Some information about conductivity

Conductivity (σ-sigma):
Definition:
Part 1. the degree to which a specified material conducts electricity, calculated as the ratio of the current density in the material to the electric field that causes the flow of current (I). It measures a material’s ability to conduct electric current (I);
Part 2. reciprocal of the resistivity [σ=1/ρ].

Basically in Ohm’s law, I=V/R, where I is current, V is voltage, R is resistance.
①Ideally, we assume V is constant, so in order to make I large, what we want for materials with higher conductivity are those whose R is small. ($$)
②Realistically, V might not be constant, then I=V/Z, Z is the impedance.

Continue on ①
So what decides the value of R? -We introduce Resistivity (ρ) here.

Resistivity (ρ-rho): -an intrinsic property that quantifies how strongly a given material opposes the flow of electric current (I).

How are Resistivity (ρ) and Resistance® related? (graph explanation here)
(#) ρ = R * A / l or R = ρ * l / A [Pouillet’s law]

R is electrical resistance (unit: ohms-Ω);
l is the length of the piece of material;
A is the cross-sectional area

Since σ = 1 / ρ (by definition Part 2), then together with (#), we have σ = l / (R * A)

So from this approach, we could see if the materials are in the same shape, what we want for materials with high conductivity are the ones with low Resistance R.This confirms our guess from the first approach at ($$).