# 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 Resistivity 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 resistivity of various insulating materials

 Material Resistivity 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