Thereotical maximum current density for copper

william chan

An unusual question,

Let's say you have a 1mm diameter solid copper wire.
How many amps maximum can you flow through it in a short time? (1 ms?)
Is there a limit?

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Beau Schwabe

william chan,

Assuming the wire is round ... 1mm diameter is about 0.0394 inches
looking at this page...

http://www.powerstream.com/Wire_Size.htm

...for an approximate diameter, that comes out between 18 and 19 gauge... So at least 15 Amps


I think I know where you are going... perhaps I'm wrong.· In a recent post, I made reference to using 1/4 inch
copper tubing as a conductor.· The tubing is 1/4 inch outer diameter, and 1/8 inch inner diameter... How to
calculate the current with a hole in the middle of your conductor? ... look at the cross sectional area (Pi are squared)

1/4 inch if it were solid would have a cross sectional area of about 0.0491 inches
1/8 inch would have a cross sectional area of about 0.0123 inches

Subtracting the "hole"·gives us a cross sectional area of about 0.0368 inches
working that backwards (Pi are squared) again we would get an effective diameter of about·0.216 inches if it were solid.

looking at the link·mentioned above...· 1/4 inch copper tubing can handle·at least·135·Amps.



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Beau Schwabe

IC Layout Engineer
Parallax, Inc.

Post Edited (Beau Schwabe (Parallax)) : 6/5/2008 4:32:46 AM GMT

jmalaysia

Wire is a resistor. The longer the wire, the greater the resistance. You can push a lot of current through a very short 1mm wire (that's where the 15amps Beau quoted came from) but once you exceed a couple of feet of wire then the ampacity drops considerably. Wire size selection is all about providing the proper voltage at the other end. How much voltage drop can you afford due to wire resistance? How much heat can you allow to be generated due to resistance before the insulation melts? Treat a piece of wire like you would a resistor.

For 1msec over a very short distance you could push an incredible amount of current through a 1mm wire.

In practice, I would have no problem using a 1mm wire to carry 15 amps for a few inches for a second or two.

As for "Is there a limit?" Well, connect a 1mm wire between the + and - on your car battery. When the wire vaporizes in your hands I think you will see that there clearly is a limit. I know that doesn't directly relate to using it for 1msec, but you get my point.

Beau Schwabe

jmalaysia,

I think I was looking at the wrong column... I should have referenced·"Maximum amps for power transmission"
which uses a conservative 700 circular mils per amp for a maximum current density rule.

... so for Williams' 1mm diameter wire you could safely push about 2 Amps all day long.
...and for the example I gave using the 1/4 inch tubing 60 Amps would be a comfortable range.


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Beau Schwabe

IC Layout Engineer
Parallax, Inc.

skylight

Bare copper can take more amps than insulated and amps are dependant on the thermal qualities of the surrounding insulation, a table to help you choose, sorry it is in metric and not gauge.

http://www.energy-solutions.co.uk/cable_conductor.html

Shawn Lowe

Doesn't current flow on the outside of a wire? If so, does it matter that your using a tube and not a wire?

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Shawn Lowe


When all else fails.....procrastinate!

stamptrol

Current flows primarily in the outer sections of the copper conductor, to a depth of 1/4" to 1/2". The depth is related to "skin effect" and varies with the frequency used.That is why large buswork in generating stations and heavy switchgear is usually hollow box or tubular sections or multiple runs of smaller cables/bars.

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Tom Sisk

http://www.siskconsult.com
·

william chan

Lets say you discharge a 100,000v fully charged 10,000uF capacitor into a short 5mm diameter copper wire that is 1cm long.
I would think that the current will not peak in the 1st pico second due to a finite slew rate of the copper.
I would also think that the peak current would be lower than expected due to quantization of the current.

