# Resistance and 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 (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*Ω m^{11} - 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

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