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 (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, Conductivity and Temperature Coefficients for some Common Materials

Resistivity of some Common Insulators

• bakelite: 1 x 10¹² Ω m
• glass: 1 x 10¹⁰ - 1 x 10¹¹ Ω m
• marble: 1 x 10⁸ Ω m
• mica: 0.9 x 10¹³ Ω m
• paraffin oil: 1 x 10¹⁶ Ω m
• paraffin wax (pure): 1 x 10¹⁶ Ω m
• plexiglass: 1 x 10¹³ Ω m
• polystyrene: 1 x 10¹⁴ Ω m
• porcelain: 1 x 10¹² Ω m
• pressed amber: 1 x 10¹⁶ Ω m
• vulcanite: 1 x 10¹⁴ Ω m
• water, distilled: 1 x 10¹⁰ 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 mm². 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

Temperature ^oC
K
^oF

Length m
km
in
ft
yards
miles
naut miles

Area m²
km²
in²
ft²
miles²
acres

Volume m³
liters
in³
ft³
us gal

Weight kg_f
N
lbf

Velocity m/s
km/h
ft/min
ft/s
mph
knots

Pressure Pa
bar
mm H₂O
kg/cm²
psi
inches H₂O

Flow m³/s
m³/h
US gpm
cfm