# 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

## Related Topics

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