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I get confused on the low-level physics of electricity from time to time. It came up in "Which way does electricity power a circuit," and I don't totally get it.

How fast does electricity flow? Is the speed of an electron different in say a resistor than in a wire? Does it matter? Or are the effects of the electron the only important thing, with lower levels of abstraction not useful in practice?

I know there are already materials on this topic, and I have read some of them. I think having the question on this site might inspire some interesting answers to the age-old question.

Bonus points for:

  • Identifying and clearing up common misconceptions
  • Explaining in a way that someone with a high school diploma could understand, without oversimplifying it so much that its incorrect
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  • \$\begingroup\$ Possible duplicate (among others): electronics.stackexchange.com/questions/39509/… \$\endgroup\$ – Shamtam Aug 9 '13 at 2:18
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    \$\begingroup\$ @Shamtam, eh, "How fast does electricity flow" is not the duplicate of "if I make a http request from europe to a server in USA, do some of electrons from my PC, in 200 ms the response takes, travel across the Atlantic ocean to USA and come back to me?" Maybe the answers are related, but the questions are very different. \$\endgroup\$ – travisbartley Aug 9 '13 at 2:21
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    \$\begingroup\$ @Shamtam I recall a passage from Clifford Stoll's book The Cuckoo's Egg (which I have only read in Swedish, so bear with me for the exact phrasing) where, after measuring the network data routing delay for the traffic as a computer intruder is using their system, Stoll pronounces "based on elementary physics, I declare that the hacker is on the moon". Packet routing is one major thing he failed to consider in that estimate. After revising the hypothesis to account for that, the conclusion was approximately "the other side of the world", which turned out to be right: California to Germany. \$\endgroup\$ – a CVn Aug 9 '13 at 14:13
  • \$\begingroup\$ Related: superuser.com/questions/391661 \$\endgroup\$ – BlueRaja - Danny Pflughoeft Aug 9 '13 at 16:12
  • \$\begingroup\$ Wikipedia: en.wikipedia.org/wiki/Drift_velocity \$\endgroup\$ – Kaz Aug 9 '13 at 19:06
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How fast does electricity flow? This is a good question, because it seems like a simple enough question, but usually it indicates some underlying misconceptions. The first difficulty in answering the question is knowing, what is electricity? Do you mean:

  1. How fast do changes in electrical fields propagate? or...
  2. How fast do electrical charge carriers move?

Usually, people asking this question actually care about the former, but are thinking about the latter. However, not having a clear understanding of the difference, their underlying concern actually can't be addressed without stepping back and addressing the underlying misconceptions which lead to the question.

Understand is this: there are forces, and there are things that transmit forces, and they are not the same thing. Here's an example: I'm holding one end of a rope, and you are holding the other end. When I want to get your attention, I tug the rope. There is the rope, and there is the tug. The tug travels as a wave of force down the rope at the speed of sound in the rope. The rope itself will move at some other speed.

Say I have two lookout towers, and when I see the approaching invaders, I shout to the other tower. Sound will travel as waves in the air at the speed of sound. How fast are the molecules in air moving? Do you care?

Some people won't let this go until the motion of the molecules is actually explained, even though it's usually not relevant to their concerns. So here's the answer: the molecules are flying around in all random directions, all the time. They fly around because they have non-zero temperature. Some are very fast. Some are very slow. They bump into each other all the time. It's very random.

When you shout, your vocal tract compresses (and rarefies, as your vocal cords vibrate) some of the air. The molecules in this compressed region want to move to a region with less pressure, so they do. But now this nearby region has too much air, and is a little more compressed than the air around it, so the compressed region expands outward a little more. This wave of compression moves through the air at the speed of sound.

All of this happens superimposed on the random motion of the molecules previously mentioned. It's unlikely that the same molecules that were in your vocal tract will be the ones that vibrate in the listener's ear. If you watch individual molecules, you will observe them going in all directions. Only if you observe a lot of them will you notice that slightly more went in one direction versus another. It is true for all things we would call "sound" that the random motion of the molecules due to thermal noise is much more than their motion due to sound. When the "sound" becomes the more relevant motion, we tend to call it not "sound" but rather an "explosion".

The situation with electricity is not much different. A metal conductor is full of electrons that are free to wander around the entire circuit in random directions, and they do, simply because they are warm. Things in our circuits make waves in this sea of electrons, and these waves propagate at the speed of light1. At the currents we typically encounter in circuits, most of the electron motion is due to thermal noise.

