# Why are cables rated for current not power?

I was wondering, since resistors are rated for power, not current (so one can blow them with both overcurrent or overvoltage), then why are cables rated only for current? Aren't resistors just stacked up wires? The question could be also asked in reverse- why are resistors rated for power, not current only?

• Because the power is 1-to-1 defined given the current. $P=I^2 R$ Oct 15 '20 at 15:51
• Cables are also rated for voltage. (More strictly, the insulation around them is). But resistors are rated for power because they dissipate that power and get hot. A cable's job is to transmit that power somewhere else : the only dissipation is from the current and its own resistance; regardless of the voltage (up to its rating). Oct 15 '20 at 15:55
• @BrianDrummond That's a bit of a circular argument. We could easily spec resistors with current limits too - the reason we use power is that you can get a whole kit of hundreds of resistors all 1/4W rated and that's simple. If they were rated on current you would need a different rating for each resistor, which is annoying and overly complicated. For wire the resistance is always nominally zero, so the current rating makes much more sense.
– J...
Oct 16 '20 at 14:03
• I like the reverse question: I can count on one hand the number of times I've needed a resistor to dissipate a certain amount of power, but I am constantly having to calculate if a resistor can withstand the current I want to put through it Oct 16 '20 at 16:07
• I believe it's because how they are connected. Cable are used to transfer power, not 'consume' it. As such they are connected in such a way as to have negligible voltage drop across their ends. The relevant quantity is the current, that also happens to be the same current that flows into the load, no matter the length of the cable. ( Also note that the voltage rating is not referred to the voltage across the cable's ends, bit to the voltage with respect to nearby conductors) Oct 16 '20 at 18:17

Resistors are all the same size no matter the resistance. It's convenient for the manufacturer to test how much power a certain-sized resistor can take before it burns up. And it's the same for all resistors of that size. Also the power rating is the same regardless of the resistor's exact resistance (within the tolerance).

Cables with different current ratings are different sizes, so there's no such shortcut.

But actually, cables aren't usually rated for current. They're rated for their size, maximum temperature, and resistance, and you have to look up the current for that size, and you'll find a different answer depending on whether the wire is on its own, or in a bundle of other wires, or in a conduit, etc. That's because it's really the temperature that matters, not the current.

• Yes, its the temperature that kills us, not the current Oct 15 '20 at 17:35
• @ŁukaszPrzeniosło and it's the current through a resistor that heats it up and when there is a dominant load in series it's easier to get at the current from that load's spec and then infer the power generated in the wire that way Oct 16 '20 at 12:19
• It certainly can be the temperature that kills us if the cable insulation catches fire which is particularly a risk for wound-up extension reels, having caused many a house fire in the past. Oct 16 '20 at 14:18
• @AndyHames Am I the only one who doesn't actually believe this wound-up extension cord thing? What kind of thin extension cords and high-current devices do you have in your country? I used to pile up the extension cord for the vacuum cleaner to see if it would get warm and it never did. Oct 16 '20 at 14:27
• @user253751 Like you I used to be a bit sceptical but I have personally seen the results of powering a 3kW fan heater via a partially wound cable reel - thoroughly melted insulation and blown fuse. (No, it wasn't me!) It was wound on a wooden drum, so not just loosely piled up; but not enclosed, though. Oct 17 '20 at 10:21

Cables are rated for power too, but somewhat indirectly. They have a stated thermal limit as well as a maximum working voltage (insulation strength). Nevertheless it's usually more convenient to think of their current handling capability since their primary purpose is to do exactly that: move current.

You would arrive at the cable's current rating from the unit resistance for the wire, and its maximum allowed thermal rise. This sets a basic current limit for a given ambient temperature (More about that in a bit.)

Unsurprisingly, larger wires have lower unit resistance, will heat less, and therefore can carry more current before they heat up so much that they burn away or melt. Wires with higher temperature ratings can also carry more current. So can wires that have better cooling to shed the heat.

Given the complexity of figuring out all this stuff, for power cables they’ve worked out those limits for you and call it ampacity, a made-up electrician word that’s a portmanteau of, you guessed it, amperes + capacity. Multiply that ampacity value times the voltage rating and you get the cable's ultimate safe power handling capability.

On the other hand, resistors are rated for power directly, again based on their allowed maximum thermal rise. Being resistors, they of course have a stated resistance; their allowable current varies inversely with resistance squared. (Recall that $$\ I = \sqrt{\frac{W}{R}} = \frac{\sqrt{W}}{\sqrt{R}} \$$).

Example:

• 1 ohm, 1W-rated resistor can safety carry 1A
• 100 ohm, 1W resistor can carry only 0.1A.

