So I was reding an article in Parade by Marilyn Vos Savant (sp?), the self proclaimed smartest woman in the world. A person wrote in and asked how long it would take for electricity to get from the East to West Coast. She replied that since elctricity travels at the speed of light, it would take .013 seconds. (or some other quite miniscule number)
Alright, I know that first of all, AC just kind of wiggles back and forth. I also know that DC current travels quite slowly under normal circumstances, and more quickly under higher voltages, etc.
I am also aware of the metaphor of electric wiring being like a full water hose. The water will come out of the other end quickly when you turn it on, even if the water is flowing slowly.
Assuming the question was “How long would it take to light a 60w light bulb with 120v house power if the supply and switch were in New York and the bulb was in L.A.?” would the speed of light answer be correct, or is the world’s smartest woman just confused?
MMarilyn is wrong. The propagation speed would probably be around 70% to 80% the speed of light (in a vacuum), depending on transmission line impedance, etc.
I guess here’s what I’m getting at. An elctron starts to vibrate in NYC, down the line the electrons begin to vibrate at 60Hz, all exciting their neighbors as they go. How long to get the electron in LA wiggling?
If I had a water hose going from one coast to the other, and making some assumptions (water doesn’t compress, hose doesn’t expand, etc.) how long before water comes on in LA after I turn on the spigot in NYC?
Interestingly, the properties of the insulator are very important in figuring out the speed of an electric wave. Is your superconducting wire running through an evacuated cylinder?
Note that the electrons don’t need to move much, since it’s the wave that’s carrying the power.
Electrical energy is not transported by the electrons inside the conductor but instead the energy is transported by the electric and magnetic fields outside the conductor. The fields propagate relativistically but the current in the conductor travels much slower.
For instance the current in a copper wire at a frequency of 1 MHz propagates at 400 meters per second.
I looked up a couple things since my earlier post, and can give a slightly better answer now.
All electrical signals are carried on transmission lines. There is a characteristic of the line called Velocity of Propagation (Vp). (Minor nitpick: I think it should really be called Speed of Propagation, since Vp never includes direction…) For a particular transmission line, Vp is dependent on such things as:
Type of conductors
Type of shielding materials
Type of dielectric
Geometry
Line impendence (redundant, since this can be calculated from the previous stuff)
[sub]I also believe it’s dependant on frequency, but I’m too lazy to look further into this thing. I’m guessing it might also be depdant on amplitude of the voltage and/or current…[/sub]
For telephone lines, Vp is usually between .6c and .7c, where c = speed of light in a vacuum. There are some fancy transmission lines where Vp = .99c.
I don’t know what Vp is for your typical 60 Hz power grid, which answers (or doesn’t answer, to be precise) your question.
Marilyn Vos Savant is an idiot. If she’s the smartest woman in the world, it’s a wonder that the other women in the world can even tie their shoes.
A little background on me so you know that I’m not blowing the wind up your skirt. I have a BS degree in electrical engineering (that’s BS in both senses of the acronymn). And I’m currently working on my computer engineering master’s degree.
Anyway, I go through all of that to say that Crafter_Man did a damn fine job in explaining it. Better than I could unless I pull my power line notes out of the attic and post all of that here for you, which would be rather boring.
However, Crafter_Man, to address your nitpick, it is and should be the velocity of propagation since there can be a reflected wave in the opposite direction if the transmission line impedences don’t match. Reflected waves are bad because they mess with the waves coming in the other direction and can really screw up the wave form. This is why you have to pay attention to the impedence of your stero speakers. If it is not right, you get a lot of distortion and it sounds really bad, if it works at all.
Shadowfyre: You’re right that waves on transmission lines reflect when encountering a mismatch, but Vp is usually (always?) given as a single value (e.g. 0.85), without reference to direction. That’s all I was saying.
Now you’re speaker comment… I may be off-base here, but I believe speaker impendence is important not because of mismatch issues with the transmission line per say, i.e. the speaker cables themselves, but because of a mismatch with the source impedance, i.e. the output transistors. (I believe speaker cables are short enough, and the frequencies low enough, that it may be approximated as a lumped-parameter system.) Low impedance speakers can over-current the output transistors, causing them to overheat and distort. It should also be mentioned that the impedance of a speaker is not constant, but a function of the frequency.
You are blowing smoke on the reason you must match impedances for stereos. You get reflections when the impedance of the cable does not match the impedance of the speaker. I have never seen speaker cable with an impedance rating on it.