So now we can answer the questions:

How fast do changes in electrical fields propagate? At the speed of light in the medium in which they are propagating. For most cables, this is in the neighborhood of 60% to 90% of the speed of light in a vacuum.

How fast do electrical charge carriers move? The velocities of individual charge carriers are random. If you take the average of all these velocities, you can get some velocity that depends on the charge carrier density, and the current, and the conductor's cross-sectional area, and it's typically less than a few millimetres per second in a copper wire. Above that, resistive losses become high in ordinary metals and people tend to make the wires bigger instead of forcing the charges to move faster.

Further reading: Speed of Electricity Flow by Bill Beaty

1: The speed of light depends on the material in which the light is propagating, just as with sound. See Wave propagation speed.

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  • \$\begingroup\$ This was difficult to answer because I wasn't sure on which of the two questions he was really asking... I'm glad I wasn't alone! Also, I am glad you put the note about the speed of light, since this speed is not fixed for all mediums. When I first read that statement, I was thinking "no where near the speed of light.." then I saw the note and thought, "well, true, the speed of light through that medium." \$\endgroup\$ – Kurt E. Clothier Aug 9 '13 at 20:15
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    \$\begingroup\$ Phil, you should write textbooks. This is a great explanation. \$\endgroup\$ – JYelton Aug 17 '13 at 18:48
  • \$\begingroup\$ Numbers, please. 2/3 speed of light for the first and 8 cm/hour for the second? \$\endgroup\$ – Peter Mortensen Jul 13 '16 at 23:51
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    \$\begingroup\$ @PeterMortensen Without knowing the particular velocity factor of the propagation medium, and the particular conductor being used and its geometry, I can't really give numbers beyond the ballpark estimations that are already in the text. \$\endgroup\$ – Phil Frost Jul 14 '16 at 14:18
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This is really more of a physics question than an electronics one... The reason being electrical and electronics engineers rarely (if ever) consider such subatomic calculations. The fact that electrons are moving at all is what really matters, how fast they move is of little consequence to the circuit. What may be useful to the engineer is knowing how fast an electric potential (voltage) can change as this will decide the maximum data transmission on a wire (wire speed) which is related to the resistance, capacitance, and inductance of the charge carrier, among other things. This is also associated with the wave propagation speed discussed in some of the other answers. These are two completely different issues...


Electricity Overview

To start, "electricity" doesn't flow. Electricity is the physical manifestation of the flow of electric charge. Although this term applies to a broad spectrum of phenomena, it is most typically associated with the movement (excitation) of electrons - negatively charged subatomic particles. When certain elements are compounded, the electrons can move freely through the outermost layer of the electron cloud from one atom to the next. A conductor easily allows the flow of electrons, while an insulator restricts it. Semiconductors (like silicon) have controllable conductivity, which makes them ideal for use in modern electronics.

As you may know, electric current is measured in amperes (amps). This is really a measurement of how many electrons are moving through a single point in one second:

1 Amp = 1 Coulomb per Second = 6.241509324x10^18 Electrons per Second

As long as there is a voltage (potential) present across a conductor, (a wire, resistor, motor, etc.) current will flow. The voltage is a measurement of the electric potential between two points, so having a higher voltage will allow for a higher current flow, that is, the movement of more electrons through a point per second.


Electron Speed

Of course, the fasted known speed is the speed of light: 3*10^8 m/s. However, electrons typically do not move anywhere near this speed. In fact, you'd be surprised to know how slowly they actually move.

The actual speed of the electron is known as drift velocity. When a current flows, the electrons don't actually move in a straight line though a wire, but sort of jiggle around through the atoms. The actual average speed of the electron flow is proportional to the current using the following formula:

v = I/(nAq) = current / (carrier density * carrier cross-sectional area * carrier charge)


This example is taken from Wikepedia, because I didn't want to look up the numbers myself...

Consider a 3A current flowing through a 1mm diameter copper wire. Copper has a density of 8.5*10^25 electrons/m^3 and the charge of one electron is -1.6*10^(-19) Coulombs. The wire has a cross-sectional area of 7.85*10^(-7) m^2. Hence, the drift velocity would be:

v = (3 Coulombs/s) / (8.5*10^25 electrons/m^3 * 7.85*10^(-7) m^2 * -1.6*10^(-19) Coulombs)

v = -0.00028 m/s

Notice the negative velocity, implying that current actually flows in the opposite direction typically thought. Aside from that, the only thing to notice is how slow this actually is. A current of 3 amps is not that small, and copper wire is an excellent conductor! Actually, the higher the resistance in the charge carrier, the faster the velocity will be. This is similar to how different settings on a shower head will cause the same pressure of water to come out of the faucet at different speeds. The smaller the hole is, the faster the water has to come out!


