Is heating element resistance linear?

Question

I know light bulbs resistance varies depending on heat. What about heating elements?

Would 2000W heating element have 26.45 Ohm (230V / 26.45 Ohm = 8.7A, so 8.7A * 230V = 2000W) resistance both in room temperatures and at 100 C degrees?

vir · Accepted Answer · 2023-10-11T16:29:34.180

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The value you're looking for is the temperature coefficient of resistance which is a term that relates the change in resistance of a given amount of your heating element material to the change in temperature. Tungsten has a TCR of 0.0045/K, nichrome has a TCR of 0.00017/K, and so forth. So (edit: if your heating element is nichrome) and has a resistance of 26.45 ohms at room temperature (let's say 20 C) then at 100 C, then the resistance should change by (80 * 0.00017) = 0.0136, or an increase of 1.36%.

edited Oct 11 '23 at 16:29

answered Oct 11 '23 at 16:17

vir

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Oh, well 1.36% not too much. – Ri Di Oct 11 '23 at 16:22
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@RiDi yes metals have a linear relationship between temperature and resistivity while semiconductors have a exponential relationship so temperature variations are more important for semiconductors.From a practical point of view if the power dissipated is in the order of W then the resistance of any metal doesnt change. – Miss Mulan Oct 11 '23 at 16:26
Well that assumes the heating element is nichrome which it may or may not be. If you're not sure, you can calculate the TCR by, say measuring the resistance when at room temperature, and calculating the resistance when hot from current, voltage, or some combination of the two. – vir Oct 11 '23 at 16:29
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Nichrome has a low temperature coefficient. The washing machine heating element may not be nichrome. Some heating elements purposely have a higher temperature coefficient so that they will tend to regulate the power output. – Mattman944 Oct 11 '23 at 16:30
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@Mattman944 still the relationship is linear.Exponential has a much higher derivative. – Miss Mulan Oct 11 '23 at 16:32
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@Mattman944 Nichrome is not the only alloy used in the heating elements, but pretty much all of them have nearly constant resistance over their usable temperature range. The washing machine heating element has in addition the luxury to be immersed in water so it has to be acceptably stable only within the narrow temperature range where water is liquid. – fraxinus Oct 12 '23 at 07:57
Just curious, does the temperature coefficient of resistance change much with temperature itself? I imagine it's not completely the same at every temperature either. – JMac Oct 12 '23 at 11:54
Also remember not to assume that the resistance element temperature is the same as the temperature of the outer element case. To deliver the required power levels through the ceramic packing, the actual element temperature can be much much higher (800C+), – colintd Oct 12 '23 at 15:24
@colintd: Of course, 800C is still nowhere near the temperature of a typical light bulb filament. – supercat Oct 12 '23 at 15:33
@supercat Agree that not as hot as a lightbulb filament, but an 800C rise is still an order of magnitude higher than the increase predicted by just considering the sheath temperature. And some high power elements have resistance members that run hotter than 800C. You'd have to look at the manufacturer datasheets to be sure. – colintd Oct 12 '23 at 15:41
@colintd: On a scale of "trivial/noticeable/significant/huge", the temperature change may advance the resistance change from "noticeable" to "significant", but I don't think it would usually come anywhere close to the "huge" change associated with typical light bulbs. I think it's worth noting that the behavior of such heating elements fall very much between that of lower-temperature elements and high-temperature devices like light bulbs. – supercat Oct 12 '23 at 16:08
@colintd: Indeed, but there's still a difference between saying resistance increases by 15% rather than 1.3%, and saying that the resistance after heating will be about an order of magnitude larger than it would be at the lower temperature (which may be true of a lightbulb, but not a typical heater). – supercat Oct 12 '23 at 16:23
@supercat Agree, and the variation with nichrome is a lot less than with tungsten. This link has interesting data on the variation of resistance with temperature https://www.eurotherm.com/machine-control-process-automation-articles/resistance-heat-process-how-you-deliver-power/ showing a 10% rise with nichrome to 1000K compared with 1700% of tungsten to 2700K (showing my earlier data for tungsten was wrong). – colintd Oct 12 '23 at 16:26

score 2 · Answer 2 · answered Oct 11 '23 at 19:09

I know light bulbs resistance varies depending on heat. What about heating elements?

