conductivityconductors
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.
The above is the formula for the inductance of parallel wires where s is distance between wires, L is the overall length and d is wire diameter and here is a calculator that uses the formula.
For series resistance you will find many references on google for this and please note that it is ambient temperature dependant. There are plenty of references for skin effect also but not so many for the formula for proximity effect but hopefully this reference from wiki might prove useful.
Finally, once you have the resistance, inductance and capacitance you can use the standard formula for characteristic impedance (applies to any length of wire of course and is still valid down to DC): -
You haven't considered "G" but this is usually a very large resistance and its effect is negligible.
So now you have the impedance looking into an infitely long line of cable. However, you want the impedance looking into 100 metres of such cable so you will then have to work with reflection coefficients and the load impedance (stated as unloaded in the question) BUT YOU CANNOT ignore these load effects (and reflections) if you want a proper answer.
Reflections will occur with any incorrectly terminated cable: -
And these can effect results significantly even at moderate frequencies like 100 kHz. At 100 kHz the wavelength is 3 km but this is probably going to be more like 2 km. Major things happen at a quarter of this wavelength i.e. an open circuit can look like a short circuit and a short circuit can look like an open circuit so 500 metres is still pretty close for creating major errors when considering a cable that is 100 metres long.
The big difference between a soldering gun and a "regular" soldering iron is the former is only heated for a few seconds, while the latter usually stays on all the time during work.
Because of that, the gun already is more efficient than a "regular" soldering iron. Very few needs to further improve it.
Apart, from that, why not choose brass? Because brass is more rigid and likely to break. That's bad for a tool which is meant to be thrown into a tool bag.
Best Answer
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.