Specific Resistance and Conductance

Specific resistance refers to the resistance of a wire made of a specific material \(1\) meter long and \(1 mm^2\) in cross-section.

Wires of equal length and same cross-section made of different materials have different resistances.

Wires of equal length and same cross section of the same material have the same resistance at the same temperature

The specific resistance has the symbol \(ρ\) (rho)

Electrical Conductance

The reciprocal of the resistivity is the electrical conductivity or the conductance.

The specific conductance indicates which length of a wire, with a cross section of \(1\) \(mm^2\), gives the resistance of \(1Ω\).

The symbol of the conductance is \(σ\) (sigma)

\(\displaystyle σ=\frac{1}{ρ}\)

The resistivity is the reciprocal of the specific conductance.

\(\displaystyle ρ=\frac{1}{σ}\)

Calculate Resistance

The resistance of a wire is proportional to its length. A triple wire length also gives a triple resistance.

\(\displaystyle R ∝ l\)

The resistance of a wire is inversely proportional to its cross section. A double cross section gives half the resistance.

\(\displaystyle R ∝\frac{1}{A}\)

Using the resistivity you get the formula:

\(\displaystyle R =\frac{ρ·l}{A}\)

Using the specific conductance, you get the formula:

\(\displaystyle R =\frac{l}{σ· A}\)