Surface conduction at 60 Hz

[Proctologically Violated©®]

Awl--

I thought I had learned that conductors carried most of the electron flow on
their surface, but recently was informed that this would only be true at
high freq (skin effect). I disputed this via Coulombic forces, but then
realized that maybe Coulomb's law does not apply to flowing current in a
conductor--sumpn about hole current as well??
But indeed, a wire carrying current to a bulb is not charged the way a
capacitor is.

But THEN,
I just happened to be reading the 1996 edition of the NEC, and I noticed an
unusual entry: Nickel plated wire has 3-4 TIMES the current-carrying
capacity as regular copper wire.

At first brush, this seemed to support my initial assertion, that conductors
DO carry their charge on the surface.
But THEN, I realized that nickel (likely) has lower conductivity than
copper, so such an effect would appear odd even if current flow did tend
toward the surface.

Finally, I seem to remember the expression "current density" as a function
of cross-sectional area, which would suggest current is distributed
throughout the wire's cross section, not just on the surface.

So what's up w/ nickel plated wire???

In my 1920's house (Yonkers, NY), the service is solid #9 (!!! heavier than
10, but lighter than 8??), and it seems to be doing the job of #6 or #4
wire. In fact, I believe *all* the wiring in the house (cloth-covered #14)
is plated, and is also in very good shape--thank god. Splices are wire
nutted AND soldered, as well.

But back to the original topic:
At DC, or 60 hz, is current density uniform throughout the wire's cross
section? If not, what type of distribution does it have?
Why does Coulomb's law moot in a current carrying conductor?

TIA.

 

[Pop]

Awl--

I thought I had learned that conductors carried most of the
electron flow on ....

But back to the original topic:
At DC, or 60 hz, is current density uniform throughout the
wire's cross section? If not, what type of distribution does
it have?
Why does Coulomb's law moot in a current carrying conductor?

TIA.

Per cubic volume, or square if you prefer a 2-D visualization,
the current passing thru a material is the same. A square foot
cross sectional area of a material, regardless of its shape
allows electron/hole flow at a consistant rate throughout its
area.

Say you have a cross sectional area of 100 pieces of one square
foot. Each square foot of area is allowing the same number of
electron/hole flow as each of the others. Now, take those
hundred squares and arrange them so they make an approximate
circle (as in the cross sectional area of a wire). Each square
foot of area still passes the same amount of current.
Then, if you look at the very center, there is only one square
foot of area tha can occupy the exact center. But, around the
outside perimeter, it takes several square feet of area to make
it all the way around the perimeter.
Therefore, if you take an area on the outside of our gigantic
wire on the outermost surface, it has many, many square feet of
area, and thus a lot more current passing through it than the
single square foot that occupies the center-most area. But, if
you limited the area you're looking ato to jsut one foot in
width, not the whole perimeter, it would be carrying the exact
same current as the square foot in the center.
THAT is why people get confused and think it's skin-effect,
which it is not. But, obviously, around the entire full outside
of the circle, there is a lot more current moving than in the
tiny center because of the greater number of square feet it takes
to make it round.

Hope that might help visualize it a little better?

Skin-effect is an entirely different phenominon and has no
relationship to what this anecdote describes. With skin effect,
current per square area of material is NOT the same - so, it's a
lot different. And, it takes high frequencies to make tha t
happen, but it's too much to go into here.

HTH,

Pop

 

[ehsjr]

Awl--

I thought I had learned that conductors carried most of the electron flow on
their surface, but recently was informed that this would only be true at
high freq (skin effect). I disputed this via Coulombic forces, but then
realized that maybe Coulomb's law does not apply to flowing current in a
conductor--sumpn about hole current as well??
But indeed, a wire carrying current to a bulb is not charged the way a
capacitor is.

But THEN,
I just happened to be reading the 1996 edition of the NEC, and I noticed an
unusual entry: Nickel plated wire has 3-4 TIMES the current-carrying
capacity as regular copper wire.

At first brush, this seemed to support my initial assertion, that conductors
DO carry their charge on the surface.
But THEN, I realized that nickel (likely) has lower conductivity than
copper, so such an effect would appear odd even if current flow did tend
toward the surface.

Finally, I seem to remember the expression "current density" as a function
of cross-sectional area, which would suggest current is distributed
throughout the wire's cross section, not just on the surface.

So what's up w/ nickel plated wire???

In my 1920's house (Yonkers, NY), the service is solid #9 (!!! heavier than
10, but lighter than 8??), and it seems to be doing the job of #6 or #4
wire. In fact, I believe *all* the wiring in the house (cloth-covered #14)
is plated, and is also in very good shape--thank god. Splices are wire
nutted AND soldered, as well.

