of 70 $^\circ$C.
The total calculated resistance of a 10 m reel is 0.13 $\Omega$ and so with 13 A passing through the reel the power dissipated as heat is 22 watts.
Still sufficient over a period of time to raise the temperature inside a tightly coiled reel to a level where the temperature rise will be quite high.
