- Definition of Electrical Conductance: Electrical conductance is defined as a property that measures how easily electric current flows through a conductor.
- Definition of Electrical Conductivity: Conductivity is defined as a material’s ability to conduct electric current, determined by its specific properties.
- Band Theory Explanation: Band theory of conductors, semiconductors, and insulators explains how the arrangement of energy bands affects electrical conductivity.
- Metals: Metals have high conductivity due to overlapping valence and conduction bands, allowing free electron movement.
- Semiconductors and Insulators: Semiconductors have moderate conductivity with a small band gap, while insulators have poor conductivity due to a large band gap.
What is Conductance?
Electrical conductance says how easily a current can flow through a conductor for a given potential difference, while resistance is the opposite property and limits that current. Conductance is the reciprocal of resistance. Conductance is written as,
Definition of Electrical Conductance
Electrical conductance is the property of a conductor that says how easily current can flow through it.
Equation or Formula of Electrical Conductance
Take a conductor of length l and cross-sectional area A. If the length increases, electrons travel farther and meet more collisions. The current then has a harder path, so the electrical conductance of the conductor falls.
Conductance is therefore inversely proportional to the length of the conductor.
If the cross-sectional area increases, more electrons can drift through the section and conductance rises.
From equation (1) and (2),
Where σ is the constant of proportionality known as conductivity or specific conductance.
Specific Conductance or Conductivity
In that conductance equation, σ (sigma) is conductivity. If l = 1 m and A = 1 m2, then G = σ. So σ is the conductance of a conductor 1 m long with a 1 m2 cross-section. Specific conductance, or conductivity, is therefore the conductance of a 1 m × 1 m2 = 1 m3 sample of the material.
Definition of Electrical Conductivity
Conductivity is a material property per unit volume.
Electrical conductivity is the material property that lets charge move through a sample. Materials with high conductivity pass current readily and are called good conductors. Materials that block current are called electrical insulators. Materials whose conductivity sits between those two groups are semiconductors.
Unit of Conductance
G equals 1/R, so conductance is the reciprocal of resistance:
The unit of resistance is the ohm, so the older unit of conductance was written as mho, ohm spelled backward. In modern electrical engineering the mho is replaced by the Siemens.
Unit of Conductivity
The conductivity equation derived above is,
The unit of conductivity is therefore,
Here, S is Siemens.
Table of Resistivity and Conductivity of Different Materials at 20oC
| Material | Resistivity at 20oC | Conductivity 20oC |
| Air | 1.3 × 1016 to 3.3 × 1016 | 3 × 10-15 to 8 × 10-15 |
| Aluminum | 2.82 × 10-8 | 3.5 × 107 |
| Annealed copper | 1.72 × 10-8 | 5.80 × 107 |
| Calcium | 3.36 × 10-8 | 2.98 × 107 |
| Carbon (amorphous) | 5 × 10-4 to 8 × 10-4 | 1.25 to 2 × 103 |
| Carbon (diamond) | 1 × 1012 | ~10-13 |
| Carbon (graphite) | 2.5 × 10-6 to 5.0 × 10-6 //basal plane | 2 to 3 × 105 //basal plane |
| Carbon steel | -1010 | 1.43 × 10-7 |
| Constantan | 4.9 × 10-7 | 2.04 × 106 |
| Copper | 1.68 × 10-8 | 5.96 × 107 |
| Deionized water | 1.8 × 105 | 5.5 × 10-6 |
| Drinking water | 2 × 101 to 2 × 103 | 5 × 10-4 to 5 × 10-2 |
| Fused quartz | 7.5 × 1017 | 1.3 × 10-18 |
| GaAs | 5 × 10-7 to 10 × 10-3 | 5 × 10-8 to 103 |
| Germanium | 4.6 × 10-1 | 2.17 |
| Glass | 10 × 1010 to 10 × 1014 | 10-11 to 10-15 |
| Gold | 2.44 × 10-8 | 4.10 × 107 |
| Grain oriented electrical steel | 4.60 × 10-7 | 2.17 × 106 |
| Hard rubber | 1 × 1013 | 10-14 |
| Iron | 1.0 × 10-7 | 1.00 × 107 |
| Lead | 2.2 × 10-7 | 4.55 × 106 |
| Lithium | 9.28 × 10-8 | 1.08 × 107 |
| Manganin | 4.82 × 10-7 | 2.07 × 106 |
| Mercury | 9.8 × 10-7 | 1.02 × 106 |
| Nichrome | 1.10 × 10-6 | 9.09 × 105 |
| Nickel | 6.99 × 10-8 | 1.43 × 107 |
| Paraffin wax | 1 × 1017 | 10-18 |
| PET | 10 × 1020 | 10-21 |
| Platinum | 1.06 × 10-7 | 9.43 × 106 |
| Sea water | 2 × 10-1 | 4.8 |
| Silicon | 6.40 × 102 | 1.56 × 10-3 |
| Silver | 1.59 × 10-8 | 6.30 × 107 |
| Stainless steel | 6.9 × 10-7 | 1.45 × 106 |
| Sulfur | 1 × 1015 | 10-16 |
| Teflon | 10 × 1022 to 10 × 1024 | 10-25 to 10-23 |
| Tin | 1.09 × 10-7 | 9.17 × 106 |
| Titanium | 4.20 × 10-7 | 2.38 × 106 |
| Tungsten | 5.60 × 10-8 | 1.79 × 107 |
| Wood (damp) | 1 × 103 to 4 | 10-4 to 10-3 |
| Wood (oven dry) | 1 × 1014 to 16 | 10-16 to 10-14 |
| Zinc | 5.90 × 10-8 | 1.69 × 107 |
Band Theory for Electrical Conductivity
Electrons in the outermost orbit of an atom feel the weakest attraction, so they are the ones that can leave the parent atom. Band theory describes what happens next.
