Conductance, Resistivity and Specific resistance

Conductance, resistivity and specific resistance are the properties of electric conductor or any other material. They all can be understood by resistance. Resistance is the amount of obstruction in the flow of current. Means resistance is the obstruction in flow of electrons. All these properties of material can be understood by resistance and also all these properties are dependent on value of resistance of that material.

Conductance

Conductance is an expression of the ease with which electric current flows through a material. Thus, conductance is a measure of how easy it is for electrons to flow through a material. As you all know resistance is the obstruction in the flow of electrons. So mathematically, conductance is the reciprocal of resistance.

Conductance = 1 / Resistance

The greater will be the resistance, the less the conductance and smaller will be the resistance, greater would be the conductance. If the resistance of material A is half than material B. Then, material A have double conductance than material B.

The symbol of conductance is capital “G” and the unit is 1 / ohm or  and it is more popularly known as mho which is ohm spelled backwards. Some years ago, mho was also replaced by a new unit Siemens.

Now if we want to find the conductance of series and parallel combination of resistors, it’s a quite easy job now.

For parallel combination of resistors,

1/R = 1/R1 + 1/R2 + 1/R3

And you know that G = 1/R. So, the total conductance would be

G = G1 + G2 + G3

Thus, total conductance of resistors in parallel combination can be expressed as addition of conductance of each individual resistor.

For series combination of resistors,

R = R1 +R2 + R3 

And you know that G = 1/R and so R = 1/G.

1/G = 1/G1 +1/G2 + 1/G3

Therefore in series combination, reciprocal of total conductance is the addition of reciprocal of the entire individual conductance.

Resistivity

Resistivity is a measure of the resistance of a given size of a specific material to electrical conduction. Resistivity is the measure of how strongly a material opposes the flow of electric current. Resistivity is also reciprocal of conductance. More will be the resistivity, less amount of current will pass through the conductor and thus amount of conductance would be less and less the resistivity, more amount of current will pass through the conductor and conductance would be more.

SI unit of resistivity is ohm meter. It is represented by symbol ρ.

Materials that conduct electrical current easily are called conductors and they have low resistivity. Those that do not conduct electric current are said to be insulators and they have high resistivity.

Formula of resistivity:

As you all know the law of resistance, R = ρ l/a where ρ is the resistivity. So we can derive the formula of resistivity

Ρ = R a/l

Thus resistivity is directly proportional to cross sectional area of the material and inversely proportional to length of the material.

Ρ α a/l

Thus resistivity is same as resistance but it is the measure of resistance. Also the formula and dependency of resistivity are different than resistance. Resistance is directly dependent on length and inversely proportional to area but resistivity is directly dependent on cross sectional are and inversely proportional to length of the material.

Specific resistance

Resistance of the conductor is directly proportional to length of the material and inversely proportional to the cross sectional area of the material.

R α l/a

So if the length of the material increases, the value of resistance also increases and if the area is decreased, the value of resistance increases. Thus value of resistance will change if there are changes in length and cross sectional area of the material. Specific resistance is a constant type of resistance being calculated for material at specific length area. Value of specific resistance of any material never changes.

Symbol of specific resistance is same as resistivity and that is ρ. And also the SI unit of specific resistance is ohm – meters which is same as the unit of resistivity. Also mathematically specific resistance is given by the formula

ρ = R a/l

SPECIFIC RESISTANCE AT 20 DEGREES CELSIUS

Material     Element/Alloy       (ohm-cmil/ft)    (microohm-cm) 

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Nichrome ------ Alloy --------------- 675 ----------- 112.2

Nichrome V ---- Alloy --------------- 650 ----------- 108.1

Manganin ------ Alloy --------------- 290 ----------- 48.21

Constantan ---- Alloy --------------- 272.97 -------- 45.38

Steel* -------- Alloy --------------- 100 ----------- 16.62

Platinum ----- Element -------------- 63.16 --------- 10.5 

Iron --------- Element -------------- 57.81 --------- 9.61 

Nickel ------- Element -------------- 41.69 --------- 6.93 

Zinc --------- Element -------------- 35.49 --------- 5.90 

Molybdenum — Element -------------- 32.12 --------- 5.34 

Tungsten ----- Element -------------- 31.76 --------- 5.28 

Aluminum ----- Element -------------- 15.94 --------- 2.650

Gold --------- Element -------------- 13.32 --------- 2.214

Copper ------- Element -------------- 10.09 --------- 1.678

Silver ------- Element -------------- 9.546 --------- 1.587

The specific resistances of some materials are given in table above. They are all calculated at 20 degree Celsius. And they are represented with unit of ohms – cmil/ft. However SI unit for specific resistance is ohm-meter (Ω-m) with 1.66243 ×  Ω - meters per Ω - cmil/ft. Values of specific resistance of any material is usually scaled at µ Ω - cm.

All these are electric properties of conductor which are very essential to figure out the right material for any particular application. If we want a material for application where resistance of that material should be maximum. So we need to choose a material whose conductance is less, resistivity is high and also the amount of specific resistance is greater than any other. Thus these properties are important to notice while choosing the right material.