Coiled extension lead
A Socratic walk-through of the coiled extension lead — reasoned out one step at a time, not lectured.
The question we started with
THE QUESTION #Why can an extension lead overheat while coiled on its reel yet run cool once the same cable is unwound?
Look at the label on a cable reel and you will usually find two ratings, not one: something like 13 amps fully unwound, and around 3 amps wound. Same copper, same plug, same appliance — and the manufacturer is telling you the cable can carry a quarter of the current when it sits on its drum.
The explanation you hear most often is that a coil of wire is an inductor, and inductance somehow heats it. That has the shape of an answer, and it is worth taking seriously enough to break. If it were right, unwinding the cable would change the electrical behaviour — and it does not.
Reasoning it through
REASONING #Start with where the heat comes from. A conductor turns a fraction of the power passing through it into heat, at a rate equal to the current squared times the resistance. So work out those two numbers for a real reel: 25 metres of cable with 1.25 square millimetre conductors. Current flows out along the live and back along the neutral, so the copper it traverses is 50 metres, not 25. Copper's resistivity is about 17 billionths of an ohm-metre, so the resistance is that times 50 metres divided by 1.25 millionths of a square metre — roughly 0.68 ohms.
Now run 13 amps through it. Thirteen squared is 169, times 0.68 ohms, gives about 115 watts. That number deserves a moment: 115 watts is an old-fashioned lightbulb, produced continuously inside the cable itself.
And notice what the calculation never mentions — the shape of the cable. Resistance depends on the copper's length and cross-section. Coil it, plait it, hang it from a tree: 0.68 ohms, 115 watts. Coiling cannot change how much heat is made. It can only change what happens to the heat afterwards.
And what should happen to it? Laid out on the floor, that 25-metre cable presents about half a square metre of surface — a thin cylinder is nearly all surface — and every stretch of it touches air no other stretch has already warmed. Using the usual rough figure of around 10 watts per square metre per degree for a small object in still air, a recalled rule of thumb rather than a constant, 115 watts over half a square metre lands somewhere near 20 degrees above ambient. Warm to the touch, and nothing worse.
Now wind it onto the drum, and ask the question that matters: for heat made in a turn buried in the middle of the coil, what is the route out?
There is no route that avoids other turns. Convection is finished — air cannot circulate between tightly packed layers inside a drum. Radiation is finished too, for a reason worth stating plainly: radiation is an exchange, and a turn surrounded by neighbours at its own temperature receives back as much as it sends. The inner cable's only escape is conduction, outward through layer after layer of PVC and trapped air, each already hot. Meanwhile the exposed area has collapsed to perhaps a fifth. Same 115 watts, far less area, and a long path to reach it — so the temperature climbs until the path can carry the lot. PVC flexible cable is typically rated for a conductor temperature of 70 degrees, past which the insulation softens and ages fast.
That is what the wound rating buys back. Cutting the current from 13 amps to 3.25 amps cuts the heat by a factor of sixteen, from 115 watts to about 7. Seven watts the drum can lose.
The analogy
THE ANALOGY #Think of a stack of dinner plates straight out of a hot oven. A single plate on the rack is cool enough to handle in a few minutes. The plate in the middle of a stack is still too hot to touch an hour later — not because it holds more heat, but because its only way out is through neighbours that are just as hot.
the plates are losing a fixed store of heat and will cool eventually, whereas the cable keeps making 115 watts indefinitely, so it does not cool slowly — it climbs until it reaches a temperature at which the escape route can carry everything being made, and that temperature has no obligation to be one the plastic survives.
Clarifying the model
THE MODEL #Now let us do the inductance claim properly, because it is not a silly idea — it is just testably wrong here, in three separate ways.
First, a coil of this cable has almost no inductance to speak of. Live and neutral run side by side within the same sheath, carrying equal and opposite currents, so their magnetic fields very nearly cancel. There is no meaningful field around the drum to be enhanced by winding it.
Second, even a real inductance would not do it. An ideal inductor stores energy in a magnetic field during part of the cycle and returns it during the next: it causes a voltage drop, not dissipation.
Third, at mains frequency the copper does not care. Skin depth in copper at 50 hertz works out around 9 millimetres, while a 1.25 square millimetre conductor is only about 0.6 millimetres in radius — so the current uses the whole cross-section and the alternating-current resistance equals the direct-current one.
Each of those is testable. Put a power meter at the plug and run the same appliance wound and unwound: the resistive account says the power drawn is unchanged within measurement noise, the inductive account says it should rise. It does not. Better still, run the reel on direct current, where inductance can play no part at all — it still overheats when wound. For the positive evidence, put a thermocouple on the innermost turn: identical power in, wildly different temperature.
What would refute my account? A wound reel drawing measurably more power than the same reel unwound, or a shifted power factor, with no temperature difference its geometry can explain. One honest limit, too: I have used one common reel's dimensions throughout, and conductor size, cable diameter and packing all move the numbers — so treat 115 watts and 20 degrees as the arithmetic of an example, not a specification for the reel in your garage.
A picture of it
THE PICTURE #How to readTwo stacks, read downward, each the route heat must take from copper to room. Both begin with the same 115 watts, because coiling changes nothing about how much heat is made. The left column reaches the room in three steps across a large open surface; the right adds two more layers, the worst being the band of neighbouring turns at the same temperature — a barrier that carries heat only if the inside gets hotter than the outside. Depth here stands for thermal resistance, not for time.
What became clearer
WHAT CLEARED #Coiling a cable does not change the electricity; it changes the plumbing for the heat. Current and resistance fix the wattage, and the only question left is how hard that heat must push to reach the room. Unwound, every metre faces fresh air. Wound, the inner turns can export heat only through neighbours at their own temperature — convection stops helping, radiation cancels out, and the temperature rises until conduction alone carries the load. The wound rating is not electrical caution; it is the current at which the heat still fits through the exit.
Where to go next
ONWARD #- Why bunched and buried circuits in a house are derated by the wiring rules on exactly this logic.
- Why a reel's thermal cutout trips on a wound drum long before its fuse would.
Key terms
TERMS #| Term | What it means |
|---|---|
| Resistive heating | power turned to heat in a conductor, equal to current squared times resistance. |
| Derating | reducing an allowed current because the installation removes heat less effectively than the reference case. |
| Thermal resistance | how many degrees of temperature difference each watt needs in order to cross a barrier. |
Every term the collection defines is gathered in the glossary.