We had a little discussion in the physics class. We were talking about resistance, and she said that when a wire is heated up, the resistance also increases; but I think that the resistance decreases because when something is heated up the electrons also gain energy, enabling them to move with lower resistance. So what is correct approach and solution to this problem?

  • $\begingroup$ To start thinking about this you need to think about why there is resistance in the first place. What prevents a charge carrier to accelerate without bound when subject to an electric field. $\endgroup$ – garyp Mar 6 '17 at 14:51
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    $\begingroup$ How did you make your user name look the same as Qmechanic's? $\endgroup$ – Brian Moths Mar 6 '17 at 14:58
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    $\begingroup$ @Qmechanic - reincarnation? Who will get my reference now? User 2451 or 147133 ? $\endgroup$ – jaromrax Mar 6 '17 at 15:01
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    $\begingroup$ @NowIGetToLearnWhatAHeadIs: User names are not unique on Stack Exchange sites. $\endgroup$ – Dennis Williamson Mar 6 '17 at 17:32
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    $\begingroup$ Dennis is correct that repeated usernames are allowed, but I would strongly urge you (the new Qmechanic) to consider changing username to one without a collision - particularly since (the old) Qmechanic is a moderator on this site, in addition to being a long-established member. It's your choice entirely, but do consider it. $\endgroup$ – Emilio Pisanty Mar 9 '17 at 11:13

Either one can be true depending on the material. In metals, the electrons don't need any additional energy to move, so the main effect of temperature is to cause the atoms to vibrate more, which interferes with the motion of the electrons, increasing the resistance.

On the other hand, in a semiconductor, the electrons do need to gain some non-zero amount of energy before they can start moving at all. In this case, raising the temperature does decrease the resistance for the reason you state.

On wikipedia it says:

Near room temperature, the resistivity of metals typically increases as temperature is increased, while the resistivity of semiconductors typically decreases as temperature is increased. The resistivity of insulators and electrolytes may increase or decrease depending on the system.

You can read more about these effects on wikipedia here and here.

  • $\begingroup$ The behavior can be complicated - phases/crystal structures can also change. $\endgroup$ – jaromrax Mar 6 '17 at 15:03
  • $\begingroup$ @jaromrax: True, but if you're talking about crystal structure changes you should probably also consider the effects of annealing, and in that case the resistance depends not only on the metal's current temperature but on its entire temperature history. $\endgroup$ – Michael Seifert Mar 6 '17 at 20:39
  • $\begingroup$ And just to make life interesting, the class of devices called thermistors exists. The common manufacturing technique is to sinter metal-oxide particles to form a block or disk. Depending on material, these can be PTC (positive temperature coefficient) or NTC (negative temperature coefficient). And a few materials have essentially zero temperature coefficient. It all depends on the material. $\endgroup$ – WhatRoughBeast Mar 6 '17 at 20:50
  • $\begingroup$ This might also be interesting to the discussion. There are tables of empirically determined coefficients floating around the internet. Depending on that coefficient (i.e. the material), the resistance might not change at all. $\endgroup$ – Dave Mar 8 '17 at 9:31

The problem with assuming that "hotter" free electrons in a metal convey more current is that their motion is random in direction and so they do not contribute to the electric current as there is no net drift of charge.
Their average velocity due to their thermal motion is zero.

The application of an electric field accelerates the free electrons and so they gain kinetic energy and now the free electrons have a net velocity along the conductor, hence this motion constitutes a movement of charges in a particular direction - an electric current.

However the free electrons collide with the lattice ions and transfer energy to the lattice ions which now have a greater kinetic energy - the temperature goes up as there has been ohmic heating.

So the free electrons have an average velocity along the wire called the drift velocity.
The drift velocity is order of magnitude 1 mm/s whereas the speed of the free electrons due to their thermal motion is order of magnitude 100 km/s.

With more kinetic energy the lattice ions vibrate more and thus there is a greater probability of the drifting free electrons colliding with them - the resistance has increased.

For a metal as the temperature increases its resistance increases because of the lattice ions vibrating more at higher temperatures.

For a lot of semiconductors and insulators raising the temperature increases the number of charge carriers and so the resistance decreases with increased temperature

  • $\begingroup$ If it helps, a specific example of heating a conductor is in the heating element in a toaster. There is no conditioning on the power going through that wire, so the only thing which limits its current is that, as it heats up, its resistance increases. $\endgroup$ – Cort Ammon Mar 6 '17 at 19:09
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    $\begingroup$ @Cort It's not that simple. You would need to know/measure this. The fact, that the conductor is also the heating element only proves that it has non-zero resistance, but doesn't say anything about it's dependency on the temperature. "There is no conditioning on the power going through that wire, so the only thing which limits its current is that, as it heats up, its resistance increases." unfortunately that is wrong, there is something called internal resistance. There is a reason why you check alkaline battery with your tongue, but should avoid it with a car battery. $\endgroup$ – luk32 Mar 6 '17 at 22:15
  • $\begingroup$ I'd be surprised if the internal resistance of a 120V power line plays a major factor. In fact, if it did that would require that the power lines in your walls heat up substantially as they dissipate power. I've seen estimates between 0.02 and 0.40 ohms internal resistance for those power lines. Testing a 120V power line with your tongue is not recommended! $\endgroup$ – Cort Ammon Mar 7 '17 at 21:57

Note that in supra-conductors the temperature is usually very low, so low temperature and apparent mobility restriction are not incompatible with low resistivity.

In fact more thermal agitation also means more vibrations so to sketch it in very simple words, these are counteracting the electric force that forces the electrons to behave and be in a certain state, but they don't want to.

To come back to the question about resistvity of wires, the phenomenon of increasing of resistivity when heating has long been used as a natural current regulator. The intensity increase, so by Joule effect the wire is heating up, so resistivity increases, so intensity decrease and so on. For instance lightbulbs have been used in such a way, as very cheap but efficient current regulators, because the filament reaches hight temperatures and the effect is notable.


protected by Qmechanic Mar 7 '17 at 12:55

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