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# 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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