For electrical conductivity silver has not much advantage copper is much cheaper. The electrical conductivity advantage for silver is in the ratio 63.0 to 59.6.
Silver 18.50 USD/oz
Copper 3.8 USD/lb
Note the different units for the comparison.
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Copper is an excellent conductor of electricity. Among metals it is second only o silver, which is too expensive for practical use in wiring. Copper is also extremely ductile, meaning it can be easily drawn into wires without breaking.
Yes, Pencil Lead does conduct Electricity. Copper, Gold and Silver though are the best conductors.
Not especially well. However, the oxidation is usually limited to the surface, so the pure silver "core" will still conduct.
Pure water, by itself, is not capable of conducting electricity. However, when other substances are added and ions make their way into water, those free ions can cause water to conduct electricity.
I don't know what "iron gold" is, but electricity will flow through any metal pretty well.