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Resistance vs. Resistivity

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 of some Common Insulators

  • bakelite: 1 x 10 12 Ω m
  • glass: 1 x 10 10 - 1 x 10 11 Ω m
  • marble: 1 x 10 8 Ω m
  • mica: 0.9 x 10 13 Ω m
  • paraffin oil: 1 x 10 16 Ω m
  • paraffin wax (pure) : 1 x 10 16 Ω m
  • plexiglass: 1 x 10 13 Ω m
  • polystyrene: 1 x 10 14 Ω m
  • porcelain: 1 x 10 12 Ω m
  • pressed amber: 1 x 10 16 Ω m
  • vulcanite: 1 x 10 14 Ω m
  • water, distilled: 1 x 10 10 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 mm 2. 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

Convert between Electrical Resistivity Units

  • 1 Ω m = 10-2 Ω cm = 2.54 10-2 Ω inch = 3.048 10-1 Ω foot

Resistivity Compared to Copper

  • Aluminum (pure): 1.6
  • Brass: 3.7-4.9
  • Cadmium: 4.4
  • Chromium: 1.8
  • Copper (hard-drawn): 1.03
  • Copper (annealed): 1.00
  • Gold: 1.4
  • iron (pure): 5.68
  • Lead: 12.8
  • Nickel: 5.1
  • Phosphor Bronze: 2.8-5.4
  • Silver: 0.94
  • Steel: 7.6-12.7
  • Tin: 6.7
  • Zinc: 3.4

Related Topics

  • Electrical

    Electrical engineering with units, amps and electrical wiring. Wire gauges, electrical formulas, motors and more.

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