You may not have noticed this, but resistors are rated for voltage too. Physically-small resistors have surprisingly low voltage ratings. This comes in to play when designing off-the-line or high-voltage electronics.

Derating

Finally, there’s one more concept that applies to both resistors and wires called derating. Simply stated, derating means that with higher ambient temperature and/or less-favorable cooling, the power dissipation allowed (that is, thermal rise) must be reduced to keep the circuit element within safe thermal limits.

Cables used for power wiring use ampacity tables to specify derating. These not only use the ambient temp, but also the wire type and the cable's environment (e.g., open air vs. conduit vs. duct) to determine the safe current for that cable.

Ampacity Table Example:

Resistors specify a maximum ambient temperature with an assumed environment, with derating applied linearly above that max ambient limit set for the device.

Resistor Derating Example:

Cables are rated for power - it's just that it's not a useful way to think about it. The upper rating on cable size will be determined by how hot it gets before its insulation is damaged - and this will depend directly both on conductor size and insulation characteristics.

Cables aren't intended to drop voltage, they are intended to carry current with an allowable maximum voltage drop. Power can be expressed as either voltage and resistance or current and resistance. Since voltage isn't normally an issue, current is the dominant concern.

"Cable" in this question is excessively broad. Conductors are rated for current (an excess causing a rise in temperature), insulation is rated for voltage (assuming that it has not been degraded by a rise in temperature), in combination the cable is rated for power.

• The current rating of a conductor and the voltage rating if an insulator do not combine in any kind of simple way to give you a meaningful power rating for the cable.
– Matt
Oct 16 '20 at 14:44
• @MarkMorganLloyd "in combination the cable is rated for power". What combination? How do they combine? My point is that they don't combine. A voltage and a current written down next to each other is not a power. I dont see what your temperature dependency question has to do with this.
– Matt
Oct 16 '20 at 14:54
• @MarkMorganLloyd "I can't for the moment think of an insulating material that has characteristics which improve as it gets hotter" is the question I'm referring to. Its not a question you are asking, but it is a question you were seemingly trying to answer for reasons I still do not understand since all of that is irrelevant to you combining current and voltage in unspecified ways to arrive at some kind of very unclear cable power rating. Being intentionally vague in answers is usually a bad strategy for conveying information.
– Matt
Oct 16 '20 at 15:23
• @MarkMorganLloyd You are the one muddying the waters by stating that you can get a meaningful power rating from the voltage rating of the insulator and current rating of the conductor (which is false) and now for some reason bringing these ceramics into it which have nothing at all to do with the question instead and saying you are being intentionally vague instead of just stating what you mean.
– Matt
Oct 16 '20 at 15:46
• If you multiply conductor current rating with insulation ratings you get insane power ratings which are useless. If you use european cable rated for 2kW and try to power 2kW in USA, the cable will melt... Oct 16 '20 at 15:51

Cables are rated for safe V and A but W, loss depends on R load =V/A. not V*A=Wload

The temp rise in cables is the safety point for insulation which is determined by Loss power=I^2R per meter and the thermal R per meter. It is not VI = W into the load.

Here I am using units A=Amp, V=Volts, W=Watts rather than symbols like U or V for volts.

Normally wires are rated by Amps for a given wire gauge, yet insulation thermal resistance is high for electrical reasons may vary. The temp rise and Ratings are linked.

• It is rather confusing to mix symbols and units. The clarification below is just a crutch. -1 if I could give one... Oct 16 '20 at 6:51
• In calculations it is often beneficial to incl. units after the numbers. I was writing to a certain audience. Thanks for your feedback @GoodbyeSE but where are my symbols . Nothing is mixed. Oct 16 '20 at 6:52
• R and I are the symbols for resistance and current. V, A and W are the units that you mostly use in the descrption. I could live with a consistent use of Units, still it would be rather "clumsy"(in lack of a better word, as a non-native speaker). But your point that in calculations you add units after the numbers is perfectly fine. You should keep in mind though that without the numbers units are out of place and you would use the symbols for the formula (as you do with I^2*R). And it is mixed here : "R load =V/A. not V*A=Wload" . The R is the symbol while the rest is units. Oct 16 '20 at 7:04
• @GoodbyeSE ok Point taken, it was a bad call on my part and verity atypical Oct 16 '20 at 9:04

Ideally wires are 0ohm conductors which is acceptable if one compare them to motors, lights, etc. When people are talking about power, they intuitively think about the power of the motor, light etc.

In the setup you have a power source of known (almost) constant voltage, the actual load resistance. The only paameter that is to adapt is current.

