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Current of AC transmission lines and electricity in general

  1. Jun 22, 2016 #1
    I realised I didn't understand the physical model of something I know the theory of pretty well. I was considering the real power loss of an AC transmission line I2*R, then I realised that from source to load the electrons in an AC line don't actually move anywhere. (as far as I know) Yet if I'm running a three phase motor, it certainly draws current.

    WARNING: Personal interpretation >> I know that 'electricity' isn't really about the movement of electrons. I'm not sure if it's the negatively charged electrons that move to contain the electric field in the conductor, or if EM energy passes through like a sound wave through the conductive media, really...The mechanism by which energy actually travels down a power line is a bit of a mystery to me. I do remember learning about TE, TM and TEM transmission lines in Adv EM, but I don't know if a simple AC or DC line is one of these. (it would be good if someone could explain it.

    To make things more complicated I'm also trying to work out how a rectifier works, because I imagine that the electrons would have to jump across the PN junction very fast, but the drift velocity of an electron is about 8cms an hour. So yeah, in brief power lines can draw a lot of amps, which is a lot of electrons per second, so how does this happen, and how is there various levels of current in an AC TL?

    Sorry if I'm re-treading old ground, but I haven't found any succinct answers.

    Hope I've made the Q's clear, thanks!
  2. jcsd
  3. Jun 22, 2016 #2


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    Although the electrons in a wire travel very slowly indeed, they still convey power. The charge of the electrons in a wire is very large, so they don't have to move much. From memory, a 1 cm cube of copper contains something like ten Amp hours of charge.
    When you first switch on a DC circuit, a wave travels along the wire at nearly the speed of light as the electrons start to move. I presume that a wave of compression travels through the electron cloud, like a sound wave or shock wave. It is like a row of railway trucks, the couplings suddenly rattling one after the other as the locomotive starts. I presume this wave to travel mainly near the surface, and to carry fields external to the wire along with it. These fields contain nearly all the energy of the wave, and their properties, which are dictated by the properties of free space, largely control the speed of the wave.
    As this wave travels so fast, the steady drift of electrons is quickly established. If the supply is reversed with a switch, the same happens again, hence AC.
    It is worth noticing that a wave travels from the switch, travelling in parallel on each wire of the cable, but in anti phase, and they meet up at the load.
    The concept of "surge impedance", used by power engineers, is a valuable one for this sort of question. It decides the ratio of the electric and magnetic fields in the wave at switch-on.
    (I seem to recall having been rebuked for this explanation in past times on the Forum! Apologies if so).
  4. Jun 22, 2016 #3


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    The electrons move back and forth at 60Hz (in the USA). They can do work moving in either direction. Frequently we want to be able to compare AC and DC circuits. Problem is what to use as the current for an AC circuit. Can't use the mean current because that's zero. To get around this we quote the RMS or Root Mean Squared value for AC current. Taking the square and then the root gets rid of the problem. Frequently the fact that it's rms is ignored. For example a power drill might be rated at 110V and 5A. Hoever they really mean 5Arms, it's not 5A like in a DC circuit.

    As for how fast power is transmitted... I still prefer the water analogy. Imagine starting with a pipe already full of water. If you inject a bit more water at one end then almost instantly a similar volume of water emerges at the other end. The molecules of water in the pipe don't move very far or very fast yet it appears as if the extra water moves from one end to the other at around the speed of sound in water.
  5. Jun 22, 2016 #4


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    Re the diode..

    The short answer is that a diode only allows electrons through in one direction. Bit like a one way valve. For a longer answer read up about semiconductors, doping, and PN junctions or google how a diode works.

    As for the velocity of electrons through a diode... That's an interesting question. I might be wrong but I've tried to ball park an answer for that.... The velocity of electrons across the junction turns out to be quite high...

    u=μE where..
    u is the drift velocity
    μ is the electron mobility (with units m2/(V⋅s)) of the material and
    E is the electric field (with units V/m).

    The electric field E is large because junctions are small, typically just 1um across. 1V across a 1um junction give a field of 1,000,000 V/m.

    u is typically of order 1400 cm2/(V·s) or 0.1400 m2/(V⋅s)

    giving a velocity of

    u=0.1400 * 1,000,000
    = 140,000 m/s
  6. Jun 22, 2016 #5

    jim hardy

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    removed , ..

    yes he's disdainful and is to be taken with a grain of salt.
    Last edited: Jun 22, 2016
  7. Jun 22, 2016 #6
    Jim, the links you provide contain some assumptions known to be false. I can't elaborate but I would recommend peer reviewed sites & journals. This site is only one opinion. BR.

