# 3 Phase Current Flow

#### GoldDigger

##### Moderator
Staff member
How is the return path provided incase of DELTA system?there are only 3 phases.so how is return path provided if we have a 3ph load for delta system.
Well, for a start, consider that the word phase, in a delta, can be used either in terms of the phase wires (A, B, C) or in terms of the phase voltage seen by the load (AB, BC, CA).
The source for current between two phase wires will be the single coil joining those two wires in parallel with the series combination of the other two coils (which, naturally enough, produces the exact same voltage.) So one phase wire is the source and the other the return at any given moment for that line-to-line phase.

Just in case somebody gets concerned about what happens when you consider all three phases at once, the law of superposition tells us that we can consider the delta to be the equivalent of three separate single phase setups just sharing the same three wires, so there is no need to be concerned about "current flowing in both directions at the same time".

#### kwired

##### Electron manager
All those quotes you attributed to me were from the OP, not me. I should have replied with quote to the OP rather than cut and paste; my bad.
And most of what he replied with has already been covered early on in the thread, I think all the non related talk scared the OP away.:ashamed:

#### mivey

##### Senior Member
But don't you agree heavier ions have lower mobility i.e lower drift velocity than lighter electrons for the same voltage?
I would say it depends on the material.

You need be specific about the surface electron initial velocity. Give a value for it. Simply stating that its velocity is near light velocity could mean any value for its {moving} mass: it could be equal to that of an adult elephant given its velocity is assumed sufficiently near that of light.
I would have to look back at my physics texts. Normally I would think it in the 0.5c to 0.9c range. 0.6c to 0.8c come to mind but that is probably just the propagation speed in a wire.

But think about it from a logical standpoint. Bes showed the speed of the electrons in the wire are very slow but we know the initial reaction propagates in the conductor much, much, much, faster than that and is closer to the speed of light than the speed Bes showed. We also know there is a delay in getting the electrons down in the wire to move (the skin effect) that shows the internal movement is much, much slower than the speed of light. Since your conductors do not fall through the floor when you cut on the switch, we are not sufficiently near the speed of light to stuff elephants in the wire.

I'll see if there was an estimate of the reaction speed given in the text. The only thing I remember is it stating that the shifting of the electrons and charge gradient that created the field took place at near light speed. I seem to recall an example given that flipping a switch did not produce an immediate reaction at the far end but there was a delay measured in near light speed.

#### ggunn

##### PE (Electrical), NABCEP certified
Well, for a start, consider that the word phase, in a delta, can be used either in terms of the phase wires (A, B, C) or in terms of the phase voltage seen by the load (AB, BC, CA).
The source for current between two phase wires will be the single coil joining those two wires in parallel with the series combination of the other two coils (which, naturally enough, produces the exact same voltage.) So one phase wire is the source and the other the return at any given moment for that line-to-line phase.

Just in case somebody gets concerned about what happens when you consider all three phases at once, the law of superposition tells us that we can consider the delta to be the equivalent of three separate single phase setups just sharing the same three wires, so there is no need to be concerned about "current flowing in both directions at the same time".
You realize it wasn't me asking that question, right?

#### ggunn

##### PE (Electrical), NABCEP certified
I would say it depends on the material.

I would have to look back at my physics texts. Normally I would think it in the 0.5c to 0.9c range. 0.6c to 0.8c come to mind but that is probably just the propagation speed in a wire.

But think about it from a logical standpoint. Bes showed the speed of the electrons in the wire are very slow but we know the initial reaction propagates in the conductor much, much, much, faster than that and is closer to the speed of light than the speed Bes showed. We also know there is a delay in getting the electrons down in the wire to move (the skin effect) that shows the internal movement is much, much slower than the speed of light. Since your conductors do not fall through the floor when you cut on the switch, we are not sufficiently near the speed of light to stuff elephants in the wire.
That's good. It's analogous to the principle that even though sound moves at 1180 feet per second, that doesn't mean that shouting at someone will hit them with an 800mph blast of wind.

