# What's the rationale behind these warnings about extension cords?

(Disclaimer: I've read the help center and I do understand that this is bordering on off-topic since it's about consumer devices. However I hope that I've managed to make enough on-topic by asking about why it is the way it is, and what is the explanation from an electromagnetic point of view - in other words, what laws of electricity and what practical considerations have gone into these decisions).

I recently bought a power tool and in its manual I found a few peculiar safety rules. I cannot see why they would be there, although reading up more it seems that they are commonplace. My understanding of electricity is limited (just about enough to be dangerous), so I'm hoping to expand it. :)

The rules are:

• Don't use an extension cord longer than 25m. Considering this is an outdoors tool, this limitation is severely restrictive. The best explanation I've seen is that longer cables would simply have too high of a resistance and the tool wouldn't be able to operate at full power. But this argument doesn't convince me. The tool is rated at 2.4kW, and it's meant to be used with 220V AC power source, which means it uses about 11 amps of current. All the extension cords I've ever come across have at least 16A limitation, so there is quite a reserve still. In addition, the power has to travel much, much further to get to my house, and even after the meter it still takes probably close to those same 25m to get to the power outlet. Why only 25m after the outlet? The resistance of the cables isn't that big, is it?
• Don't daisy-chain extension cords. I suspect this is a variation of the above - don't exceed 25m; every connection adds additional contact resistance; water in the outdoors connections can be a problem - in general, it just adds risk. However, apart from the water in the contacts, the rest seems to me to be practically negligible. Is there really a significant contact resistance? Assuming that the extension cords are in a good shape.
• Make sure that the power cord is entirely unrolled. This is another odd one. My suspicion is that it has to do with inductive resistance. But is it really that strong? Wherever I've seen people actually wanting to create an electromagnet, it's pretty much hard work. You need a lot of neat, tightly-wound loops of wire. An extension cord has a lot of insulator around it, spacing the wires pretty far apart, and the loops are very chaotic. In addition, if that was a problem, why do extension cord rollers exist? They're used especially when you need a very long extension cord, and you don't need to unroll them completely every time you want to use them. Solved: OK, I was off the mark. The correct answer (also a separate question) has to do with the wire heating up from being used close to its limits. When coiled together, the temperature can go pretty high and melt the cables. Not fun.
• The unrolling requirement is probably more about the cord heating up than about inductance. – The Photon Aug 6 '18 at 22:54
• Bear in mind that heat=I^2*R. So what is safe at low currents, gets 4x as hot if you double the current. Which explains why the plug burnt off the end of the extension cable charging my car shortly after I replaced the standard 8A charge cable with a 16A charger. – Henry Crun Aug 6 '18 at 23:01
• Possible duplicate of Why is it dangerous use a coiled extension cord – Dmitry Grigoryev Aug 7 '18 at 8:26

Let's say you're extension cables are 1 mm² cross-sectional area.

• The loop resistance is 33.6 mΩ/m.
• A 25 m cable will have a loop resistance of 840 mΩ.
• The voltage drop at 11 A will be given by V = IR = 11 x 0.84 = 9.24 V. On a 220 V supply this is a reduction of 4.2%.
• Power dissipated as heat in the cable is given by P = VI or P = I²R = 11² x 0.84 = 102 W. This is a waste of 4.2% power (as we would expect from the previous calculation).
• String four cords together for a 100 m run and you'll only get 220 - (9.24 x 4) = 183 V.

The situation is a little more complicated than the calculations above suggest because when you add in the cable resistance the current will reduce too. For a 2.4 kW, 220 V load we can calculate $R = \frac {V^2}{P} = \frac {220^2}{2400} = 20.2\ \Omega$. Add in our 100 m loop cable resistance of 4 x 0.84 Ω and the total resistance is now 23.6 Ω resulting in a max current of only 9.3 A which at 183 V (calculated above) reduces the power to VI = 183 x 9.3 = 1700 W which is only 71% of the rated power. The "square" term in the power equation makes the power loss proportional to the square of the voltage loss.

Don't use an extension cord longer than 25m. ... and the tool wouldn't be able to operate at full power. But this argument doesn't convince me.

Be convinced by the maths.

All the extension cords I've ever come across have at least 16A limitation, so there is quite a reserve still.