A light bulb filament is made of metal, just like many heating elements. The main difference is temperature rise: light bulb filaments run very hot compared to enclosed heating elements in, say, a water heater. But open-coil elements, cooking elements and oven-style elements run above red hot, so their resistance change is quite significant - not ulike a light bulb.

In general, all resistances are nonlinear when heated, just to a different degree. Some resistance wire alloys and their assemblies are designed to be very linear in spite of heating, but the temperature range for that is more like a couple percent of the range a light bulb filament goes through.

Usually, the whole system that uses the heater/resistor is designed to accept the nonlinearity. For example, mains-rated switches are made to survive the inrush current transients into cold light bulbs... or into discharged switching power supplies for that matter :)

score 2 · Answer 3 · edited Oct 12 '23 at 14:58

Heating elements, like those found in electric heaters or ovens, are generally made of materials with a positive temperature coefficient of resistance, meaning their resistance increases with temperature. This is in contrast to some semiconductor materials which have a negative temperature coefficient. One common material used for heating elements is nichrome (a nickel-chromium alloy).

The resistance of a heating element when cold (room temperature) will typically be lower than when it's hot (operating temperature). This is why, if you measure the resistance of a heating element when it's at room temperature, you might get a reading that's somewhat lower than what you'd expect based on its power rating at a given voltage.

Given your example, if a 2000 W heating element is designed to operate at 230 V:

$$P = \frac{V^2}{R}$$

Where:

\$P\$ is power (2000 W in this case)
\$V\$ is voltage (230 V in this case)
\$R\$ is resistance

Rearranging the equation for resistance, we get:

$$R = \frac{V^2}{P}$$

Substituting in the given values:

$$R = \frac{230^2}{2000} = 26.45 \text{ ohms}$$

However, this 26.45 ohms would be the resistance of the heating element when it's at its operating temperature, not necessarily when it's cold. If you were to measure the resistance of the element at room temperature, you might find it's somewhat lower than 26.45 ohms. When you power it up and it heats to its working temperature, its resistance would increase to the 26.45 ohms value (or close to it), which would result in the 2000 W power consumption at 230 V.

To determine the exact resistance at room temperature, one would need to know the specific material properties of the heating element and how its resistance changes with temperature. However, in many practical scenarios, for safety and design reasons, this "cold" resistance value is less crucial than the "hot" resistance value which determines the power consumption and performance of the device.

score 1 · Answer 4 · answered Oct 12 '23 at 08:15

There are 3 main groups of materials in regard to electrical resistance vs temperature: pure metals, alloys and semiconductors.

Tungsten in the lightbulb is as pure as practical and its resistance is nearly proportional to the absolute temperature. A cold lightbulb is ~300K and up and running lightbulb is ~3000K so the resistance is 10 times higher. It's the same with copper, but it is easier to melt and ruin the experiment. On the other hand, a lot of automotive temperature sensors are a platinum coil, calibrated to show 1 ohm for each kelvin of absolute temperature. Easy, isn't it? (Why copper does not work well in this role is an extended question, but it boils down to copper having ability to oxidize and its resistance also depending on mechanical stress and annealing.)

Semiconductors: their resistance goes down with heating, generally exponentially.

Alloys: They do whatever they like, but a lot of them show nearly constant resistance over an extended temperature interval. This is what most heating elements are made of. The possibility of having constant resistance over some temperature interval is great, because it simplifies engineering.

score 0 · Answer 5 · answered Oct 11 '23 at 16:22

Those who are made of semiconducting materials yes.According to Wikipedia a heating element can be built from a metal or a semiconducting material.What if it is?.It doesnt change anything.The resistance simply is a function of time \$R=R(t)\$ just like a light bulb.For example to calculate heat now you cant multiply \$\frac{V^{2}}{R}t\$ but you integrate over t.

Is heating element resistance linear?

5 Answers5