Resistance vs. 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 (m 2 )
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 o C .
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 mm 2 can be calculated as
R = (1.7 x 10 -8 Ω m) (10 m) / ((1.04 mm 2 )(10 -6 m 2 /mm 2 ))
= 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 mm 2 )(10 -6 m 2 /mm 2 ))
= 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
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