But back to the original topic:
At DC, or 60 hz, is current density uniform throughout the wire's cross
section? If not, what type of distribution does it have?
Why does Coulomb's law moot in a current carrying conductor?

TIA.

Forget skin effect at 60 hZ. The effect at such a low
frequency is of no practical concern. Even at the high
end of audio frequencies ~20kHz the effect is negligible.
Here's one audio site that makes that point:
http://www.audioholics.com/techtips/audioprinciples/interconnects/SkinEffect_Cables.htm

Watch for line wrap in the above.
Ed

 

[Pop]

I will take up a number of issues in sequence.

Forget about electrons, holes, and the like. They have no
practical
significance in almost all cases except when ELECTRONIC DEVICE
operation is
to be considered.

I don't believe the statement that nickel coated wire can
higher currents
than uncoated copper. In most cases, the limitation is going to
be the
maximum allowable temperature of the insulation. Skin depth is
going to be
greater for nickel than for annealed pure copper because nickel
has a lower
electrical conductivity. Countering that is the higher magnetic
permeability
of nickel which will reduce skin depth. The nickel plating will
dissipate
more power and reach a higher temperature than plain copper. In
any event, I
would like to se a reliable citation.

Skin depth at 60Hz in copper is about 6 mm. While that is large
compared to
typical wire radii in house wiring, it often cannot be
neglected. That is
why why power transmission lines often are fabricated with
steel cores clad
with copper or aluminum. Aluminum is preferred much of the time
because of
its low density and greater skin depth.

Bill

-- Ferme le Bush

Jeez, you've made some really bad rationalizations there! Better
go back to class for awhile!

 

[ehsjr]

I will take up a number of issues in sequence.

Skin depth at 60Hz in copper is about 6 mm.

Incorrect. It's > 9 mm

While that is large compared to
typical wire radii in house wiring, it often cannot be neglected. That is
why why power transmission lines often are fabricated with steel cores clad
with copper or aluminum. Aluminum is preferred much of the time because of
its low density and greater skin depth.

So you are saying that *the reason* 60 Hz power transmission
lines are fabricated with steel cores clad with copper or
aluminum is *because* skin effect cannot be neglected in that
situation. And your reference for that is ?

Putting it another way, you imply that the transmission
line could not be made out of the same amount of copper that
is used in the cladded line you are talking about because of
losses due to skin effect. Do you have numbers that support
that idea?

With the lines you are talking about, would the greater
ductability and lower strength of a purely copper cable
(if it was made that way) preclude its use? Do you think
this might be a more compelling reason for using steel
core?

Ed

 

[Bud--]

Short of vaporization, and ignoring insulation, which is most definitely
not the subject of the OP's question, what exactly determines the
ampacity of a metal wire?

If it is not temperature, then what else is there?

Skin depth relates to resistance or impedance. These may influence the
suitability of a wire for a particular purpose, but they are not the
basis for ampacity ratings. There is no direct relationship between
resistance and ampacity if temperature is not considered.

A quick web search will reveal that nickel-plated copper wires DO carry
a higher temperature rating than tin-plated copper wires. Or, put
differently, they can carry higher currents at a particular temperature.
Look here, for example:

http://www.jamesmonroewire.com/conductors.html
Copper Conductor Information - Wire and Cable

Chuck

Copper wire run at high temperature will oxidize badly and that is the
limiting factor. I believe nickle-plated wire can operate at higher
temperatures without oxidizing. Same is true with high temp crimp lugs.
High temp nickle-plated wire will of course have high temp insulation.

bud--

 

[Paul Hovnanian P.E.]

Awl--

I thought I had learned that conductors carried most of the electron flow on
their surface, but recently was informed that this would only be true at
high freq (skin effect). I disputed this via Coulombic forces, but then
realized that maybe Coulomb's law does not apply to flowing current in a
conductor--sumpn about hole current as well??
But indeed, a wire carrying current to a bulb is not charged the way a
capacitor is.

But THEN,
I just happened to be reading the 1996 edition of the NEC, and I noticed an
unusual entry: Nickel plated wire has 3-4 TIMES the current-carrying
capacity as regular copper wire.

At first brush, this seemed to support my initial assertion, that conductors
DO carry their charge on the surface.
But THEN, I realized that nickel (likely) has lower conductivity than
copper, so such an effect would appear odd even if current flow did tend
toward the surface.