As the wires are not ideal and they have, among others, nonzero resistance. But for the setup, resistance is known but voltage drop is not, the current is known instead.

Then we go what cause the wire to fail. It is either breaking the connection or connecting two wires that are not to be connected (usually hot-to-neutral or hot-to-ground). This can be achieved by excessive temperature melting/burning the insulation or melting/evaporating the wire by even more excessive temperature.

So any real wire is heating up by the current through it through Joule heat (u x i=R x i^2) and heat dissipation is cooling it down to ambient temperature. If the current is too high the tempreature will exceed the integrity margins, the insulation melts,...

If one keeps the ambient temperature within limits, the current ratings are the simplest ratings to tabelate. And to be honest, if you are about to lay cables where temperature is not expected to stay within safe limits you shall know what you do for sure.

Say you want to connect 2.2kW setup in the kitchen on one branch and you have 110V supply. Easy math say that 20A is the expected current draw, lets go for 25A wires at least. Job's done.

If the wires were power rated, and say in EU, you will get cables rated 2.3kW which seems almost safe. Nope, for this wattage they are expected for 10A load, because of 230V circuits, but you will draw 20A, you know. Fire! So tehy would need to be rated 2.3 kW at 230V to be safely labelled - which is 10A rating but using much more text.

Also you may choose between 3-phase connection or 1-phase. Then your cables would need to contain information about this as well. With just current ratings you can calculate the safety margins the way thet is more fool-proof or smartass-reppelent.

In a line of 1/4 watt resistors, they're all the same size with similar construction and packaging, no matter what the value is. The power they dissipate is turned into heat, and no matter what the value is they can dissipate 1/4 watt of heat power before they get too hot and stuff melts.

Wires, on the other hand, are sold and used by the foot and you can buy whatever length you want. The power you can make them safely dissipate is proportional to their length. It doesn't make sense to sell "6 watt wire", for example, because when you use 20 feet of it you can safely dissipate twice as much power as 10 feet of wire.

It would make more sense to sell, say, "6 watt/foot wire", but that's not convenient, because in order to calculate how much power you're dissipating in a wire, you'd have to know its resistance, and that's not on the list of top 10 things circuit designers are thinking about. Wire is supposed to be as close to 0 as possible, and the power lost to wires is generally small compared to the stuff that does real work.

So, instead of making you figure out the resistance/conductance of your wire and then multiplying by the square of current to figure out how much power is dissipated per foot so that you could compare it to a watt/foot limit... Kinds of wire products are rated in terms of current, because that is something you do know, and its square is proportional to watts/foot. The constant of proportionality depends on characteristics of the wire that are known to the manufacturer, but which you would usually rather not think about.

## Wires DO have a power rating!!!

The power rating is how many watts per foot/metre of energy they can dissipate before exceeding their thermal limits.

This is exactly the same thermal limits as a resistor is concerned with.

For instance a #12 THHN wire has insulation rated for 90C. One foot of #12 has a resistance of 1.6 milliohms. NEC 310.15B16 says to allow 30A on that wire at thermal limits of 90C ( disregarding 240.4D).. Ohm's Law says that 1’ of wire will drop 48 millivolts, which means effective wire power rating is 144 milliwatts per foot.

As others have mentioned, cables do have power ratings, and power through a resistive element is proportional to current squared.

The reason we see the limited phrased in current terms rather than power terms is that current is easily measured and controlled.

Its very hard to measure power drop across a cable because it's typically a very small factor in the total power dissipation. This would make it very hard to prove that you are within the cable's limits, if all you had were power numbers.

Likewise, if all you have is a schematic, and you're trying to prove that it will be safe to turn a device on, current is a much easier thing to use. In a typical (non-short) situation, the current calculated assuming an ideal wire will be a pretty darn good approximation of the current through the real wire. (Obviously, power dissipation in an ideal wire is 0, so that's not all that helpful for modeling the safety of using the real circuit)

Resistors ARE rated for current. A resistor of a given value will have a max current it can sustain indefinitely. But since watts generated are a function of current times voltage, wattage is equal to I squared times R. And, for a given form factor, maximum wattage is reasonably independent of the particular resistance value.

So it's easier to spec resistors in terms of max wattage rather than max current.

Current and voltage ratings are given for cables whose purpose is to convey non-trivial amounts of current through wires whose potential may differ by a non-trivial amount. Although cables may dissipate power during use, that is not their intended purpose. By contrast, the purpose of a resistor is to consume energy from electrons that flow through it, so that the electrons that leave have less electric potential energy than the ones that enter. A "resistor" that didn't dissipate power wouldn't be functioning as a resistor, but either as an ideal conductor, inductor, capacitor, or insulator.