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The numerical simulation of this nerdy question shows that the resistance decreases with the number of nodes along longest side, and converges to a finite value when the # of nodes approaches infinite.

Here comes my question: Can such grid or mesh design be utilized to reduce the resistance in wires/cables for long distance transport? Let's say one unit-length segment of copper wire can be treated as one unit resistor, so a copper wire mesh is basically equivalent to a grid of resistors.

Of course there exist many different ways to reduce the resistance, such as using a thicker wire (increase the cross section area), lowering the temperature, or even changing the material. But here I specifically wonder what simple circuit or topological design can do the trick, and whether it is practical or not.

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kakemonsteret's answer is perfectly correct, and complete as far as DC resistance goes, but people still make stranded wire such as Litz wire. Why is that?

If you have DC current flowing through a normal conductor, the current spreads out so that the current density is approximately constant throughout the cross section of the conductor. This is good for making low-resistance wires because you can make the wire thicker and the current actually flows through the whole cross-section, so the resistance decreases in proportion to the area.

However, if you have AC current flowing back and forth at a relatively high frequency (which depends on the relevant length dimensions), the current will not distribute itself evenly over the cross-section - instead it will become concentrated at the surface. This is called the skin effect and it's caused by the magnetic field of the current causing a Lorentz force on itself.

Because of the skin effect, if you want to reduce the impedance (generalization of resistance) of a wire at some frequency, just making it thicker and thicker is not very effective. This is part of the reason why stranded and woven wire like Litz wire is used. If you look at the cable from a lightning rod that's designed to handle the lightning current, it will often have many copper strands woven together. Lightning current is DC, but the current ramps up from zero very quickly, which means the current signal has high-frequency components.

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That is a very good answer. I'd also add that wire may be braided in order to make it flexible, as well as to accomodate skin effects. – Omega Centauri Jan 21 '11 at 17:42

No, using one wire between two points A and B will beat any other topology for the same R, in terms of (total mass of wire)/(distance A-to-B), thus also ofcourse less cost. Just imagine you got a 2xN grid, how long do you want to make the connections between the two wires, clearly as short as possible until you got 1 wire.

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protected by Qmechanic Mar 8 at 16:33

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