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

Electrical resistance of a conductor can be calculated as

R = ρ L / A

   = L / (σ A)                                    (1)

where

R = resistance of the conductor (ohms, Ω)

ρ = resistivity of the conductor material (ohm metre, Ω m)

σ = electrical conductivity (1/ohms m, 1/Ω m, siemens/m, S/m, mho/m)

L = length of conductor (m)

A = cross-sectional area of conductor (m²)

Resistivity of some Common Conductors

• Aluminum: 2.65×10^-8 Ω m (0.0265 μΩ m)
  
• Carbon: 10×10^-8 Ω m (0.10 μΩ m)
• Copper: 1.724×10^-8 Ω m (0.0174 μΩ m)
  
• Iron: 10×10^-8 Ω m (0.1 μΩ m)
• Silver: 1.6×10^-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: 1×10¹² Ω m
• glass: 1×10¹⁰ - 1×10¹¹ Ω m
• marble: 1×10⁸ Ω m
• mica: 0.9 ×10¹³ Ω m
• paraffin oil: 1×10¹⁶ Ω m
• paraffin wax (pure) : 1×10¹⁶ Ω m
• plexiglass: 1×10¹³ Ω m
• polystyrene: 1×10¹⁴ Ω m
• porcelain: 1×10¹² Ω m
• pressed amber: 1×10¹⁶ Ω m
• vulcanite: 1×10¹⁴ Ω m
• water, distilled: 1×10¹⁰ 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 = (1.7×10^-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 mm ². The increase in resistance can be calculated to

R = (1.7×10^-8 Ω m) (10 m) / ((0.205 mm²)(10^-6 m²/mm²))

= 0.83 Ω

Convert between Electrical Resistivity Units

• 1 Ω m = 0.001 kΩ m = 10² Ω cm = 39.37 Ω inch = 3.28 Ω foot

Resistivity Compared to Copper

• Aluminum (pure): 1.6
• Brass: 3.7-4.9
• Cadmium: 4.4
• Chromium: 1.8
• Copper (hard-drawn): 1.03
• Copper (annealed): 1.00
• Gold: 1.4
• iron (pure): 5.68
• Lead: 12.8
• Nickel: 5.1
• Phosphor Bronze: 2.8-5.4
• Silver: 0.94
• Steel: 7.6-12.7
• Tin: 6.7
• Zinc: 3.4