Finally, I seem to remember the expression "current density" as a function
of cross-sectional area, which would suggest current is distributed
throughout the wire's cross section, not just on the surface.

So what's up w/ nickel plated wire???

Its not so much the nickel plating as the maximum operating temperature
of the conductor and insulation. The nickel plating only serves to
protect the copper conductor from reactions with oxygen at higher
temperatures.

The NEC ratings are based on conservative calculations of the ability of
a conductor to radiate or conduct the thermal energy away that is
produced by I^2R losses and still remain within the temperature limits
of the surrounding insulation. The are affected by insulation thermal
resistance and ambient temperature, among other factors.

 

[Paul Hovnanian P.E.]

High tension lines are just that. Very high tensile forces are on
the line. That is why it HAS to be steel cables. The point at which
at attaches to the towers has several thousand pounds of weight
hanging on it. Aluminum or copper either one would creep and cause
breaks in the line. 5mm of Aluminum cladding reduces the resistance of
a tower to tower traverse quite a bit at 60Hz. Way better than plain
steel.

The aluminum, or copper cladding IS for better conduction. Even
though losses at such high voltages are not that great, minimizing
them is STILL part of the job, and in the case of high tension lines
at 60Hz, cladding the cable in a better conductor such as aluminum or
copper does make a better transmission line. Remember also that the
lines are grouped in bundles of 3 or 4 cables, separated by a few
inches of air, between towers. So they maximize the tower's capacity
for weight, and they maximize the amount of aluminum or copper that is
actually carrying flow, getting the most out of the tensile capacity
the steel core wire has.

All correct, except that the reason for the multiple phase conductors
has to do with the system voltage, not skin effect. At high voltages,
the E field strength in the vicinity of a small radius conductor will
exceed the ionization potential of the surrounding air. This ionization
will result in power loss (it can be modeled by an equivalent resistance
from conductor to ground per mile). A conductor bundle simulates a
single conductor with a diameter equivalent to the bundle spacing. The
field strength around this larger radius 'surface' is reduced below the
ionization potential.

 

[Don Kelly]

All correct, except that the reason for the multiple phase conductors
has to do with the system voltage, not skin effect. At high voltages,
the E field strength in the vicinity of a small radius conductor will
exceed the ionization potential of the surrounding air. This ionization
will result in power loss (it can be modeled by an equivalent resistance
from conductor to ground per mile). A conductor bundle simulates a
single conductor with a diameter equivalent to the bundle spacing. The
field strength around this larger radius 'surface' is reduced below the
ionization potential.

In addition, the use of bundled conductors appreciably reduces the series
inductance of the line even though it does produce a small increase in
capacitance to ground and ground level fields. This is not a negligable
factor.

 

[Don Kelly]

----------------------------

Per cubic volume, or square if you prefer a 2-D visualization, the current
passing thru a material is the same. A square foot cross sectional area
of a material, regardless of its shape allows electron/hole flow at a
consistant rate throughout its area.

Say you have a cross sectional area of 100 pieces of one square foot.
Each square foot of area is allowing the same number of electron/hole flow
as each of the others. Now, take those hundred squares and arrange them
so they make an approximate circle (as in the cross sectional area of a
wire). Each square foot of area still passes the same amount of current.
Then, if you look at the very center, there is only one square foot of
area tha can occupy the exact center. But, around the outside perimeter,
it takes several square feet of area to make it all the way around the
perimeter.
Therefore, if you take an area on the outside of our gigantic wire on
the outermost surface, it has many, many square feet of area, and thus a
lot more current passing through it than the single square foot that
occupies the center-most area. But, if you limited the area you're
looking ato to jsut one foot in width, not the whole perimeter, it would
be carrying the exact same current as the square foot in the center.
THAT is why people get confused and think it's skin-effect, which it is
not. But, obviously, around the entire full outside of the circle, there
is a lot more current moving than in the tiny center because of the
greater number of square feet it takes to make it round.

Hope that might help visualize it a little better?

Skin-effect is an entirely different phenominon and has no relationship to
what this anecdote describes. With skin effect, current per square area
of material is NOT the same - so, it's a lot different. And, it takes
high frequencies to make tha t happen, but it's too much to go into here.

HTH,

Pop

Unfortunately, except at DC, that is not true. For AC there are inductive
effects and one result of this is a non-uniform current density
distribution. For 60 Hz, except for large diameter conductors, this is
negligable as the "depth" is larger than the conductor. A related
phenomena is proximity effect where the current in one conductor modifies
the current distribution in another conductor.