  8. Jun 23, 2016 #7


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    I hate the water analogy because it so often leads to the misconception that current (delivery of water or electrons to the far end) is the same as power. In other words P=I rather than P=VI. I know that @CWatters understands that, but students can easily mis-learn from that water analogy. If we keep in mind that the load could be superconducting with R=0, then it is clear that we can have any amount of current flowing with no power delivery.

    I was thinking of an Insights article complaining about the water analogy. I see so many posts from students who imagine electrons as being little capsules of energy transported around, thus supporting the P=I fallacy. I suspect that their science teachers believe in the same fallacy because they too learned via the water analogy.

  9. Jun 23, 2016 #8
    Yes, I did consider that sort of model, it would make sense, so from memory that's different from TEM, TM or TE transmission.

    Interesting, I'll have to look into that.

    Yeah I'm not a big fan of the water analogy either. As for RMS though, yes I understand the concept well, but my crisis is really about current. So I'm just rambling off the top of my head, but could I say that what we call current, rather then talking about volume of charge electrons, is actually how much EM energy was transmitted by them? So it's not like the pipe is moving the electrons, it's like the electrons are the pipe, and the EM energy absorbed by the load or radiated away by the TL as heat actually does result from the agitation of electrons, but as far as the transmission line itself goes, it's more of an energy equivalence type scenario?

    Aah, cool!

    [WTF, I have no idea what's going on, lol]

    Imagine that you were in hyper time, and a single second seemed like an eternity well for the first half of the AC cycle the current would look DC, then finally after as it reversed it would look DC again, just the other way. Fair way of looking at it? So say that the distance moved by the electrons was a scalar not a vector...I might need to draw a picture:
    What if the total amount of electrons moving over an infinitesimally thin line over the line frequency oscillation, was the same as the total amount of current as DC? Does that sound right?
    If we've got an open circuit TL from a source, do the electrons still jiggle?
    Moreover, what's the difference between a HV cable, to a lower voltage cable, with respect to the electrons? I would imagine that there is a much stronger electric field in the cable, but wouldn't that mean the electrons were subject to some sort of exaggeration?

    My whole understanding of [how and why] power is 'Volts * Current' is breaking down :nb)?:)
    I feel like I understand voltage, but not current.
    Say I have a high voltage low current component and a lower voltage, higher current component using the same power, then I really wonder how they're using the same power physically...??? Like less electrons move but with more kinetic energy (or vise versa)?
    Last edited: Jun 23, 2016
  10. Jun 23, 2016 #9

    jim hardy

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    The water analogy isn't so bad except we were accustomed in childhood to open systems where it is free to run out on the ground and soak in.
    i prefer hydraulic oil because it goes in a closed loop back to the pump and when we see it leak out of the system we know there's a containment( insulation ) failure..
    In that sense hydraulic analogy is to me more intuitive.

    Voltage is analogous to pressure, like pv term in thermo , and British used to call voltage "Pressure" ..

    Current is the number of electrons or hydraulic oil molecules drifting past a point at any instant, coulombs or moles per second.

    "Like less electrons move but with more kinetic make that potential ? energy" and i'd agree

    There are folks who claim the energy in a circuit is not carried by the charges but by the fields along the conductors. They are able to write equations for that.
    I can only envy them.
  11. Jun 23, 2016 #10


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    If we need to use analogy the water one is IMO a poor one. The one I generally use is the bike chain analogy because it handles energy 'flow' with AC current nicely where the chain links are charge carriers (current as electrons in a wire) and chain tension (voltage/potential difference) transfers energy from the pedals to the rear wheel. This is a mechanical analogy that's a little more abstract than hydraulic systems but it's less likely IMO to lead to confusion on charge vs energy and it might be related to the origin of the somewhat archaic term of electrical 'high' tension that survives today.


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  12. Jun 24, 2016 #11


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    The first thing to understand is that every current is wrapped by a magnetic field. There can be no such thing as a current without a magnetic field. Indeed, it is a magnetic field in the generator that starts the current flowing. That flowing current is surrounded by an extension of the field from the generator, a field that is guided by the current in the conductors to the load. When we measure current we are actually measuring the strength of the guided magnetic field.

    It takes a “circuit” of two conductors to transfer electrical energy, the return conductor returns the current. The currents flowing in the two conductors are equal and opposite. Outside the cable, because the currents are travelling in opposite directions, the magnetic fields of the two conductors tend to cancel. Between the conductors, the combined magnetic field does not canel, it is doubled.

    There is a voltage difference between the conductors. So between the conductors we also have an electric field. The E and M fields are perpendicular. The cross product of those two fields gives the poynting vector which is the direction of energy flow. That direction is from the generator to the load.

