Specific Resistance and Conductance

Description and calculation of specific resistance and conductance

Specific Resistance

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

\(\displaystyle R =\frac{l}{σ· A}\)


Overview of the specific resistance and the specific conductance of various conductive materials

Material Resistance ρ Conductance σ

Silver 0.016 62.5
Copper 0.018 56
Gold 0.023 44
Aluminium 0.029 35
Magnesium 0.045 22
Tungsten 0.055 18
Zinc 0.063 16
Nickel 0.08 ... 0.011 13 ... 9
Iron 0.10 ... 0.15 10 ... 7
Tin 0.11 9
Platinum 0.11 ... 0.14 9 .. 7
Lead 0.21 4.8
Mercury 0.96 1.04
Bismuth 1.2 0.83
Carbon 100 0.01
     

Overview of the resistance of various insulating materials

Material Widerstand ρ

Amber 1018
Glas 1014
Mica 1014 ... 1017
Rubber 1015
Hard rubber 1012 ... 1018
Ceramics 1012
Resin 108 ... 1014
Marble 109 ... 1011
Paraffin 1016
Polystyrene 1018
Pressboard 1010
Porcelain 1014
Shellac 1016