Electrical conductivity. Dependence of current on voltage
The quantity inverse to electrical resistance is the electrical conductivity γ = 1/R, with unit 1 siemens = 1 S = 1/Ω. That current in metals is the ordered motion of free electrons was confirmed by the Stewart–Tolman experiment (1916): the specific charge of the charge carriers they measured matched the electron’s. In the Drude–Lorentz theory a metal consists of lattice ions with free electrons moving randomly among them like a gas (in copper n ≈ 8.5·10²⁸ m⁻³). Without an external field the current is zero; in a field the electrons drift in an ordered way and collide with the ions, which produces resistance. Ohm’s law for a section of a circuit (G. Ohm, early 19th century): I = U/R = γU. The resistance of a conductor is R = ρl/S, where ρ is the resistivity (Ω·m), l the length and S the cross-section. The graph of current against voltage is the current–voltage characteristic; for a metal at constant temperature it is a straight line. Silver is the best conductor; in practice copper (γ ≈ 58 MS/m) and aluminium (≈ 36 MS/m) are used, and alloys such as nichrome make heater coils. In electrolytes conductivity grows with temperature (in metals resistance grows).
Only by calculation (no experiments with mains electricity): in your notebook make a table of U and I values, draw the current–voltage characteristic and find the resistance from U/I; compare the lines for two different wires.