#### kwired

##### Electron manager
That's good. It's analogous to the principle that even though sound moves at 1180 feet per second, that doesn't mean that shouting at someone will hit them with an 800mph blast of wind.
It usually works that way in the cartoons though

#### GoldDigger

##### Moderator
Staff member
That's good. It's analogous to the principle that even though sound moves at 1180 feet per second, that doesn't mean that shouting at someone will hit them with an 800mph blast of wind.
Very very good analogy in several ways!
In the propagation of a sound wave the individual air molecules move a relatively short distance (unless the wavelength and amplitude get REALLY large). In the propagation of an alternating current the individual electrons may not move very far or very fast.
The speed at which the electrons have to move to support the current (even DC) will depend strongly on how many electrons free to move are contained within a small volume of the material. Enough electrons per second have to pass any cross section, but if the number moving is large the speed will be correspondingly small.
"Still water runs deep."

Staff member

#### mivey

##### Senior Member
All those quotes you attributed to me were from the OP, not me. I should have replied with quote to the OP rather than cut and paste; my bad.
I thought you knew better, but really was not paying attention.

#### mivey

##### Senior Member
That's good. It's analogous to the principle that even though sound moves at 1180 feet per second, that doesn't mean that shouting at someone will hit them with an 800mph blast of wind.
Oh if that were only true what fun we could have.

#### Sahib

##### Senior Member
But don't you agree heavier ions have lower mobility i.e lower drift velocity than lighter electrons for the same voltage?
I would say it depends on the material.
In which material is it violated?
None.
I would have to look back at my physics texts. Normally I would think it in the 0.5c to 0.9c range. 0.6c to 0.8c come to mind but that is probably just the propagation speed in a wire.

But think about it from a logical standpoint. Bes showed the speed of the electrons in the wire are very slow but we know the initial reaction propagates in the conductor much, much, much, faster than that and is closer to the speed of light than the speed Bes showed. We also know there is a delay in getting the electrons down in the wire to move (the skin effect) that shows the internal movement is much, much slower than the speed of light. Since your conductors do not fall through the floor when you cut on the switch, we are not sufficiently near the speed of light to stuff elephants in the wire.

I'll see if there was an estimate of the reaction speed given in the text. The only thing I remember is it stating that the shifting of the electrons and charge gradient that created the field took place at near light speed. I seem to recall an example given that flipping a switch did not produce an immediate reaction at the far end but there was a delay measured in near light speed.
So contrary to what you stated below
[/QUOTE]
the surface electrons on a metallic conductor move near light speed when a electric field is applied.
it is the change in electric and magnetic field of the conductor, when a supply of direct electric current is switched on, that travels at very near the speed of light and not the electrons at the surface or inside the conductor.

Duplicate.

#### mivey

##### Senior Member
In which material is it violated?
None.
Mobility is a material property.

So contrary to what you stated below...it is the change in electric and magnetic field of the conductor, when a supply of direct electric current is switched on, that travels at very near the speed of light and not the electrons at the surface or inside the conductor.
No. Think. What causes a change in the electric field and magnetic field? Changing electric fields and moving charges create magnetic fields. Changing magnetic fields and charge imbalance creates electric fields.

The electric fields change surface charges and surface charges create electric fields so there is a feedback mechanism.

The field changes propagate AT the speed of light for the medium and act as a feedback mechanism in the circuit. The response of the surface electrons begins during the first feedback loop (the time it takes light to travel across the circuit). So at times NEAR light speed, the surface electrons have already begun to re-align. As the feedback continues, internal current leads to additional surface charges being added and re-aligned until the circuit reaches steady state.

The re-alignment steps towards the steady-state surface charge gradient is like a sloshing back-and forth through the circuit that talks place as the feedback process continues and the circuit currents stabilize. The time to steady-state will vary with the circuit complexity and signal but on a simple DC circuit a clear field pattern will have been established within the first or second light cycle that begins to look like the steady-state condition except in the more complex parts of the circuit like interfaces.

