Electrical Resistivity

Introduction

When a potential difference is introduced across a material, electrons begin to move from the negative electrode to the positive electrodes, causing current to flow through the material. However, when electrons travel, they collide with other electrons along their route. The movement of electrons is obstructed by these collisions. This is defined as the resistance of the material. The material’s resistivity is beneficial in electrical circuits. The resistance value of a material is affected by a combination of factors. The value of a material’s specific resistance provides us an idea of its resistive capacity.

Electrical Resistivity

At a given temperature, a material’s electrical resistivity is defined as its resistance per unit length and per unit cross-sectional area.

Resistivity, often known as electric resistivity, is opposite of the electrical conductivity or we can say inverse of electrical conductivity. 

A material’s resistivity is a fundamental characteristic that indicates how well it resists or conducts electric current.

Conductors are materials that easily carry electrical current and have a low resistance. Insulators are materials that are difficult to conduct electricity and have a high resistance.

The resistivity of different materials is important for choosing materials for electrical wiring, as well as resistors, integrated circuits, and other electronic components.

The value of resistivity is also affected by the temperature of the material; resistivity tables typically provide values at 20° C. Metallic conductors’ resistivity increases as temperature rises, but semiconductor’s resistivity, such as carbon and silicon, decreases as temperature goes up.

Resistivity Formula 

Derivation

The resistance R is obviously proportional to the conductor’s length. That is, resistance rises as the length of the conductor increases.

Therefore, resistance R ∝ L    ——–    eq 1

R is inversely related to the cross-sectional area of a given conductor. 

That means when the area of the conductor increases, Resistivity decreases. 

That means when the area of the conductor increases, Resistivity decreases.  More conductor area results in a more efficient flow of electric current via a larger area, results in lowering of resistance.

Hence, R ∝ 1/A       ———-    eq  2

From eq 1 and eq 2

R ∝ L/A

Or, R = ρ L/A       eq  3

From eq 3 

ρ = RA/L

ρ (rho) is the resistivity of the  material.

Equation

From derivation we got the equation of resistivity that is

ρ = RA/L

Where, ρ = resistivity, R =Resistance , A = Area of cross sectional, L = Length

Resistivity Unit

ρ = RA/L

ρ = ohm × (m2/m ) = ohm m

The S.I unit of resistivity is Ohm meter (Ω⋅m)

Classification of resistivity in Materials

The temperature has a big impact on these materials. When the temperature of a conductor rises, the speed of electrons travelling through the materials rises as well. This results in numerous collisions. As a result, the average time of collision of the electrons decreases. Material has an inverse relationship with the average time of electron collision. As a result, as the average time of the collision decreases, the conductor’s resistivity value increases.

When the temperature of a semiconductor material rises, more covalent bonds are broken. The number of free charge carriers in the material grows as a result. With a rise in charge carriers, the substance’s conductivity increases, lowering the resistance of the semiconductor material.

It helps in the comparison of different materials based on their capacity to conduct electricity. It is the inverse of conductivity. Conductors have a high conductivity and a low resistance. Insulators have a high resistance and a low conductivity. The resistivity and conductivity values for semiconductors are in the middle.

Resistor Colour-Coding

Colours are used to distinguish the value and function of components and cables.

Resistor colour coding uses coloured bands to instantly identify a resistor’s resistive value and tolerance percentage, with the resistor’s physical size indicating its wattage rating.

When the resistor’s body is large enough to see the print, such as large power resistors, the resistance value, tolerance, and wattage rating are usually displayed as numbers or letters on the resistor’s body.

However, because the print on a smaller resistor is too small to see, the specifications must be shown in another method.

Conclusion

Electrical resistivity is a critical property for materials used in electrical and electronic systems. Insulators are substances that have a high electrical resistance and can be utilized for this purpose. Anything can be an excellent conductor with a low degree of electrical resistance and may be used in a variety of applications ranging from wire to electrical connections and much more. Moreover various resistors are used in almost every kind of electrical appliances and we can determine them uniquely using colour codes. Hope this resistivity topic is clear to you.