 

[ehsjr]

The purpose of the steel core is to provide the tensile strength that allows
longer spans (fewer towers) and less thermal expansion.

Exactly. The steel is required for strength, *not* to increase
the amount of copper at the surface. The copper at the surface
is required to reduce the electrical resistance of the cable,
as copper or aluminium is a much better conductor than steel.

Because of skin
effect, copper in the center of a large conductor is wasted.

Your are comparing steel clad copper versus copper clad steel,
by implication. Do you seriously believe that, for a given
core diameter and a given cladding thickness, a copper core,
steel clad cable would be as strong as a steel core, copper
clad cable for the transmission lines we're talking about?

Whether copper in the center would be wasted or not is
irrelevant. The need for a large steel core for strength
puts the copper or aluminum on the surface in the first
place, so there is no need to consider skin effect.

Ed


Skin depth is

 

[Don Kelly]

----------------------------

The purpose of the steel core is to provide the tensile strength that
allows
longer spans (fewer towers) and less thermal expansion. Because of skin
effect, copper in the center of a large conductor is wasted. Skin depth is
about 6 mm. How much steel core and haw much copper or aluminum is placed
on
top of the core is an economic decision. Remember that the radii of
conductors could be in the neighborhood of 20mm.

If copper were very cheap and spans small, wasting a bit of conducting
metal
would not be a big deal.

Bill
-- Ferme le Bush

Even in 1930+ when the lines from the then Boulder Dam to LA were built,
the advantages of a larger diameter conductor were apparent as was the extra
weight of a solid conductor considering skin effect. Rudenberg was one who
did an in-depth analysis of this. The conductors used there were about
2.5cm diameter and were made of twisted "barrel staves" about 3 to 4 mm
deep (working from memory of a sample). ACSR simply gave us the advantage of
the larger diameter with the strength of a steel core (not intended for
current carrying). Bundled conductors were a further improvement in terms of
surface fields and reduced inductance as well as mechanical and construction
advantages.

 

[Don Kelly]

----------------------------

It may be so, but it is not immediately obvious to me that parallel
bundles
of spaced wires will lower the electric field at the cylindrical surfaces.
Locally, the cylindrical surface of the individual conductor is going to
have the same radius as the conductor. To convince me, I would have to go
through a Schwarz transformation to solve the two dimensional potential
problem. I am not moved to do that.

Except for the skin effect, the velocity of propagation in the TEM mode
along the line will be the speed of light. This means that the product of
inductance and capacitance of the line stays relatively constant.

Bill

-- Ferme le Bush

I have done it the easy way -through computer modelling. The model used is
valid, external to the conductors, for multiple conductors above a ground
plane. The assumption in the program is that the charge of a conductor is at
its center, which is excellent for the typical distances involved -the
distance between the line charge location within the conductor to make it
an equipotential surface, and the true center of the conductor is
negligable. Corrections can be made but except for special cases such as
cables where distances are short, there is no point in doing so.
Input information is dimensional data (radii, height above ground plane,
spacing, etc) and voltage (instantaneous or rms) of each conductor with
respect to ground. There will be a reduction in surface E field and in a
short distance from the conductor bundle,-say 2 or 3 bundle radii- the field
will be near that of a single conductor of much large radius . Here is a
simple case. Single conductor radius 2 cm at height 10m and voltage of 100kv
surface field under conductor is 724.+ kV/m and at side it is 723+ kV
Two conductors, same size and voltage, spaced 30cm apart
field below =453kV/m, inside =418 kV/m and outside 478 kV/m
I also see that the charge on each conductor is appreciably lower than that
on the single conductor at the same voltage although the total charge is
greater.
The effective radius of the bundle is about 7.75cm in this case.
The ground level field is increased slightly in the bundled case as the
field is a bit more uniform. The line capacitance is increased by bundling
and the inductance is decreased. The decrease in line inductance is of more
importance, in most cases, than the increase in C. Note that in general
capacitance is based on the conductor radius while, for inductance, the
concept of GMR is considered and this takes into account internal flux
linkages. For ACSR, the GMR is measured but it can be calculated different
geometries in the absence of magnetic materials.

 

[Pop]

....

Unfortunately, except at DC, that is not true. For AC there are
inductive effects and one result of this is a non-uniform
current density distribution. For 60 Hz, except for large
diameter conductors, this is negligable as the "depth" is
larger than the conductor. A related phenomena is proximity
effect where the current in one conductor modifies the current
distribution in another conductor.

