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The way I understand it, electric wires heat up because there is too much current passing through them. There are tables for various materials, how much current can pass through a given cross-section without a significant heat-up. That's also why we use high voltage in the big power lines to transfer a lot of power - this allows us to make the wires thinner (cheaper).

But is there an upper limit to this trick? Would it be (theoretically) possible to raise the voltage to petavolts, and pass all the power of the entire planet through a wire no thicker than a hair?

Added: To clarify, I'm wondering how far the voltage can be pushed, what the problems would be (ok, so insulation is the first one), and if there are any theoretical limits that cannot be surpassed no matter how much technology improves.

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    \$\begingroup\$ At a certain voltage the insulation, air, and even vacuum kinda becomes a parallel conductor, also the wire stops being a wire and becomes a rapidly expanding plasma \$\endgroup\$ – PlasmaHH Aug 2 '18 at 12:17
  • \$\begingroup\$ @Vilx: Have you considered the insulation problem? You need to consider this in the wires and step-up / step-down devices at each end of your wire. \$\endgroup\$ – Transistor Aug 2 '18 at 12:18
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    \$\begingroup\$ Even the high-voltage transmission is practically limited to 1000ish kV. See this for example \$\endgroup\$ – anrieff Aug 2 '18 at 12:23
  • \$\begingroup\$ Partial discharge will become a problem at high voltages and will pose an upper practical limit for the wire alone, but transformers, insulators, bushings and everything else will put economical limits before that. \$\endgroup\$ – winny Aug 2 '18 at 14:25
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You can keep increasing the voltage on a wire up to a point. Unfortunately higher voltage does require thicker wire, and it's nothing to do with heating.

The electric field at the surface of a single wire of given radius is proportional to the voltage/radius. Once the electric field exceeds the breakdown field of the dielectric that's insulating the wire, it begins to break down the insulation. This creates corona if the dielectric is a gas, like air of SF6, and damages the insulation if it's a solid.

This is handled on overhead wires by making a bundle of thin wires. This behaves, as far as corona is concerned, as a much thicker wire. Each wire is 'shielded' to some extent by the others, which reduces the electric field at its surface. While the 275kV grid tends to use a bundle of four wires, MV grids use several 10s of wires and a bundle more than 1m in diameter.

Many of us have seen pictures of high voltage switchgear. The conductors between nodes are often very large diameter tubes. This is simply to allow air insulation to be used with minimal corona

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  • \$\begingroup\$ I want to see a wire which is more than 1m in dia. Can you post a link please. Thanks \$\endgroup\$ – Whiskeyjack Aug 2 '18 at 14:34
  • \$\begingroup\$ @Whiskeyjack I've tried, but my goolefoo is not working well. There's wall-to-wall 4-conductor bundles on images when you search 'grid corona conductor bundle high voltage'. Remember this is an open bundle, not a solid bundle. Changing the search to Van der Graff shows another thing where large radius is necessary to reduce the electric field to avoid corona or breakdown at high voltages. \$\endgroup\$ – Neil_UK Aug 2 '18 at 14:57
  • \$\begingroup\$ Googling send me back to EE: electronics.stackexchange.com/questions/33725/… \$\endgroup\$ – Oldfart Aug 2 '18 at 15:54
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Ideally, that would work...practically, there are limits, as some commenters have pointed out.

If you'd like to see the principle in action, find those high-tension wires on those huge metal poles. They're up there on those big glass insulators so that the extremely high voltages keeping the current (and losses) down don't begin arcing around. As it's distributed, transformers reduce the voltage to levels that are (more or less) safe for consumers--meaning more current, but at that point it's completed most of its travel.

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  • \$\begingroup\$ I know of those high tension wires, I tried to describe them in the question. :) That's what gave me the idea/question - how far can this principle be pushed, and what will be the next problems? \$\endgroup\$ – Vilx- Aug 2 '18 at 12:38
  • \$\begingroup\$ I would think that at some point you run into the problem of being able to isolate windings in the transformer that steps the voltage up, and then later, back down. \$\endgroup\$ – CrossRoads Aug 2 '18 at 12:48
  • \$\begingroup\$ @CrossRoads - Good point. Unless there's some novel super-isolator material, that's probably the end of it. \$\endgroup\$ – Vilx- Aug 2 '18 at 12:54
  • \$\begingroup\$ Also keep in mind that those high-tension wires, with all the savings that HV does, still carry non-trivial amount of current, hundreds of amperes, in order to actually be useful in bulk power transmission. People have very strong incentives to push the voltage even higher, but are limited by materials... That novel super-isolator would be a HUGE breakthrough in power transmission :) \$\endgroup\$ – anrieff Aug 2 '18 at 12:58
  • \$\begingroup\$ I found a series of articles here electricityforum.com/td/utility-transformers/… am reading now to get some ideas of how the voltage can be stepped up to 345,000 volts! minnelectrans.com/transmission-system.html I see lots of articles on substations that bring the voltage down via multiple transformers, ending with 2 or 3 phases of 120V at the end user typically, but not so much on getting up to 345,000V (345KV). \$\endgroup\$ – CrossRoads Aug 2 '18 at 13:10

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