# Electrical resistance and resistivity

Electrical resistance of an electrical conductor depends on

• The length of the conductor
• The material of the conductor
• The temperature of the material
• The cross-sectional area of the conductor

and can be expressed as

R = ρ L / A               (1)

where

R = resistance of the conductor (ohms, Ω)

ρ = resistivity of the conductor material (ohm metre, Ω m)

L = length of conductor (m)

A = cross-sectional area of conductor (m2)

#### Resistivity of some Common Conductors

Aluminum: 2.65 x 10-8 Ω m (0.0265 μΩ m)

Carbon: 10 x 10-8 Ω m (0.10 μΩ m)

Copper: 1.724 x 10-8 Ω m (0.0174 μΩ m)

Iron: 10 x 10-8  Ω m (0.1 μΩ m)

Silver: 1.6 x 10-8 Ω m (0.0265 μΩ m)

Note that resistivity depends on temperature. The values above are for temperatures 20 oC.

Resistivity, Conductivity and Temperature Coefficients for some Common Materials

#### Resistivity of some Common Insulators

bakelite: 1 x 1012 Ω m

glass: 1 x 1010 - 1 x 1011 Ω m

marble: 1 x 108 Ω m

mica: 0.9 x 1013 Ω m

paraffin oil: 1 x 1016 Ω m

paraffin wax (pure): 1 x 1016 Ω m

plexiglass: 1 x 1013 Ω m

polystyrene: 1 x 1014 Ω m

porcelain: 1 x 1012 Ω m

pressed amber: 1 x 1016 Ω m

vulcanite: 1 x 1014 Ω m

water, distilled: 1 x 1010 Ω m

Note that good conductors of electricity have low resistivity and good insulators have high resistivity.

Example - Resistance of a Conductor

The resistance of 10 meter gauge 17 copper wire with cross sectional area 1.04 mm2 can be calculated as

R = (1.7 x 10-8 Ω m) (10 m) / ((1.04 mm2)(10-6 m2/mm2))

= 0.16 Ω

Example - Cross-sectional area and Resistance

The copper wire above is reduced to gauge 24 and cross-sectional area 0.205 mm2. The increase in resistance can be calculated to

R = (1.7 x 10-8 Ω m) (10 m) / ((0.205 mm2)(10-6 m2/mm2))

= 0.83 Ω