    When we measure the rate of energy transfer from generator to load by multiplying the current by the voltage to get power in watts, we are in effect (cross-)multiplying the electric and magnetic fields.
    The energy travels through the insulation and air between the wires, guided by currents in the surface of the wires.
  13. Jun 24, 2016 #12
    Sure, I'm not wedded to it.
    Yeah, my maths isn't too flash, but I'd be inclined to agree, or rather my gut would, intuitively.
    I don't really like analogies in general, but the chain one isn't too bad, not too good for AC. Where the electrons are either moving moving a tiny distance, but still able to do work, OR they are acting as a medium themselves.
    That's why I was hoping someone would have commented on my in-articulate statement:
    Except for Jim (who touched on it).
    Specifically my reasoning that over a short enough time-frame each half of the AC wave is just like DC, so really there is no difference. The point being, it doesn't matter how far they moved, the point is they moved, any movement is enough to do Work.(?)

    So @jim hardy , you're saying that if I have a large HV load, the individual electrons in the load each have a larger electric field energy, but there are fewer of them, like those electrons wiz through [or back and fourth if AC] the load faster, but there are less of them, than a low voltage load with a higher current? To do the same Work.
    And so since real loss of a TL is proportional to electrons, the way to cheat is to use fewer electrons, but each of them have some sort of [trying not to delve into QM] greater potential due to the field.
    Yeah, I really like what you're saying; I've always felt it was all about the electric field and that the electrons are sort of just a medium. So conduction is different from a TEM, TM or TE, TL?
    Do you mean inside the cable the field is doubled? Because I remember way back in HS watching a video of two cables each carrying current the other way (return path) and they repulsed each other [magnetically] due to the right hand rule.

  14. Jun 24, 2016 #13

    jim hardy

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    power is volts X amps
    power is joules per coulomb(that's volts) X coulombs per second(that's amps) = joules / sec (that's watts)

    But academics will fuss at you if you say electrons instead of coulombs.

    Whiz is a poor word. They move slowly, like water molecules in the Gulfstream or oil molecules in a hydraulic hose or like the links of the a chain in a weight driven Grandfather clock.
    They don't have inertia like water or oil does,, their tendency to remain in motion comes from their magnetic field...
    I suppose it makes little difference whether you think of their potential to do work as residing in the electric field surrounding the wires or in the electric fields between individual charge carriers. Work put in one end of a wire either comes out the other end or gets radiated away into space as an E-B field..

    Transmission line not just a wire in a circuit ?
    There's the ohmic loss from charges shaking the conductor's atoms as they hop along, heating them
    there's dielectric loss by the transverse E-field shaking the atoms of whatever separates the wires
    there's radiative loss as the length of the wire approaches a goodly fraction of a wavelength becoming an antenna and the universe becomes receptive to the longways E-B field. That's a few thousand miles at grid frequency.


    Corrections welcome - old jim
  15. Jun 24, 2016 #14


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    Why confuse things by using waveguide mode classification when phase velocity is not relevant because the distance between the wires is very very much less than a wavelength. EM radiation in space is TEM, just as are the fields between the good conductors that make up a circuit.

    The cable is a bundle of two or more insulated conductors. Currents flow on the surface of those conductors, under the insulation. The conductors make the complete circuit, so the sum of currents on all wires in the cable is zero. That is why the external fields cancel. But between conductors that carry opposite currents in the cable, the fields sum, they do not cancel.
    Take a look at this link. http://amasci.com/elect/poynt/poynt.html
    A different reference is attached as a pdf.

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  16. Jun 24, 2016 #15


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    I agree about analogies in general.
    Old analogy joke.
    The bike chain one is OK for AC if you understand the system as a means of energy transfer (hand on the pedal to another hand pressed to the wheel to get hot) and not something that just makes wheels, chains and sprockets move round and round.

    The energy doesn't care about the wheel's rotation. The energy flows one-way, from one hand to the other unmoving "friction" hand, even if the wheel reverses direction back and forth.
  17. Jun 25, 2016 #16


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    Not really relevant to understanding AC in basic terms, but regarding the modes which occur during the passage of a switch-on impulse, may I suggest the following?
    If a wire is in isolation, I would expect the impulse to be accompanied by electric field lines parallel to the wire, and growing magnetic field lines wrapped around it. Once the impulse has passed, these longitudinal electric field lines will almost disappear (just remaining due to resistance) but the magnetic field lines will remain.
    If the second wire is near to the first, then some of the field lines will link between the two, and we see a TEM mode in addition to the "single wire mode" that I have described.
    In addition to the travelling fields on an isolated wire, there are also radiated fields, which are caused by the acceleration of the charges. If a second wire is brought close to the first, these fields tend to be cancelled, as the impulses on the two wires are in anti-phase. If an isolated wire is very long, radiation is small because it is concentrated along the wire by array action.
    I am very interested in the propagation of waves on wires and have done some experiments on this subject.
  18. Jun 25, 2016 #17