See if you can find the cross-sectional area for those cables and recalculate.

In addition, the power has to travel much, much further to get to my house, and even after the meter it still takes probably close to those same 25m to get to the power outlet.

Ideally your local transformer will be fairly close to your house and, in Ireland, the connection will be using at least 25 mm² cable. You can get some idea of the source "resistance" to your house by monitoring the voltage while you switch on and off a large load such as an electric oven and all the hobs.

Don't daisy-chain extension cords. ... the rest seems to me to be practically negligible.

It may be tolerable (depending on your load) but it's not negligible.

Is there really a significant contact resistance?

This is usually not a factor.

Make sure that the power cord is entirely unrolled.

Our calculations showed that the power dissipated in the cable is 100 W. With the cable tightly rolled the coil temperature will rise. Imagine you wound the cable around a 100 W filament light bulb: what temperature do you think would be reached? Would it get close to melting the insulation?

Figure 1. Source: Why is it dangerous use a coiled extension cord.

My suspicion is that it has to do with inductive resistance.

The term you are looking for is "impedance" for AC resistance. Actually there will be almost zero inductance as the live and neutral currents are in opposite directions and cancel out. I used this trick in work when I needed to create a test load for a 30 A, 30 V 50 Hz supply. We first wound a coil of 1.5 mm² cable of the correct resistance but it was really hopping when we powered it up. When we unwound it, folded in half and rewound it there was no buzz.

Figure 2. Inductance cancellation. See my answer to the question linked above.

But is it really that strong? ... You need a lot of neat, tightly-wound loops of wire.

Or a high current in a low number of turns.

• If 25m of cable causes a 4.2% volt drop, then a 100m one could result in such a large volt drop that the power tool may stall or malfunction as it is running well outside its specified voltage. – Simon B Aug 7 '18 at 8:34
• What materials did you use for the calculation? I get that number for Calcium, but I haven't heard of extension cords with that kind of material. With copper I get 0.42Ω for a 25m/1mm² cable; Aluminium gives 0.705Ω. Anyway, very interesting. The numbers are indeed much higher than I would have thought. Also, in my case (rural area) the transformer is actually several km away. The wiring inside the house also isn't the latest edition... I'll have to think about it. Or better yet - take a multimeter with me and proceed with caution. – Vilx- Aug 7 '18 at 10:59
• I was updating the answer as you commented. The word you missed is "loop" in the second sentence. Your 25 m of cable is 50 m of copper. Double your 0.42 Ω to get my 0.84 Ω. Thank you for accepting my answer. – Transistor Aug 7 '18 at 11:13
• Ahh, indeed! Good point! You're welcome about accepting - this is the answer that I was looking for - a thorough explanation with numbers attached. :) – Vilx- Aug 7 '18 at 11:25
• Oh, and a good update too! Definitely food for thought. – Vilx- Aug 7 '18 at 11:39

There are no laws of physics that are being violated by any of these "rules". These rules should be considered "rules of thumb". For example, a 10W light bulb on the end of a 26m extension cord run for 20 minutes would cause no significant danger due to resistive heating, while a 15A load on the end of a 24m cord (well within the "rules" of your question) run 24 hours a day might be a real concern.

These are common sense safety suggestions. Extension cords are designed for temporary usage, and these suggestions are to help the common user safe.

• I understand that, but I'd like to know in detail - what are the specific risks? In other words - every good advice comes with a rationale, so you can know when to disregard it. I want to understand these rules, so I know when and how it's safe to break them. And, of course, increase my general knowledge about electricity, so I can apply it not only in this case, but in others as well. :) – Vilx- Aug 6 '18 at 22:53
• I would rather call them "rules of dumb". i.e. designed to protect manufacturer from lawsuit in case someone does not fully insert extension plug, or steps into coiled cable and trips, stuff like that – Maple Aug 7 '18 at 0:48
1. If you use an extension cord longer than 25m on a branch circuit that just barely meets the voltage requirement under full load (220V -6% I believe) the tools motor could stall and draw excess current.

2. Don’t circumvent 1, plus each connection potentially has a significant resistance associated with it which will reduce the allowable length more.

3. The heat from the resistance of the wires is all concentrated, potentially overheating the insulation and causing a fire.

