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Resistance and Resistivity

Electrical resistance and resistivity

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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 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

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