When many atoms sit close together, the electrons of one atom feel the forces of neighbouring atoms. That effect is strongest in the outer orbits. Energy levels that were sharp in an isolated atom spread into energy bands. Two of those bands matter here: the valence band and the conduction band.
Valance Band
The outermost filled band of an atom, where electrons are bound tightly enough that they are not free to carry current.
Conduction Band
This is the higher-energy band in which electrons are free enough to move and carry current.
Band Gap
An energy gap separates the valence band from the conduction band. That gap is the forbidden energy gap.
Electrical Conductivity of Metal
In metals, tightly packed atoms put nearby forces on the electrons, so the valence and conduction bands sit close together or overlap. A small energy input from heat or an applied field then lets electrons occupy higher levels and move as free electrons. Those free electrons flow toward the positive terminal when a source is connected, and that flow is the current. Metals have a high density of free electrons, so they have high electrical conductivity.
Table for Conductivity of Different Metals
| Metals | Conductivity in Siemens/meter at 20oC |
| Silver | 6.30 × 107 |
| Copper | 5.96 × 107 |
| Aluminium | 3.5 × 107 |
| Annealed copper | 5.80 × 107 |
| Calcium | 2.98 × 107 |
| Carbon steel (1010) | 6.99×106 |
| Constantan | 2.04 ×106 |
| GaAs | 5 × 10−8 to 103 |
| Gold | 4.10 × 107 |
| Grain oriented electrical steel | 2.17×106 |
| Iron | 1.00×107 |
| Lead | 4.55 × 106 |
| Lithium | 1.08 × 107 |
| Manganin | 2.07 × 106 |
| Mercury | 1.02 × 106 |
| Nichrome | 9.09 × 105 |
| Nickel | 1.43 × 107 |
| Platinum | 9.43 × 106 |
| Stainless steel | 1.45 × 106 |
| Tin | 9.17 × 106 |
| Titanium | 2.38 × 106 |
| Tungsten | 1.79 × 107 |
| Zinc | 1.69 × 107 |
Electrical Conductivity of Semiconductor
In a semiconductor the valence band and the conduction band are separated by a forbidden gap of useful width. At low temperature almost no electron has enough energy to enter the conduction band, so little charge can move. At room temperature some electrons do gain that energy and make the transition. The conduction-band electron density is still far below that of a metal, so the material conducts less well than a metal. The electrical conductivity of semiconductor sits between a metal and an insulator. That middle range is why the material is called a semiconductor.
Table for Conductivity of Different Semiconductors
| Semiconductor | Conductivity in Siemens/meter at 20oC |
| Germanium | 2.17 |
| Silicon | 1.56 × 10− 3 |
Electrical Conductivity of Insulator
The ideal electrical conductivity of an insulator is zero. The atoms in an insulator are electrically stable, with filled outer shells. The forbidden gap is large, so an electron needs a large energy to reach the conduction band. Insulators therefore do not conduct electricity readily. The electrical conductivity of insulator materials is very low.
Table for Conductivity of Different Insulators
| Insulator | Conductivity in Siemens per meter at 20oC |
| Air | 3 × 10-15to 8 × 10−15 |
| Fused quartz | 1.3 × 10-18 |
| Glass | 10-11 to 10-15 |
| Hard rubber | 10-14 |
| Paraffin wax | 10-18 |
| PET | 10-21 |
| Sulfur | 10-16 |
| Teflon | 10-25 to 10-23 |
| Wood | 10-16 to 10 -14 |