#### Sahib

##### Senior Member
Mobility is a material property.
Yes. Ions have lower mobility than electrons and so lower drift velocity and consequently,lower current for monovalent ions for the same voltage.
No. Think. What causes a change in the electric field and magnetic field? Changing electric fields and moving charges create magnetic fields. Changing magnetic fields and charge imbalance creates electric fields.

The electric fields change surface charges and surface charges create electric fields so there is a feedback mechanism.

The field changes propagate AT the speed of light for the medium and act as a feedback mechanism in the circuit. The response of the surface electrons begins during the first feedback loop (the time it takes light to travel across the circuit). So at times NEAR light speed, the surface electrons have already begun to re-align. As the feedback continues, internal current leads to additional surface charges being added and re-aligned until the circuit reaches steady state.

The re-alignment steps towards the steady-state surface charge gradient is like a sloshing back-and forth through the circuit that talks place as the feedback process continues and the circuit currents stabilize. The time to steady-state will vary with the circuit complexity and signal but on a simple DC circuit a clear field pattern will have been established within the first or second light cycle that begins to look like the steady-state condition except in the more complex parts of the circuit like interfaces.
One crux in your explanation is the movement of surface electons at near light speed. Since there are trillions and trillions of surface electrons, an appreciable increase in their mass, due to their movement at near light speed, can lead to a detectable, albeit extremely small, transient increase in mass of the conductor, whenever a DC supply is switched on. The same effect on permanent basis may be expected for AC supply. But neither effect is reported in the technical literature.

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#### mivey

##### Senior Member
Yes. Ions have lower mobility than electrons and so lower drift velocity and consequently, lower current for monovalent ions for the same voltage.
I would say it depends on the material. The mobility of an electron in one material may very well be less that the ion mobility in another material.

One crux in your explanation is the movement of surface electrons at near light speed. Since there are trillions and trillions of surface electrons, an appreciable increase in their mass, due to their movement at near light speed, can lead to a detectable, albeit extremely small, transient increase in mass of the conductor, whenever a DC supply is switched on. The same effect on permanent basis may be expected for AC supply. But neither effect is reported in the technical literature.
THE technical literature? I have not had the time to review all of them so I'm glad you have.:roll:

So you think that, as a percent of the conductor weight, the relativistic mass increase of the relatively few electrons on the surface is a significant statistic? Think about it before you answer. Maybe even try your hand at some math. Look at the mass increases of 0.05%, 0.5%, 5%, 50%, 500%, etc. for the surface electrons. At what point does it become significant?

#### GoldDigger

##### Moderator
Staff member
I would say it depends on the material. The mobility of an electron in one material may very well be less that the ion mobility in another material.

THE technical literature? I have not had the time to review all of them so I'm glad you have.:roll:

So you think that, as a percent of the conductor weight, the relativistic mass increase of the relatively few electrons on the surface is a significant statistic? Think about it before you answer. Maybe even try your hand at some math. Look at the mass increases of 0.05%, 0.5%, 5%, 50%, 500%, etc. for the surface electrons. At what point does it become significant?
:thumbup:
The mobility of electrons in water or any aqueous electrolyte is very low, for example. Negative charges move as hydroxyl or other negative ions.

The mass gain of the conductor is irrelevant since the surface electrons do not move at anything near light speed.

Tapatalk...

#### ggunn

##### PE (Electrical), NABCEP certified
:thumbup:
The mass gain of the conductor is irrelevant since the surface electrons do not move at anything near light speed.
Don't they, though, for teeny tiny distances and then stop for comparatively huge amounts of time? Their masses could increase by immense amounts but such a small fraction of them would be moving at any instant that the overall increase in mass of the conductor would be negligible.

CAVEAT: The above is merely speculation.