Making Sense of This

If electrons move so slowly, then how is it possible to transmit data so quickly? Or even, how can a light switch control a light instantaneously from so far away? This is because there is not a single electron that must flow from one point in the circuit to another for anything to work. Actually, there are many free electrons (the amount depends on the elemental make up of the carrier material) in every point of the circuit at all times which move as soon as a great enough potential (voltage) is applied.

Think of water in a pipe. If there is no water in the pipe to begin with, it will take some time for the water to reach the faucet when a spout is turned on. However, in a home, there should already by water in every point of the pipe, so the water flows out of the faucet as soon as it is turned on. It does not have to travel from the water source to the faucet because it is already in the pipe, just waiting for the potential to push it through. It is the same with a wire: there are already so many electrons in the wire, just waiting to be pushed through by the presence of the voltage potential. The speed it would take for one electron to move from one point in the wire to another is completely irrelevant.

On the other hand, the speed of data transmission through a physical medium is important and does have a theoretical maximum, as discussed in this wonderful question and answers so I won't get into that here.

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  • \$\begingroup\$ The question asks if the electron itself, or its effects are useful in practice which, I would argue, places it firmly in engineering land. Theres nothing really wrong with this answer but its missing something. After reading it I still dont have the intuition to say what the fastest rate a voltage can change, and if that is even vaguely related to the speed of the electrons which cause the voltage to change in the first place. \$\endgroup\$ – travisbartley Aug 9 '13 at 3:47
  • \$\begingroup\$ Voltage has as much to do with electrons as water pressure has to do with hydronium ions. \$\endgroup\$ – Ignacio Vazquez-Abrams Aug 9 '13 at 4:17
  • \$\begingroup\$ @IgnacioVazquez-Abrams, right! That's the spirit. Put that in an answer and expand on it. \$\endgroup\$ – travisbartley Aug 9 '13 at 4:21
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    \$\begingroup\$ @trav1s: Well... the thing is that calling you out and saying "Who cares? It's not like this actually has any effect on anything you'll do in electronics." is not only rude and unhelpful, it's also against the entire spirit of Stack Exchange. \$\endgroup\$ – Ignacio Vazquez-Abrams Aug 9 '13 at 4:24
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    \$\begingroup\$ @user606723 That is exactly right. Similar to how a wave moves across a surface of water... the wave moves through the water much faster than the water itself moves. The electrons are always there; however, when the potential is removed (such as an open circuit or dead battery) there is no wave left to propagate them through the wire. \$\endgroup\$ – Kurt E. Clothier Aug 9 '13 at 21:46
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The electrons are misleading you. Ignore them. They go in the wrong direction, anyway. People love to build little animated models that show them moving around - which is true, and observe that electronic communication is near instant - true, and conclude that electrons move near-instantaneously - which is false.

  1. How fast does electricity flow?

    There are two possible interpretations: "how fast do electrons move?" and "how fast does an electronic signal travel?"

    Kurt has already answered "how fast do electrons move?" with drift velocity. However, electronic signals are defined by the electromagnetic wave propagating through the material with the assistance of the charge carriers. The signal propagates at some fraction of the speed of light, affected by the properties of the transmission line.

    This imposes real limitations on high speed systems. In practice it takes about a nanosecond for a signal to propagate along 30cm of PCB. There is a minimum latency between parts of a computer as a result.

    Line inductance and capacitance restrict how "sharp" you can make an edge and send it down a line. It will get smeared out towards a sinewave shape.

    Note that the amount of data you can put through a carrier is different still, governed by its signal to noise ratio. Propagation speed determines minimum latency, not bandwidth.

  2. Is the speed of an electron different in say a resistor than in a wire?

  3. Does it matter?

    From above we know that the answers are "yes" and "no", for speeds of electrons.

    Wave propagation speed is affected by capacitance, inductance, and the dielectric constant of both the material you are propagating through and any nearby insulators to ground planes. Therefore a signal will propagate at a very slightly different speed through a resistor than a wire, as it's made of a different material and stands off the board.

