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This page is all about:What is Conductance?Definition of Electrical ConductanceEquation or Formula of Electrical ConductanceSpecific Conductance or ConductivityDefinition of Electrical ConductivityUnit of ConductanceUnit of ConductivityBand Theory for Electrical ConductivityValance BandConduction BandBand GapElectrical Conductivity of Metal

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Table for Conductivity of Different MetalsElectrical Conductivity of SemiconductorTable for Conductivity of Different SemiconductorsElectrical Conductivity of InsulatorTable for Conductivity of Different Insulators

What is Conductance?

When we apply same potential difference across different conductors, we will see different currentsflow through them. Actually how much current will flow through a specific conductor for certainapplied potential difference across it, depends upon a specific property of the conductor, calledelectrical conductance . This property determines how easily a current can flow through a conductor.

As we know resistance is such a property of a conductor which resists the flow of current through it.That means, electrical conductance is reciprocal property of resistance. Generally conductance isdenoted as,

Definition of Electrical Conductance

Electrical conductance is defined as a special property of a conductor which determines how easilyan current can flow through it.

Equation or Formula of Electrical Conductance

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Let us take a piece of conductor of length l and cross sectional area A. If length of the conductor isincreased, the electrons have to drift more paths. Hence more chance of inter atomic collision. Thatmeans current gets much harder path to travel, means electrical conductance of the conductor isreduced.

Thus conductance is inversely proportional to length of the conductor.

If cross sectional area of conductor is increased then current gets more drift electrons. Hence,conductance of the conductor is increased.

From equation (1) & (2),

Where, σ = constant of proportional known as conductivity or specific conductance .

Specific Conductance or Conductivity

In the equation of the conductance we have already mentioned the term σ or Sigma as conductivity.Now in that equation if we put l = 1 m & A = 1 m then G = σ. That indicates σ is the conductance of aconductor whose length is 1 m & cross sectional area is 1 m . That mean specific conductance orconductivity is the conductance of a conductor whose volume is 1 m × 1 m = 1 m .

2

2

2 3

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Definition of Electrical Conductivity

Conductivity is the conductance of a material per unit volume.Electrical conductivity is a basic property of material. Due to this property one material can conductelectricity. Some materials are good conductor of electricity that means current can pass throughthem very easily; again some materials do not allow current to flow through them. The materialthrough which current passes easily, called good conductor of electricity in other words, theelectrical conductivity of these materials is high. On the other hand the materials do not allow thecurrent to flow through them are called electrical insulators. There are some materials whoseelectrical conductivity is not as high as conductor and also not as poor as insulator, they have anintermediate conductivity and these type of materials are known as semiconductors.

Unit of Conductance

As we mentioned earlier conductance is reciprocal of resistance of resistance. That is,

Unit of resistance is ohm & that is why unit of conductance is generally written as mho – the reversespelling of ohm. A modern electrical engineering, mho is named by Siemens.

Unit of Conductivity

The equation of conductivity, we have already deducted as,

Hence, unit of conductivity is,

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Here, S is Siemens.

Table of Resistivity and Conductivity of DifferentMaterials at 20°C

MATERIAL RESISTIVITY AT 20°C CONDUCTIVITY 20°C

Air 1.3 × 10 to 3.3 × 10 3 × 10 to 8 × 10

Aluminum 2.82 × 10 3.5 × 10

Annealed copper 1.72 × 10 5.80 × 10

Calcium 3.36 × 10 2.98 × 10

Carbon (amorphous) 5 × 10 to 8 × 10 1.25 to 2 × 10

Carbon (diamond) 1 × 10 ~10

Carbon (graphite) 2.5 × 10 to 5.0 × 10 //basal plane 2 to 3 × 10 //basal plane

Carbon steel -10 1.43 × 10-7

Constantan 4.9 × 10 2.04 × 10

Copper 1.68 × 10 5.96 × 10

Deionized water 1.8 × 10 5.5 × 10

Drinking water 2 × 10 to 2 × 10 5 × 10 to 5 × 10

Fused quartz 7.5 × 10 1.3 × 10

GaAs 5 × 10 to 10 × 10 5 × 10 to 10

Germanium 4.6 × 10 2.17

16 16 -15 -15

-8 7

-8 7

-8 7

-4 -4 3

12 -13

-6 -6 5

10

-7 6

-8 7

5 -6

1 3 -4 -2

17 -18

-7 -3 -8 3

-1

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Glass 10 × 10 to 10 × 10 10 to 10