In North America, electrical codes (the regulations that govern these kinds of things) are a mix of physics, engineering, and hard-won experience.

You're asking for physics, or perhaps engineering, based answers. Particularly for your (1) and (2), it may well be that regulatory bodies noticed a higher incidence of adverse outcomes from long cords or cascaded cords, and set the rule on that basis. I.e. "We've noticed that people have gotten an arc flash and fire when they pull coupled cords apart, particularly when they were lying on grass" (that's a hypothetical example; I have no idea what the actual adverse events were, if any)

A lot of electrical safety regulation is based on observing how the technologies are used and abused, not on any first-principle calculation.

• In a volatile atmosphere or in the presence of volatile chemicals that's absolutely a concern. – K H Aug 7 '18 at 7:58

If necessary you can build yourself oversize extension cords for such use. If you buy a 100ft construction grade 15 amp extension cord, you'll probably find it has been oversized to 12 guage. You can build your own 10 guage cord if it suits you, and as long as you accommodate for volt drop you should be fine. Be aware that the warnings on the cord tend to be based on a combination of worst-case scenario, reported user error, and a calculated probability in the regions that company operates that people will sue over safety risks.

You can see a lot of the hazards that can appear with cords in a construction environment. Sometimes long cords are necessary and sometimes it becomes necessary to string several together. For new construction, general contractors often accommodate for this by putting in either multiple temporary generators or a single large generator or mains connection to feed a network of temporary power panels that spider out to feed receptacles so that the maximum necessary cord to any part of the work area is limited.

Sometimes multiple-minor-error problem occur too. I run a 80ft extension cord to where I'm working, and I plug a splitter into it, work for the last 2 hours and go home for the night, not cleaning up my cord. The next morning I go work on something else and someone comes along, plugs into the splitter, runs a long cord and so does another guy. Even in these situations though, usually before any tools are damaged, someone notices lightbulbs flickering too much or a breaker pops because a guy ran his drill at the same time as someone ran their saw or hammer drill. Then one guy says sorry and runs his own cord to a separate outlet.

These warnings are part "best practice" and part "idiotproofing" and in reality with a bit of common sense you probably can avoid the situations that necessitate them. That said if it's part of a legal code, not just a manufacturer's warning, there's no sense risking your accreditation over it.

Extension cords and other wires have higher current rating in free air (unrolled) than they do in a confined environment (rolled).

A good rule of thumb for AWG wires is that going up or down 3 wire sizes doubles or halves the resistance per foot, respectively. So if you want to double the length of your cable, you double it's resistance and you can increase it by 3 AWG sizes across most of the AWG size range to cancel this.

Low cable impedance is essential for fuses to work correctly.

When a device on a very long or thin cable shorts out, high cable resistance will limit the short circuit current. If the short circuit current gets too low, the fuse may take very long (or forever) to blow, turning the cable into a distributed heater/toaster/ignitor/electrocutor neatly draped around the house.

• Interesting point. I never thought of that. However... if the cable is indeed so long, that its impedance is actually large enough to NOT trigger the resistor, then isn't the heat distributed neatly along it too? Unless the cable is rolled up, it shouldn't heat up that much, no? Or another way to look at it - the cable only heats up when there is too much current passing through it. The higher its impedance, the lower the current. Fuses blow when the current limit is exceeded. If the current is below the fuse's limit, then the cable shouldn't heat up that much either, no? – Vilx- Aug 8 '18 at 8:27
• @Vilx: In essence, yes, this answer is a bit weird. To limit a short circuit current to (say) 20 amps would require an in-or-di-nate amount of normal cords. If you could store all this cable in a spaced fashion you might get rid of the heat, yes. But it's not a very practical problem. – peter Aug 10 '18 at 9:19
• @Vilx: Much more practical is this: An Arduino enthousiast hooking up LED lamps through the house using long, thin breadboard wires: "No Dad, it's fine, it's only a few milliamps...", "Feel; Cables don't heat up a bit...". Here a 10 ohm cable resistance is imaginable. And these wires will not remain cool while conducting 20A. – peter Aug 10 '18 at 9:29
• Is this something you've ever actually seen/heard about, or is this purely theoretical? – Vilx- Aug 10 '18 at 10:03