Speed Of Electricity

[TrueSceptic]

This seems like a simple question but is it?

We all know that the speed of light is about 300,000 km/s (186,000 mi/s) in a vacuum and that this applies to all other electromagnetic waves too. We also know that this figure is reduced when travelling through air, water, glass, etc.

It is often said that electricity in a conductor also travels at the speed of light. I cannot see how this can be the case but what is the figure? Electricity in this sense is the flow of electrons. Are electrons considered as particles or waves in this case?

 

[Terry]

The drift velocity of the electrons is very small, much much smaller than their thermal motion. However, the electric field which causes the electron drift propagates much faster than the drift velocity - the speed depends largely on the nature of the insulation round the wire.

 

[TrueSceptic]

The drift velocity of the electrons is very small, much much smaller than their thermal motion. However, the electric field which causes the electron drift propagates much faster than the drift velocity - the speed depends largely on the nature of the insulation round the wire.

Thanks.

I suppose one of the problems is defining "electricity" in this context.

What sort of effect would the insulation have? Are we talking about a small or large %age of c? How much would it vary?

 

[sol invictus]

Thanks.

I suppose one of the problems is defining "electricity" in this context.

What sort of effect would the insulation have? Are we talking about a small or large %age of c? How much would it vary?

In an AC circuit, zero net electrons flow down the wire. And as Terry says, the average speed with which they move is pretty low.

But that's probably not what you meant - you probably wanted to know how long it will take a light bulb to light up after you flip a switch. If so, the relevant speed is the speed of electromagnetic waves in or around a copper wire, which I think is quite close to the speed of light in vacuum (I'd have to look up the exact value).

As for insulation, do you mean around the wire? That shouldn't do much... I suppose it may introduce some dispersion (frequency dependent speed of light) depending on exactly what it's made out of. But in fact even if you cut a small section of wire and replace it with insulation nothing much will happen for a high frequency AC signal - the waves will simply propagate across the gap into the wire on the other side.

 

[PingOfPong]

This seems like a simple question but is it?

We all know that the speed of light is about 300,000 km/s (186,000 mi/s) in a vacuum and that this applies to all other electromagnetic waves too. We also know that this figure is reduced when travelling through air, water, glass, etc.

It is often said that electricity in a conductor also travels at the speed of light. I cannot see how this can be the case but what is the figure? Electricity in this sense is the flow of electrons. Are electrons considered as particles or waves in this case?

A distinction should be made between the movement of single charges and the movement the electric "signal". The signal is a wave and will propagate along a conductor at the speed of light for that particular kind of conductor.

[latex] $ c = \frac{1}{\sqrt{\epsilon\mu}} $ [/latex] where epsilon is permitivity and mu is permeability

You may wonder how a DC signal can be a wave. Without getting into the math, a DC signal can be decomposed into into an infinite sum of waves (Fourier analysis).

If you're asking about the movement of individual charges then that depends on drift velocity which is determined by the properties of the material at the atomic scale.

ETA: I should have added that the speed of propagation often depends on the geometry and composition of a transmission line (eg coaxial cable, twisted pair, untwisted pair, PCB trace, etc.). In those cases, an effective permitivity is used.


[latex] $ c = \frac{1}{\sqrt{\epsilon_{effective}\cdot\mu}} $ [/latex]

 

[TrueSceptic]

In an AC circuit, zero net electrons flow down the wire. And as Terry says, the average speed with which they move is pretty low.

But that's probably not what you meant - you probably wanted to know how long it will take a light bulb to light up after you flip a switch. If so, the relevant speed is the speed of electromagnetic waves in copper, which I think is quite close to the speed of light in vacuum (I'd have to look up the exact value).

Yes, that is what I mean. How close?

As for insulation, do you mean around the wire? That shouldn't do much... I suppose it may introduce some dispersion (frequency dependent speed of light) depending on exactly what it's made out of. But in fact even if you cut a small section of wire and replace it with insulation nothing much will happen for a high frequency AC signal - the waves will simply propagate across the gap into the wire on the other side.

I understand about the gap. The insulation was Terry's suggestion, but I'm open to all reasonable ideas.

 

[sol invictus]

Yes, that is what I mean. How close?

Well.... on further reflection I don't think there's a simple answer. You'd have to ask a more precise question. The very leading edge of an EM wave always travels at the speed of light (c) no matter what the medium is. But to a good approximation, in a dielectric material it travels at c/n (n is called the index of refraction). A wire is not a dielectric, but the vacuum and/or insulation around it is, at least for some range of frequencies... so precisely how fast the signal goes will depend on many factors, including the metal, the insulation, the shape of the wire, and the frequency of the signal. Fold that all in, and for reasonable situations the answer will be some not-so-small fraction of the speed of light.