Further more audio signals don’t really go much above 30KHz and really you only hear up 22KHz to if you have really good ears. The maximum distortion occurs when the reflection comes back 1/2 a period off. So the signal much be delayed by 16.7 us for a 30KHz sine wave. Assuming 1/2 the speed of light is the propagation speed as per some of the above numbers. That means the signal needs to travel 5000m the achieve maximum distortion. Now nobody has 5000m speaker cable. What will really happen is the signal will bounce back and forth on the cable. Lets assume you have 20m speaker cables. (The longer they are the worse the problem so I chose a long cable my own are probable 3m). That means the signal bounces back and forth 250 times before achieving maximum distortion. Now there are really 2 reflections we are concerned about the one at the speakers and the 1 at the amp. They will reflect differently lets assume 100% of the energy is reflected at the amp and 75% is reflected at the speaker. Again these are really high values. There is 25% energy lost every other reflection so at maximum distortion you have .75^125 or 2.4 e-14% distortion due to reflections. That is totally minuscule. Assuming you want better than 90db of distortion you need the reflections to be less than 84%
This is correct in general, but for TEM (two-conductor) transmission lines, V[sub]p[/sub] is the speed of light in the medium the transmission lines are in. If there are multiple dielectric (e.g. an electric cord where you have the insulator and air), V[sub]p[/sub] will be somewhere in-between, but if most of the energy in the fields is in just one of the regions, V[sub]p[/sub] will be close to the speed of light in that region.
For trans-continental electric transmission lines, the dielectric is pretty much just air, so V[sub]p[/sub] is (almost) the speed of light.
There is a frequency dependance, but for TEM lines, it only comes through frequency dependance of the dielectric constants of the materials. There’s no voltage or current amplitude dependance until you get to unreasonably large amplitudes (transmission line is glowing), or use non-linear devices (diodes, transistors, etc.)
I think this would be relevant for DC current, or if you somehow dumped a bunch of charge into the wire at one end. Water flow would be analagous to electron flow, and the speed of sound in water would be analagous to the speed of propagation of the electron disturbance through the wire.
When a DC source is first switched on, transient electric and magnetic fields are generated outside the conductor. It is this transient electromagnetic wave that causes the electrons to come out the other end PDQ (so to speak).
Forgive me if I’m wrong - I’m just a country boy trying to make a living in the big city - but…
Except for the very brief EM field generated from the transient due to line capacitance and line inductance, why would there be an electromagnetic wave in a DC circuit after you close the switch?
Seems to me that, in a DC circuit, the only things created are: a) a static (DC) magnetic field around the conductors, and b) a DC electric field inside the conductors. But no EM wave. And what makes the electrons “move at the other end” is not an EM wave, but the electric field inside the conductors that is created after you flip the switch.
Perhaps you’re thinking of a DC circuit terminated with an open circuit. If that’s the case you’re correct that there will be current transients due to line impedance, and thus a transient EM field, but even then no electrons will “come out the other end.”
Anytime you apply a change to a system of harmonic oscillators you introduce both a transient and steady state response. The transient response is the time varying electromagnetic field. This is what initially transfers the power to the load, and establishes the initial conditions for the Poynting vector at steady state.
Do you know what “so to speak” means. That was a joke for Christs sake.
Ok, I admit it. I’m guilty of oversimplification. I’m guilty of this alot. I try to make my explanations as simple as possible so they are not so wordy and boring, otherwise the OP wouldn’t read it anyway. But your right. I was going to use splicing a power line, but I figured the stereo would be a better “well known” example.
Please don’t hate me too much. It’s been years since I’ve done this stuff.
BTW, Wouldn’t a negative Vp indicate a reflected wave heading in the opposite direction, thus giving direction to the scalar value?
Your assumptions are not trivial! If the water were completely incompressible, the cylinder of water in the hose would behave like a rigid bar and the signal would propagate at infinite speed, arriving in LA instantaneously.
In this way, the speed of light c imposes a theoretical limit on incompressibility!
A similar “paradox” relates to a pair of scissors so long that when you move the handles, the blade tips move faster than light. But this can’t happen because no material can be sufficiently rigid.
No, and no. Any two (or more) conductor transmission line will support TEM waves (for a homogeneous dielectric, at least).
I was thinking in terms of, if you added charge to the end of the wire, you’d have essentially a pressure wave traveling inside the wire. You will have transient fields outside the wires, propagating at the speed of light in the outside medium, but I think you’d also have a pressure wave traveling at some other speed, dependant on the conductor material.
Interesting. In that thread, chronos referenced a Cecil article: http://www.straightdope.com/classics/a940722b.html and called it accurate. In that article, Cecil went with 1/3 the speed of light … although he did so in such a way that he could blame “a junior member”.
If the 2/3 number is closer to reality, then Cecil was “half right” whereas MvS was triple wrong. (Can you tell where my loyalties lie?)