# Which is a better conductor, a very thick rubber wire or a very thin copper wire?

I read somewhere that very thick wires are generally better conductors than very thin ones. Is this true? If yes, then would a very thick rubber wire be a better conductor than a very thin copper wire?

Edit: By rubber wire, I mean a wire made entirely of rubber, not a copper wire insulated with rubber. This is purely a theoretical question.

• What does the datasheet say? – user98663 Jul 5 '19 at 13:21
• Rubber wires don't conduct. Rubber insulated metallic wires will. – Transistor Jul 5 '19 at 13:23
• What do you mean by a rubber wire? – Daniel K Jul 5 '19 at 13:26
• @Transistor There is no perfect isolator. You can calculate the diameter a "wire" of rubber would have to have to reach the same resistance. – jusaca Jul 5 '19 at 13:31
• Consider that the large diameter of the rubber wire would greatly increase its capacitance, impacting frequency response. – Hot Licks Jul 6 '19 at 1:03

The thin copper wire. Copper has a much higher conductivity than rubber.

The equation of relevance here is as follows:

$$R = \frac{l}{σA},$$

where $$\R\$$ is total resistance, $$\l\$$ is the length of the wire, $$\A\$$ is the wire's cross-sectional area (a measure of how thick it is), and $$\σ\$$ is a quantity called electrical conductivity, which is a property of the material in use.

As you can see here, thicker wires have lower resistance, but also higher-conductivity materials have lower resistance. Copper has a conductivity of about 6·107 S/m, while rubber has a conductivity of about 10-14 S/m, a difference of 21 orders of magnitude, so to have the same resistance, a rubber wire would have to have 6000000000000000000000 times the cross-sectional area of the copper one. That's six sextillion times the area, or 77.5 billion times the diameter.

Conductivity values given above are sourced from this wiki article. The rubber used for this is hard rubber, the type used for things like hockey pucks. Yes, there are other more conductive rubbers, and they would not need as large a wire to equal the conductivity of a copper one, but it would still be a very big one. Many of the more conductive rubbers are actually composite materials with carbon or other additives added to enhance conductivity.

• So I guess, while far-fetched, theoretically it is possible for such a thing to happen, right? – Dastan Jul 5 '19 at 13:42
• +1, This only applies when dealing with ideal giant rubber wires. – user98663 Jul 5 '19 at 13:44
• @Dastan I'm not sure there's that much rubber in the world. To get a resistance equal to that of a normal 1mm² copper wire, you'd need a 6,000,000,000 km² rubber wire. For reference, the surface area of the earth is 510,000,000 km², so your rubber wire would have enough cross-sectional area to cover the earth eleven times over and then some. – Hearth Jul 5 '19 at 13:48
• It should be noted that this equation only applies to cylindrical wires if they are either long compared to their diameter or if you somehow ensure that each end of the wire is at a uniform potential/perfectly conductive. You can't just build a huge hockey puck shaped rubber “wire” and stick it between two standard-size multimeter probes ;-) – wrtlprnft Jul 5 '19 at 21:55
• So ... if you had an insulator large enough (and it would be ridiculously large, as you've shown), you actually have a conductor. – Lawrence Jul 6 '19 at 10:08

It depends on the actual dimensions. The ratio of conductivity (between hard rubber and copper) is around 21 orders of magnitude ($$\10^{-14}\,\mathrm{S/m}\$$ vs. $$\6 \times 10^7\,\mathrm{S/m}\$$ ) so a 1 nanometer diameter copper wire would be as conductive as a 77 meter diameter rubber wire (conductivity increases with the square of wire diameter). Make the rubber 100m in diameter and rubber wins.

If the rubber is loaded with graphite or other conductive substance (as in the elastomer keyboard contact rubber) the ratio could be much, much less, but still large.

• I feel like conductivity probably stops being as straightforward when you have nanometer-scale devices. That wire is only six-ish atoms across. – Hearth Jul 5 '19 at 19:42
• @Hearth quite possibly, which is why I didn't go any lower than 1nm. I'll leave it to the physicists to say whether that was sufficiently fat for conductivity to behave "normally". This article would seem to indicate that they might not have much weirdness, especially at room temperature. – Spehro Pefhany Jul 5 '19 at 19:46

In general, the resistance of a conductor is defined as

$$\ R = \rho \frac{l}{A}\$$

where $$\\rho\$$ is the electrical resistivity of the material, $$\A\$$ the cross-sectional area and $$\l\$$ the length of the wire.

The resistance is getting smaller, the bigger the cross-sectional area $$\A\$$.

If both cables are made of copper, simply look at the conductor cross-section.

• And if the rubber wire is bigger in cross section by the same factor as copper is better is electrical resistivity. If the rubber wire is even bigger, then yes, in theory the rubber wire would be the better conductor. But in reality copper is SO much more conductive, that the cross section had to be ridiculously huge. – jusaca Jul 5 '19 at 13:25
• You would also have to inject current everywhere into the large end of the rubber why or just the resistance travelling across the surface at the tip would be excessive. – DKNguyen Jul 5 '19 at 14:21