 

[TrueSceptic]

Well.... on further reflection I don't think there's a simple answer. You'd have to ask a more precise question. The very leading edge of an EM wave always travels at the speed of light (c) no matter what the medium is. But to a good approximation, in a dielectric material it travels at c/n (n is called the index of refraction). A wire is not a dielectric, but the vacuum and/or insulation around it is, at least for some range of frequencies... so precisely how fast the signal goes will depend on many factors, including the metal, the insulation, the shape of the wire, and the frequency of the signal. Fold that all in, and for reasonable situations the answer will be some not-so-small fraction of the speed of light.

Exactly.

I can't ask a more precise question because I don't know enough about what matters most.

 

[TrueSceptic]

A distinction should be made between the movement of single charges and the movement the electric "signal". The signal is a wave and will propagate along a conductor at the speed of light for that particular kind of conductor.

(I take it that you are using "light" as shorthand for EM at any frequency.)

Where can I find these speeds?

[latex] $ c = \frac{1}{\sqrt{\epsilon\mu}} $ [/latex] where epsilon is permitivity and mu is permeability

You may wonder how a DC signal can be a wave. Without getting into the math, a DC signal can be decomposed into into an infinite sum of waves (Fourier analysis).

If you're asking about the movement of individual charges then that depends on drift velocity which is determined by the properties of the material at the atomic scale.

ETA: I should have added that the speed of propagation often depends on the geometry and composition of a transmission line (eg coaxial cable, twisted pair, untwisted pair, PCB trace, etc.). In those cases, an effective permitivity is used.


[latex] $ c = \frac{1}{\sqrt{\epsilon_{effective}\cdot\mu}} $ [/latex]

This is looking useful, but how can I obtain real-world figures?

Thanks.

 

[shadron]

A distinction should be made between the movement of single charges and the movement the electric "signal". The signal is a wave and will propagate along a conductor at the speed of light for that particular kind of conductor.

where epsilon is permitivity and mu is permeability

You may wonder how a DC signal can be a wave. Without getting into the math, a DC signal can be decomposed into into an infinite sum of waves (Fourier analysis).

Ah, yes, you're right, but only trivially. A DC current that has existed from infinity backwards in time and will continue forwards infinitely in time is, of course, simply a voltage constant, and Fourier analysis will also say so, because all the sine waves drop out with amplitude = 0 except at frequency = 0. But we're not interested in a always-on DC current here, because it can't carry any information; instead we want to analyze a step change in voltage levels at time t from 0 to some DC voltage level (perhaps that is what you meant when you say "DC signal". Also, an AC voltage level would also work here, adding a constant amplitude 60Hz sine wave component). Fourier analysis of this is much more fruitful, and it shows a whole series of harmonics that mutually cancel out except in a small region around t; there, they all sync up to start rising from 0 to n at the same time. It is the propagation of those wave fronts that sync up at t you want to investigate the speed of.

By the way, Fourier uses harmonic sine waves at various amplitudes and harmonic frequencies to analyze a voltage phenomenon; you can do the same with exponential waves using LaPlace analysis, and there are literally an infinity of other analysis methods.

The point about insulation, I think, is in the capacitative effect that insulation has between the wire and that nebulous "ground" that completes the circuit. The capacitance between them has the effect of shorting out and eliminating the higher frequencies, thus in effect slowing down the point where the DC level lifts above some certain threshold value (the high frequencies carry that information the most accurately simply because they rise faster) as the wave front proceeds down the wire. The capacitance is a function of the size of the conductor (in x-section area facing the ground), the length of the conductor, the distance separating the conductor and ground, and the dielectric constant of the materials between the conductor and the ground (the "insulation").

This is looking useful, but how can I obtain real-world figures?

You need to consider the frequency response of the medium (wire, wave guide) you are wanting to use. Effectively, the point where the frequency response dives through the 3db below plateau is the highest frequency your wire will carry. The amount of time delay is that wave time period (= 1 / frequency) divided by 4; that is the amount of time required for that frequency to rise from 0 to +v. Divide the distance to be traveled by that time to get the velocity of the wave front (actually, you should use a Lorentz transformation rather than simple division here, so that the maximum speed results in c rather than infinity, but for quick and dirty with real wire available today, this works). Your speed will probably be a rather small fraction of c.

 

[PingOfPong]

This is looking useful, but how can I obtain real-world figures?

Thanks.