  4. Or are the effects of the electron the only important thing, with lower levels of abstraction not useful in practice?

Most of the time, you don't have to worry about electrons. They get involved directly in cathode ray tubes, vacuum fluorescent displays and thermionic "valves".

This is also true of semiconductors, where the physics is hard and sometimes counterintuitive, but the basic knowledge of how to use a transistor, FET or diode in a circuit is much simpler.

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Consider a line of dominos - push one over at this end and the disturbance travels to the other. The speeds of the individual pieces and that of the disturbance or wave-front are very different, and no individual pieces travel from here to there.

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There are a number of ideas that are relvant

  • How fast do electrons move?
  • How fast do electrons drift when a current is flowing?
  • how fast does a signal propagate along a copper wire

You can relate this to the old water-in-pipes analogy

  • H2O molecules are always jiggling about in the liquid state (or any state above 0 Kelvin?)
  • H2O molecules in a hose pipe also slowly drift from tap to nozzle
  • When you turn on the tap, the pressure wave travels much faster than drift velocity.

The actual answers for electrons are

  • Don't know, pretty fast. 2 x 10^6 m/s? (ref†)
  • A typical value might be 1 metre per hour.
  • A fraction of the speed of light. (ref‡)

† For an electron in a specific orbit, probably a lot different for "free" electrons in copper :-).
‡ For a signal in brine, probably a lot different for copper :-)

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Another aspect of this:

Before anyone can answer the OP question, first we must define the word "Electricity." When electrons flow, is that a "flow of electricity?" No. And yes! Different textbooks contradict each other. There is no simple answer upon which the experts can agree.

Physics says that the Quantity of Electricity is defined as coulombs; as charge. (See the CRC Handbook for example. Or the NIST, or the MKS SI standards for physics units.) Under this definition of "electricity," we'd say that the electron carries a small amount of electricity with it as it moves along. In metals the flowing electricity, the electric current, is slow-drifting electrons.

Why is this a problem? Simple: most non-physics textbooks completely disagree. Instead they state that "electricity" means "electron flow" or current. For them, "electricity" is not the coulombs, instead it's the flow-rate; the amperes. For them, whenever the flow stops, the "electricity" has vanished.

But for physicists, when the flow stops, the electricity just sits unmoving in the wires, since density of carriers does not change when amperes change. For physicists, all wires are already full of electricity; always containing an "electron sea;" the mobile carriers of all metals. But for non-physics textbooks, wires are like empty pipes where "electricity" zooms along at nearly the speed of light.

What then is electricity? The physics standards (MKS, the SI standards convention) clearly define electricity. But our school books ignore this, or they silently pretend that physics standards can be changed as desired. Instead, school textbooks all agree to define "electricity" in a very different way: not as quantity of charges, but as the flowing motion of the charges.

What then is electricity? (Or more facetiously, is electricity ...the flow of the electricity? And whenever electricity starts flowing, do we call this flow by the name "...electricity?")

:)

This craziness even infects engineering language. Physicists say that electrons are the charge-carriers in metals. Engineers instead call them ...current-carriers? Yep. Check any university engineering text. Physicists know about conservation of charge. It's a basic law. But we engineers learn about ...The Conservation of Current?! We're taught that current is the "stuff" that flows through wires. EE textbooks are rife with the phrase "flow of current," and rarely if ever do mention the correct version, "flow of charge."

The traditional solution to such problems is well known: develop standards and define technical terms narrowly. Then carefully adhere to those language standards. Don't use popular definitions, instead exclusively employ narrow scientific terminology. This cuts through all the fog and the BS and confusion. Yet in this case there would be an uphill battle, since using physics standards would mean that thousands of non-physics science/electronics/engineer textbooks and generations of experts are wrong in a fundamental way. Because of their constant misuse of basic scientific terminology, many generations of students now have no idea what "electricity" really is, and so must constantly ask whether it flows slowly along with Drift Velocity (the charge flow,) or does Electricity zoom along at nearly lightspeed (the propagation of currents across circuits.)

More BS-cutting: currents don't flow, instead they propagate. When we push on one end of a rod, the motion doesn't flow. Instead it propagates as a wave. Same thing with currents in circuits: flow of charges yes, but wave-propagation of currents. The near-lightspeed propagation of currents is the same thing as an EM wave.

And finally, ask yourself this critically important question: in rivers and streams, is "current" flowing along? Or is the stuff actually called "water?"

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