Specific Resistance and Conductance

Material properties that determine how easily electricity flows through a conductor

Overview

Different materials have different electrical properties. Specific resistance (also called resistivity) describes the resistance of a standardized piece of material: a wire that is 1 meter long and has a cross-section of 1 mm².

Key Insight:

Materials with the same length and cross-section have different resistances. This difference is due to their specific resistance property, which depends on the material composition, not its size.

Specific Resistance (Resistivity)

Specific resistance (symbol: \(\rho\) rho) refers to the resistance of a conductor with:

  • Length: 1 meter
  • Cross-section: 1 mm²
  • At a specified temperature (usually 20°C)
Definition:

Specific resistance is a material property that indicates how strongly the material opposes the flow of electric current. It is independent of the wire's length or cross-section.

Wires of the same material, same length, and same cross-section have identical resistance at the same temperature.

Electrical Conductance (Conductivity)

The reciprocal of specific resistance is the electrical conductance or conductivity (symbol: \(\sigma\) sigma).

Definition:

Conductance indicates how easily a material conducts electricity. A material with high conductivity has low resistivity.

Relationship Between Resistivity and Conductivity

\(\displaystyle \sigma = \frac{1}{\rho}\)     and     \(\displaystyle \rho = \frac{1}{\sigma}\)

Calculate Resistance from Material Properties

The resistance of a wire depends on three factors: the material (resistivity), length, and cross-section.

Resistance is Proportional to Length

Doubling the wire length doubles the resistance:

\(\displaystyle R \propto l\)

Resistance is Inversely Proportional to Cross-Section

Doubling the cross-section halves the resistance:

\(\displaystyle R \propto \frac{1}{A}\)

Complete Formula Using Resistivity

\(\displaystyle R = \frac{\rho \cdot l}{A}\)
Formula symbols
  • \(R\) = resistance in Ω (ohms)
  • \(\rho\) = specific resistance (resistivity)
  • \(l\) = length in meters
  • \(A\) = cross-section in mm²

Formula Using Conductivity

\(\displaystyle R = \frac{l}{\sigma \cdot A}\)

Conductive Materials Reference Table

This table shows the specific resistance (ρ) and conductivity (σ) of common conductive materials at 20°C:

Material Resistivity ρ (Ω·mm²/m) Conductivity σ (m/(Ω·mm²))
Silver 0.016 62.5
Copper 0.018 56
Gold 0.023 44
Aluminum 0.029 35
Magnesium 0.045 22
Tungsten 0.055 18
Zinc 0.063 16
Nickel 0.08 ... 0.11 13 ... 9
Iron 0.10 ... 0.15 10 ... 7
Tin 0.11 9
Platinum 0.11 ... 0.14 9 ... 7
Lead 0.21 4.8
Mercury 0.96 1.04
Bismuth 1.2 0.83
Carbon 100 0.01

Insulating Materials Reference Table

Insulating materials have extremely high resistivity values (at 20°C):

Material Resistivity ρ (Ω·m)
Amber 1018
Glass 1014
Mica 1014 ... 1017
Rubber 1015
Hard Rubber 1012 ... 1018
Ceramics 1012
Resin 108 ... 1014
Marble 109 ... 1011
Paraffin 1016
Polystyrene 1018
Pressboard 1010
Porcelain 1014
Shellac 1016

Key Points

  • Specific resistance (ρ) is a material property independent of size
  • Conductivity (σ) is the reciprocal of resistivity
  • Resistance of a wire: \(R = \frac{\rho \cdot l}{A}\)
  • Silver and copper are the best electrical conductors
  • Resistance increases with length and decreases with cross-section
  • Insulating materials have resistivity values > 10¹⁰ Ω·m
  • Material selection depends on application requirements


Resistor and Conductance
Ohm`s Law
Specific Resistance
Voltage Drop
Power


















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