The permeability of the material between the conductors will usually be equal to the permeability of free space. It will only be different if the material is magnetic. The permittivity of the material in between will usually be defined like this:

[latex] $ \epsilon = \epsilon_r \cdot \epsilon_0 $ [/latex] Epsilon sub r is the relative perm. and epsilon sub 0 is the perm. of free space.

We note that the speed of light in open space is:

[latex] $ c = \frac{1}{\sqrt{\epsilon\mu}} = \frac{1}{\sqrt{\epsilon_0\mu_0}} $[/latex]

and the speed of light in a transmission line is:

[latex] $ v_p = \frac{1}{\sqrt{\epsilon\mu}} = \frac{1}{\sqrt{\epsilon_r\epsilon_0\mu_0}} = c \codot\frac{1}{\sqrt{\epsilon_r}} $[/latex]

So all you need to know is the relative permittivity to calculate the speed. I took a quick glance at some figures and the number 4 came up alot for wire insulation. That would yield a speed of one half the speed of light in a vacuum. 1.5x10^8 m/s

Don't worry to much about effective permittivity. It's not that important if all you want is a rough estimate. Effective permittivity becomes critical when you're trying to match impedance and phase in a radio circuit.



Shadron, I know, I know. However, it goes without saying that one has to turn DC sources on, off, or both.

 

[shadron]

Shadron, I know, I know. However, it goes without saying that one has to turn DC sources on, off, or both.

It sure didn't go without saying in the math classes.

 

[PingOfPong]

Picky, picky. I should never have mentioned Fourier. I just wanted to hint that even DC signals could be treated as waves when you're turning something on.

 

[shadron]

Picky, picky. I should never have mentioned Fourier. I just wanted to hint that even DC signals could be treated as waves when you're turning something on.

No, quite the contrary. Fourier analysis is exactly the right tool to use here. It explains why the information conveyed by the step is not conveyed at c; it explains the exact parameters that affect that speed. Namely, the better the frequency response of the wire the higher the speed. It can be used to predict that speed.

Without Fourier analysis, it is all just hand-waving. He (and you) done good.

 

[Soapy Sam]

*Waves hand*
I just switched on a light and timed the delay between switching it on and the light coming on. (I used a digital watch).
Allowing for the time it took the switch to move and the time it took the filament to warm up to incandescence, it took...dammit, no microsecond hand on this cheap Casio watch. Can you believe that?

 

[TrueSceptic]

The permeability of the material between the conductors will usually be equal to the permeability of free space. It will only be different if the material is magnetic. The permittivity of the material in between will usually be defined like this:

[latex] $ \epsilon = \epsilon_r \cdot \epsilon_0 $ [/latex] Epsilon sub r is the relative perm. and epsilon sub 0 is the perm. of free space.

We note that the speed of light in open space is:

[latex] $ c = \frac{1}{\sqrt{\epsilon\mu}} = \frac{1}{\sqrt{\epsilon_0\mu_0}} $[/latex]

and the speed of light in a transmission line is:

[latex] $ v_p = \frac{1}{\sqrt{\epsilon\mu}} = \frac{1}{\sqrt{\epsilon_r\epsilon_0\mu_0}} = c \codot\frac{1}{\sqrt{\epsilon_r}} $[/latex]

So all you need to know is the relative permittivity to calculate the speed. I took a quick glance at some figures and the number 4 came up alot for wire insulation. That would yield a speed of one half the speed of light in a vacuum. 1.5x10^8 m/s

Don't worry to much about effective permittivity. It's not that important if all you want is a rough estimate. Effective permittivity becomes critical when you're trying to match impedance and phase in a radio circuit.

So, as I suspected, what seemed like a simple question is not.

Shadron, I know, I know. However, it goes without saying that one has to turn DC sources on, off, or both.

But then you are describing a step function...

 

[lomiller]

So, as I suspected, what seemed like a simple question is not.

As a general rule the speed of an electrical signal in a wire actually depends on the permeability of insulation. ~2/3 the speed of light is a fairly typical value, but other insulators give different values like ~83% the speed of light.

 

[lomiller]

So, as I suspected, what seemed like a simple question is not.

As a general rule the speed of an electrical signal in a wire actually depends on the permittivity of insulation. ~2/3 the speed of light is a fairly typical value, but other insulators give different values like ~83% the speed of light.

 

[Paulhoff]

Good old Velocity factor.

http://en.wikipedia.org/wiki/Velocity_factor

Paul

 

[shadron]

You hams. You have an answer for everything, don'tcha?

Good old Velocity factor.

http://en.wikipedia.org/wiki/Velocity_factor

Paul