Resistance and Resistivity of a Conductor

The German physicist George Simon Ohm made significant contributions to the study of electricity by formulating a law that describes the relationship between current, voltage, and resistance in a conductor. This law, now known as Ohm's Law, provided a way to measure the resistance of a conductor and established its importance in understanding electric circuits.

• In recognition of his groundbreaking work, the unit of electrical resistance was named the Ohm, symbolised by the Greek letter Ω.
• Resistance is a measure of how much a conductor opposes the flow of electric current, and it plays a critical role in designing and analysing electrical and electronic systems.
• Ohm's contributions laid the foundation for modern electrical engineering and technology.

George Simon Ohm

A conductor contains a large number of free electrons. These electrons are constantly in random motion within the conductor. 

Motion of free electrons

Effect of Potential Difference:

• When there is no potential difference, the random motion of electrons does not result in a net flow of charge, hence no current.
• When a potential difference is applied between the two ends of the conductor, the free electrons move directionally from the lower potential end to the higher potential end.
• The directional movement of electrons due to the applied potential difference causes an electric current to flow through the conductor.

Collisions and Hindrance:

As the electrons move through the conductor, they collide with the atoms and ions present in the material. These collisions create a hindrance to the motion of electrons, which slows down the flow of current.

Resistance:

The hindrance caused by collisions is called the resistance of the conductor. Resistance is an essential property in electric circuits, as it controls the amount of current that flows for a given potential difference. Resistance opposes the flow of electric current and depends on factors such as:

• The material of the conductor.
• The length and thickness of the conductor.
• The temperature of the conductor.

Resistivity:

At a given temperature, the resistance ($R$) of a conductor depends on its length (L), area of cross-section (A) and the material it is made of.

If the resistance of a conductor is R, then
R ∝ L

Also, R ∝ `"1"/"A"`

R ∝ `"L"/"A"`

R = ρ `"L"/"A"`

ρ  is the constant of proportionality and is called the resistivity of the material. The unit of resistivity in SI units is Ohm metre (Ωm). Resistivity is a specific property of a material and different materials have different resistivity.

Resistivity of some materials
Copper - 1.7 × 10⁻⁸ Ωm
Nichrome - 1.1 × 10⁻⁶  Ωm
Diamond - 1.62 × 1013 to 1.62 × 1018 Ωm