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    It is not totally uncommon to use a chain in a reciprocating mechanism (steering a boat, for instance). The only problem is the slop in the many links and any sag in the chain. A similar ' one legged' mechanism that mimics AC could be a connecting rod between two cranks of a crank and a wheel (a pedal sewing machine drive for instance).
    Last edited: Jun 25, 2016
  19. Jun 26, 2016 #18
    I've let this thread get away from me.
    So I am aware, but I wonder what the implications are in a non-analogous sense of what it actually means to say Volts times Amps.'I have a potential [Volts] over a resistor, and there is an amount of current flowing through the resistor' I'm sort of trying to picture how the amount of potential over the resistor (if the same amount of current is flowing through it) makes any difference to the amount of power it dissipates.

    As always Jim, I accept your expertise, I'm just having difficulty mentally picturing the power equivalence. I just looked up this: DriftVelocity = I /(n*Q*A) = (by my reckoning is ) V/(R*n*Q*A) So presumably the amount of voltage does impact the electron speed, but I'm not sure by how much. Regardless why I'm so confused, is that I was thinking, it's the same amount of charge (each electron has the same charge, and it's the same amount of current) flowing through the load, so how does applying a greater potential mean that there is more POWER on the load? (e.g. for a comparison of the same current on a load but an increased voltage)
    I sort of get your analogy about a greater potential being like more tension, but if the bike chain moves the wheel the same amount, it doesn't matter how much tension there is between cogs....if that makes sense.

    I think of every wire as being a TL (unless I shouldn't?), so yeah an humble wire too.
    That is a nice succinct way of talking about the losses.
    I didn't mean waveguide, but I was thinking a pair of wires is not that different from a microstrip or coax (but I might be saying something stupid because it's been a while). I am actually thinking about long AC vs DC transmission, what was why I wanted to consider that way of thinking and see how or if it applied.
    Sorry, what specifically do you mean by "the fields between the good conductors"? Like outside the wires of the circuit, or in the wires themselves? (silly question I know)
    I"m sure I know what you're saying, it's just the phraseology that is throwing me, so like I said before, two long wires side by side making a circuit will repulse each other. Or a loop of current carrying wire will cancel the magnetic field outside the wire, but there will be an MMF coming out from the loop. This is what you're saying isn't it?
    Thanks for the links.
    Haw Haw.
    I understand what you're saying about the direction of energy flow, but what I'm getting at is the perturbation of the pedal cog isn't really important with AC electricity, but if you did that with a bike chain you wouldn't have any energy transfer. You'd have to move the pedal like 30degrees or something significant, then back again [repeat] to get enough movement on the wheel to cause friction heat. But the point I'm making about AC electricity is that the distance the electron oscillates is pretty much irrelevant because any movement at all still looks like DC because on that scale time is completely different than our macroscopic world. Anyone care to comment? @sophiecentaur
    I really like your comment, I'll have to re-read it to fully digest it.

    Thanks a lot all
  20. Jun 26, 2016 #19

    jim hardy

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    remember i said voltage analogous to pv ?

    a gas expands at the expense of its internal energy
    steam going through a turbine expands cools comes out with a whole lot less energy than when it entered
    pv is potential energy
    BTU/lb analogous to Joule/Coulomb, potential, and there's a potential drop just as surely as an enthalpy drop

    that;s unfmailiar to me.

    have you been here ?

    it's not the amount of charge going through the load it's the energy shed by that charge, joules per coulomb or ev per electron converted to thermal work in the load
    it's not the pounds of steam going through the turbine its the energy shed by that steam, BTU's per pound converted to mechanical work in the turbine.

    ?? does work - Force X Distance ?
  21. Jun 26, 2016 #20


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    If the AC is a high frequency, then the modes described become important.
    Just for completeness, regarding the radiated fields, of course these will travel away for ever as lost energy. The electric radiated component is at right angles to the longitudinal E field near the wire and so it can have a different value. These are the radiated and induction E fields encountered with antennas. However, it seems that the magnetic radiated component is wrapped around the wire and cannot be distinguished from the transmission line field, with which it is identical. So close in to the wire, we cannot distinguish radiated and induction components of the magnetic field. The magnetic field from the part of the wire behind the impulse, where the current is steady, initially falls off with 1/D, but when the distance is about greater then the length of the wire, it will fall off very rapidly. The radiated component will continue to fall off slowly as 1/D for ever. This action of waves on wires seems to be very interesting.
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