Resistivity of Materials

Resistance to essentials is as important as making the materials to be used in the right places in the electrical and electronic components.

Items used as conductors, for example in a standard electrical outlet need to be able to have a low resistance level. This means that in a given cross-sectional area, the resistance of the fence will be lesser. Choosing the right material depends on knowing its properties, one of which is its resistivity.

For example, copper is a good conductor as it offers a low level of resistance, its cost is not very high, and it also provides other physical features that are useful in many electrical and electronic functions. 

Copper is often the most preferred material. Material like copper and aluminum imparts low resistance levels which makes them suitable for the use of power cords and cables. Silver and gold have very low resistivity, but as they are very expensive, they are not widely used. However, silver is sometimes used to refine wires where its low resistance is important, and gold light is used in the joints of many electronic connectors to ensure advanced contacts. Gold is also good for electrical connectors as it does not contaminate or emit oxygen like other metals.

What is Resistivity?

Resistivity is the measure of how much an electrical conductor opposes the flow of current through it.

Resistance has an application in protecting the circuit from high current flow.

When a potential difference (acceleration) is applied across the conductor (to car), the electrons start moving from the negative to the positive electrode).

The current flow increases, the resistance acts as a speed breaker to the accelerated car (high current flow).

The magnitude of the resistance is called resistivity.

Hence it is the magnitude of the resistance of a given size of a specific material or a conductor to electrical conduction.

Resistivity Formula

The resistivity of a material is defined in terms of the measurement of the electric field (E) across it that generates current density (J). 

The formula for resistivity is given by,          

Where ρ is the proportionality constant known as the resistivity of the material which  is the characteristic property of each material.

A = Area of cross-section

L = Length of the material of a conductor

Derive Resistivity

The resistivity of a material depends upon the following factors:

1. Length

Consider two conductors each of length ‘L’ and the area of cross-section ‘A’

Let V be the same potential difference applied across the ends of two slabs. 

The current ‘I’  flowing across each slab will be I/2. 

Then resistance via each slab is,

R = V/I (Ohm’s law)

Rs = V/ I/2 = 2 R

So, R increases with the increase in length 

R α L …(1)

2. Area of Cross-section 

Each slab of length ‘L’ has a cross-sectional area of A/2.

Similarly, on halving the area of the conductor, the resistance through each of the half slabs will be

R’  =   V/ I/2 = 2 R

R increases with the decrease in the area of each half slab.

R α 1/A…(2)

Combining (1) and (2) we get

R   α L/A    

Removing the proportionality sign we get 

Here, ρ is called the electrical resistivity or specific resistance of the material.

Resistivity Definition

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The formula for the resistivity is given by,

R = ρ L/A…(a)

If L =1, A =1, then  R = ρ 

Thus, the electrical resistivity of a material of a conductor is defined as the resistance offered by the unit length and unit cross-sectional area of a wire of the given material.

Unit of Resistivity

The unit of resistivity is derived from eq(a)

If  R = ρ L/A

Then ρ = R.A/L ….(b)

Given unit of R = Ohm (\[(\Omega)\]),  A = m² and L = m 

Putting in eq(b)  we get

Define Resistivity of a Material

The resistivity is an attribute of each material that is useful in comparing various materials on the basis of their ability to conduct electric currents. 

Let’s Discuss the Resistivity of Some Materials is Discussed Below:

Relation Between Conductivity and Resistivity 

The relation between conductivity and resistivity can be understood through an example.

You water a lot to the plants during the summer seasons.

If you just sprinkle a few drops of water and won’t supply enough water, after some time, they will get dried and hence die.

Therefore, the more is the resistance to a sufficient supply of water to the plants, the lesser will be their growth (conductivity).

Therefore, high resistivity signifies poor conductors.

Resistivity is symbolized by the Greek letter  ‘ρ’ pronounced as ‘rho’ and the conductivity as σ.

So,  σ =  1/ ρ  or ρ = 1/ σ

Since conductivity is the inverse of resistivity.

Therefore, its unit is mho .m-1\[\Omega\] m^-1

Another Unit:  Siemens per meter S m¹⁷

On What Does Resistivity Depend?

The amount of resistivity also depends on the temperature of the asset; opposing material tables usually set values ​​at 20 ° C. Resistance to steel conductors usually increases with increasing temperature; but resistance to semiconductors, such as carbon and silicon, usually decreases with increasing temperature.

Conductivity is a reciprocal of resistivity, and, again, reflects things on the basis of how well electricity flows through them. The second-kilometer unit of conductivity is mho meter or ampere per volt-meter. There is high conductivity and low resistance in good electrical conductors. Fine insulators, or dielectrics, have high resistivity and low conductivity. Semiconductors have values ​​between both.

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