No. It is true to all but the most extreme purists of the world
who will waste much time and energy on things that are not
discernible in the real world. At 60 Hz and much, much higher
frequencies, it will take some very expensive equipment to even
theorize the still negligible effects of it. People who think
like this are of no practical use for such areas as this thread;
it's been pretty well pointed out.
You sound like the kind who will claim your weight also varies
because you go from the first to the second floor of a building;
true, but of no use to anyone but an extreme purist or anecdotal
collector of trivia, just as your weight "changes" when you walk
into a tunnel but don't change your relation to the center of the
earth. interesting but useless information to the real world.

Pop

 

[daestrom]

...

No. It is true to all but the most extreme purists of the world who will
waste much time and energy on things that are not discernible in the real
world. At 60 Hz and much, much higher frequencies, it will take some very
expensive equipment to even theorize the still negligible effects of it.
People who think like this are of no practical use for such areas as this
thread; it's been pretty well pointed out.

Yeah, right. "Standard Handbook for Electrical Engineers, Ninth Edition" (a
really old copy), Tables 13-8 and 13-9 so DC, 25Hz, 50Hz and 60Hz
resistances for large cables.

For example, ACRS 900,000 circular mils, 0.115, 0.116, 0.118 and 0.119 ohms
per mile per conductor. 3.5% difference may not be anything *you* care
about, but some of us work with cables larger than what you work with. The
larger cables most definitely do have a difference resistance thanks to
skin-effect.

Building transmission lines is considered a 'practical use' by most folks.

daestrom

 

[daestrom]

Exactly. The steel is required for strength, *not* to increase
the amount of copper at the surface. The copper at the surface
is required to reduce the electrical resistance of the cable,
as copper or aluminium is a much better conductor than steel.



Your are comparing steel clad copper versus copper clad steel,
by implication. Do you seriously believe that, for a given
core diameter and a given cladding thickness, a copper core,
steel clad cable would be as strong as a steel core, copper
clad cable for the transmission lines we're talking about?

Whether copper in the center would be wasted or not is
irrelevant. The need for a large steel core for strength
puts the copper or aluminum on the surface in the first
place, so there is no need to consider skin effect.

He didn't explicitly mention steel clad copper.

But he may be referring to bus-work used in substations. For short runs
between circuit-breakers, lightning arrestors, disconnects and other
components, you will often see hollow tubing used for the conductors. If
the same cross-sectional area of material were in the form of a solid bar,
it would have higher resistance owing to the skin effect. By simply
reshaping the material into a tube with a larger OD, more material is in the
region near the 'skin', providing lower resistance.

(the tube also has more structural strength than a solid bar of the same
material cross-section).

daestrom

 

[Pop]

OK, I'll rephrase and say what I meant, politeness aside since
you're so thick: Idiots who depart substantially from the post
topic in order to attempt a shot at some sort of infamy whether
it be good or negative in nature, and which serves to do nothing
but confuse and create a sense of information based on
misinformation, and under the guise of being a know it all. If
you were a fraction of what you say you are, you'd have a lot
more things to do than puppet around these groups.

There's no future in discussing anything further here as I
consider you to be an intentional moron in this area. Too bad
you never went to a real school.

Pop



"daestrom"daestrom@NO_SPAM_HEREtwcny.rr.com> wrote in message

 

[Pop]

He didn't explicitly mention steel clad copper.

But he may be referring to bus-work used in substations. For
short runs between circuit-breakers, lightning arrestors,
disconnects and other components, you will often see hollow
tubing used for the conductors. If the same cross-sectional
area of material were in the form of a solid bar, it would have
higher resistance owing to the skin effect. By simply
reshaping the material into a tube with a larger OD, more
material is in the region near the 'skin', providing lower
resistance.

(the tube also has more structural strength than a solid bar of
the same material cross-section).

daestrom

Previous point proven.

 

[Pop]

I was thinking a bit more about this and have resolved the
paradox in my
mind.

For a given power capacity of a line, the voltage required is
going to be
proportional to V^2/Zo. By putting multiple conductors in
parallel, (per
unit length) the inductance is decreased while the capacitance
is increased.
This lowers the characteristic impedance of the line. Thus, the
voltage
required to transmit the original power is dropped, and the
likelihood of
corona is diminished.

Bill
-- Ferme le Bush

Actually, that's not bad; good going!

Pop

 

[Paul Hovnanian P.E.]

Meaningless questions like this from extremely uninformed people come
up all the time.

It doesn't stop well informed, well intentioned people trying to read
minds and rushing in with replies. Stop here.

You're right. We shouldn't be answering questions for people unless they
already know the answer.