#### GoldDigger

##### Moderator
Staff member
Caveat accepted, and as a former physicist I can confidently say that it does not happen that way. The available force is limited by the total voltage drop in the wire divided by the distance, so the acceleration is strictly limited. Even when you look at the quantum level (which is not necessary).
P.S. The EM radiation caused by your proposed violent accelerations would be horrendous.

Tapatalk...

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#### mivey

##### Senior Member
The mass gain of the conductor is irrelevant since the surface electrons do not move at anything near light speed.
Their feedback reaction is what happens at near light speed. But playing to Sahib's question, even if they did what would it take to notice it? I'll do the math since Sahib is more likely to argue without basis rather than actually put any thought into the argument.

So just for grins let's assume that all of the electrons are on the surface of copper. Let's also use 35 neutrons, 29 protons and 29 electrons so the electron is 0.02465% of the simplified copper mass. Now accelerate the electrons and look at the relative increase in the weight of the copper. For different speeds I show the light speed, millions of mph, increase in electron mass and increase in copper mass.

0.010c, 6.706 Mmph, 0.005% electron, 0.000 001 233% cu
0.020c, 13.412 Mmph, 0.020% electron, 0.000 004 932% cu
0.040c, 26.825 Mmph, 0.080% electron, 0.000 019 746% cu
0.050c, 33.531 Mmph, 0.125% electron, 0.000 030 875% cu
0.100c, 67.062 Mmph, 0.504% electron, 0.000 124 199% cu
0.200c, 134.123 Mmph, 2.062% electron, 0.000 508 369% cu
0.300c, 201.185 Mmph, 4.828% electron, 0.001 190 380% cu
0.400c, 268.247 Mmph, 9.109% electron, 0.002 245 655% cu
0.500c, 335.308 Mmph, 15.470% electron, 0.003 813 877% cu
0.600c, 402.370 Mmph, 25.000% electron, 0.006 163 323% cu
0.700c, 469.432 Mmph, 40.028% electron, 0.009 868 221% cu
0.800c, 536.493 Mmph, 66.667% electron, 0.016 435 527% cu
0.900c, 603.555 Mmph, 129.416% electron, 0.031 905 237% cu
0.950c, 637.086 Mmph, 220.256% electron, 0.054 300 427% cu
0.970c, 650.498 Mmph, 311.345% electron, 0.076 756 795% cu
0.980c, 657.204 Mmph, 402.519% electron, 0.099 234 155% cu
0.990c, 663.910 Mmph, 608.881% electron, 0.150 109 251% cu
0.999c, 669.946 Mmph, 2,136.627% electron, 0.526 748 908% cu

So even at 0.7c the impact is only 0.001% of the copper weight. So even if the individual electron accelerated to a very high %c, the impact on the mass is irrelevant: that was the point of that exercise.

Now moving right along...

#### mivey

##### Senior Member
the acceleration is strictly limited.
Acceleration can be quite large and the results are limited by distance and time. Just 100 volts across a 1 foot thick plate can cause an electron to accelerate at 7.00E+14 m/s^2. The key is that these movements are very small (maybe a few atoms distance) and occur at near light speed (the jump from one spot to the next takes place within a few light cycles).

So we could for an electric field wave front impressed across dimensions of the atomic order, it is over in pico-seconds. So while the electrons respond at near light speed with the wave propagation, what about the individual electrons with the massive acceleration but short-lived time and short distance?: Individual electron speeds from rest may be on the order of 1E^6 to 1E^7 m/s.

How fast is that and how close to light speed is it? At the scale of drift speed it is close to light speed. Something on this order:
Light speed in vacuum : 300,000,000 m/s
Individual electron speed: 10,000,000 m/s
Drift speed : 0.000 010 m/s

So compare the numbers (leading and trailing zeros used to help the alignment) and the individual can decide if the electrons move near light speed or near drift speed:
300,000,000 . 000 000 000 000 000 000 m/s
010,000,000 . 000 000 000 000 000 000 m/s
000,000,000 . 000 010 000 000 000 000 m/s