Gold 2.44 × 10 4.10 × 10

Grain oriented electrical steel 4.60 × 10 2.17 × 10

Hard rubber 1 × 10 10

Iron 1.0 × 10 1.00 × 10

Lead 2.2 × 10 4.55 × 10

Lithium 9.28 × 10 1.08 × 10

Manganin 4.82 × 10 2.07 × 10

Mercury 9.8 × 10 1.02 × 10

Nichrome 1.10 × 10 9.09 × 10

Nickel 6.99 × 10 1.43 × 10

Paraffin wax 1 × 10 10

PET 10 × 10 10

Platinum 1.06 × 10 9.43 × 10

Sea water 2 × 10 4.8

Silicon 6.40 × 10 1.56 × 10

Silver 1.59 × 10 6.30 × 10

Stainless steel 6.9 × 10 1.45 × 10

Sulfur 1 × 10 10

Teflon 10 × 10 to 10 × 10 10 to 10

Tin 1.09 × 10 9.17 × 10

Titanium 4.20 × 10 2.38 × 10

10 14 -11 -15

-8 7

-7 6

13 -14

-7 7

-7 6

-8 7

-7 6

-7 6

-6 5

-8 7

17 -18

20 -21

-7 6

-1

2 -3

-8 7

-7 6

15 -16

22 24 -25 -23

-7 6

-7 6

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Tungsten 5.60 × 10 1.79 × 10

Wood (damp) 1 × 10 to 4 10 to 10

Wood (oven dry) 1 × 10 to 16 10 to 10

Zinc 5.90 × 10 1.69 × 10

Band Theory for Electrical Conductivity

The electrons in the outer most orbit of an atom experiences least attraction force. So the outermostatom can easily be detached from the parent atom. Let’s explain the details with band theory

When a number of atoms are brought together, the electrons of one atom experience forces of otheratoms. This effect is most pronounced in outer most orbits. Due to this force, the energy levels, whichwere sharply defined in an isolated atom, are now broadened into energy bands. Due to thisphenomenon generally two bands result, namely valance band and conduction band.

Valance Band

The outermost orbital of an atom, where electrons are so tightly bounded that; they cannot beremoved as free electron

Conduction Band

-8 7

3 -4 -3

14 -16 -14

-8 7

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This is the highest energy level or orbital in outer most shell, in which electrons are free enough tomove.

Band Gap

There is one energy gap that separates these two bands, the valance band and conduction band. Thisgap is called forbidden energy gap.

Electrical Conductivity of Metal

In metals, the atoms are so tightly packed that electron of one atom experience sufficientlysignificant force of other closed atoms. The result, the valance band and conduction band in metalscome very closer to each other and may even overlap. Consequently, by receiving very small amountof energy from external heat or electrical energy source, the electrons readily ascend to higher levelsin the metal. Such electrons are known as free electrons. These free electrons are responsible forcurrent that flows through a metal. When external electric source is connected to a piece of metal,these free electrons start flowing towards higher potential terminal of the source, causing current toflow in the metal. In metal, density of free electrons in conduction band is much higher than othermaterials, hence metal is referred as very good electrical conductor. In other words electricalconductivity of metal is very good.

Table for Conductivity of Different Metals

METALS CONDUCTIVITY IN SIEMENS/METER AT 20°C

Silver 6.30×10 7

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Copper 5.96X10

Aluminium 3.5X10

Annealed copper 5.80X10

Calcium 2.98X10

Carbon steel (1010) 6.99X10

Constantan 2.04X10

GaAs 5X10 to 10

Gold 4.10X10

Grain oriented electrical steel 2.17X10

Iron 1.00X10

Lead 4.55X10

Lithium 1.08X10

Manganin 2.07X10

Mercury 1.02X10

Nichrome 9.09X10

Nickel 1.43X10

Platinum 9.43X10

Stainless steel 1.45X10

Tin 9.17X10

Titanium 2.38X10

Tungsten 1.79X10

Zinc 1.69X10

7

7

7

7

6

6

−8 3

7

6

7

6

7

6

6

5

7

6

6

6

6

7

7

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Electrical Conductivity of Semiconductor

In semiconductor the valance band and conduction band are separated by a forbidden gap ofsufficient width. At low temperature, no electron possesses sufficient energy to occupy theconduction band and thus no movement of charge is possible. But at room temperature it is possiblefor some electrons to give sufficient energy and make the transitions in conduction band. The densityof electrons in conduction band at room temperature is not as high as in metals, thus cannot conductcurrent as good as metal. The electrical conductivity of semiconductor is not as high as metal butalso not as poor as electrical insulator. That is why, this type of material is called semiconductor –means half conductor.

Table for Conductivity of Different Semiconductors

SEMICONDUCTOR CONDUCTIVITY IN SIEMENS/METER AT 20°C

Germanium 2.17

Silicon 1.56X10

Electrical Conductivity of Insulator

Ideally electrical conductivity of an electrical insulator is nil. The atoms in the insulator molecules areelectrically stable enough. The outer most shells of these atoms are completely filled with electrons.In such material where forbidden gap is very large and as a result the energy required by the electronto cross over to the conduction band is practically large enough. Insulators do not conduct electricityeasily. That means the electrical conductivity of insulator is very poor.

Table for Conductivity of Different Insulators

INSULATOR CONDUCTIVITY IN SIEMENS PER METER AT 20°C

Air 3X10 to 8×10

Fused quartz 1.3X10

Glass 10 to 10

Hard rubber 10

Paraffin wax 10

− 3

−15 −15

−18

−11 −15

− 14

−18

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PET 10

Sulfur 10

Teflon 10 to 10

Wood 10 to 10

Objective Questions on Resistance (MCQs)

What is electrical conductance?What is electrical conductivity or specific conductance of a conductor?What is electric conductor?

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−16

−25 −23

− 16 -14