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Beau Schwabe

william chan,
·
Taking a step back here, and looking at the basics, there·is an actual value you are looking for·as far as what the maximum current density is.
·
Basically what you are looking for is how much energy·you can·put into the wire before it melts or begins to melt... or unless you are equipped to deal with molten copper conductors, how much energy·can you·put into the conductor·before it·turns into a gas.
·
Assuming the first scenario,·based on the length of wire and it's cross sectional area; you can determine what the resistance of that piece of wire is.
Depending on what that resistance value is·and the amount of voltage you are pushing through the wire, you can calculate the amount of Power in Watts that your particular section of wire would experience.·
·
Although the melting point of copper is 1357.77·K I'm not sure·how to calculate the required amount of energy to raise a·known amount of·copper from·an ambient room temperature to its melting temperature.· If you find out that, then you should be able to compare that to the amount of energy you are forcing upon the section of wire of interest.· This might at least give you something tangible to work with.
·

BTW) 100kV might be hard to do in air without it arching first before you even make·a solid contact.· Just to accomplish the 100kV test you will need to arrange your equipment for a special·setup in a vacuum or some inert gas that won't react with the copper or breakdown at that voltage.
····


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Beau Schwabe

IC Layout Engineer
Parallax, Inc.

Post Edited (Beau Schwabe (Parallax)) : 6/5/2008 5:01:41 PM GMT

pharseid

To determine a current level you definitely shouldn't attempt, you should check out the exploding wire technique for metal deposition. They've pretty much worked out current levels you definitely don't want to reach. Your setup, charging a 10,000 uF capacitor to 100,000 volts actually sounds like a good way to get a wire to explode.

-phar

LoopyByteloose

Forgive me if this sounds a bit off, but doesn't current flow on the outside of an AC wire and completely through a DC conductor?

NUTS AND VOLTS had a article within the last year about conductors and current capacity. It is surprising to see how flat conductors perform differently than round ones.

At the end of the day, I was left with the impression that the whole topic is nearly impossible to generalize about. And, it only becomes an issue if the losses are causing a problem within a particular design context.

Here in Taiwan, I do see hollow aluminum cable being used quite often for 10KV transmission lines.

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Leon

It depends on the frequency, the skin effect is negligible at 50/60 Hz.

Leon

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skylight

Kramer said...

Here in Taiwan, I do see hollow aluminum cable being used quite often for 10KV transmission lines.

This is mainly to do with cost and weight, a Heavy cable will sag and stretch and have to be constantly winched up, the savings in hollowing is substantial also.

Due to the very high voltages used and thus smaller currents (Power=V(olts)I(amps)) the cable can be relatively small in CSA thus saving on material cost.

LoopyByteloose

100KV seems like an unrealistic bench test as not even power distribution lines and generation plants go that high. As Beau mentioned, it is nearly impossible to make connections work without huge spark and leakage problems.

It would be more pragmatic to observe how a 22KV power grid design specifies, fabricates and provides distribution cables. I have great doubts that they are pure copper though. I've never seen a power grid above 22KV. My best guess would be that is tops, but I'm sure some one will prove me wrong again by citing a 30KV system or something else. { I did once work for an outfit called Bechtel Power Corp.}

Also, the metallurgical questions are quite a distraction.
First is the question of whether resistance remains constant over the whole temperature range. You cannot really expect to apply a linear equation. There are huge wastes of energy as one converts more and more electricity to heat. As one shifts from solid to liquid or to gas, there is another huge demand of energy input to attain a phase change from the solid state to whichever. And, are you going to limit yourself to pure copper conductors for naive reasons when there are likely to be alloys that have better physical strength and conduction properties.

To answer the original question - Yes, of course there is a limit.

A 1mm wire copper wire will eventually act like any household fuse. Why wouldn't there be a limit?

I suppose one could just go through the physical chemistry and figure out exactly how much heat it would take to achieve molten copper of a 1mm dia by 0.1mm length and convert that to an electrical energy equivalent. That would likely be your very near your limit.

Before one gets into all that quantum mechanics and such, just consider that plain old physics and chemistry can identify the failure of a simple peak current because the electricity converts to heat.

If the majority of the current is on the outside, I suppose that the wire would simply get smaller as it gets hotter. The failure would cascade once it got started.

And, I suspect that the correct quantified question is NOT 'how many amps', but 'how many watts?'

{Now I am wondering how that 100KV ever got into the discussion. Is someone trying to obscure the real issues.}

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PLEASE CONSIDER the following:

Do you want a quickly operational black box solution or the knowledge included therein?······

···················· Tropically,····· G. Herzog [noparse][[/noparse]·黃鶴 ]·in Taiwan

Post Edited (Kramer) : 6/13/2008 6:07:59 PM GMT