What is resistivity & how is it depends on temperature?

Resistivity, often denoted by the Greek letter ρ (rho), is a fundamental property of materials that quantifies how strongly they resist or conduct electric current. It is the inverse of electrical conductivity. A low resistivity indicates a material that readily allows the flow of electric current.

Resistivity is commonly represented by the formula:

ρ = R * (A / L)

where:

• ρ is the resistivity,
• R is the resistance of the object,
• A is the cross-sectional area, and
• L is the length.

The resistivity of most materials changes with temperature. If we consider a simple conductor such as a metal wire, the resistivity increases with the temperature. This is because, as the temperature rises, the atoms of the material vibrate more rapidly and this increases the likelihood of collisions with the charge carriers (usually electrons) as they pass through, which increases the resistance to their flow.

The temperature coefficient of resistivity, denoted by α, is a measure of how much the resistivity of a material changes with temperature. It is usually expressed in terms of per degree Celsius or per Kelvin.

The relationship between resistivity, temperature and the temperature coefficient of resistivity is given by the formula:

ρ(T) = ρ(0) * [1 + α * (T - T0)]

where:

• ρ(T) is the resistivity at temperature T,
• ρ(0) is the resistivity at a reference temperature T0, and
• α is the temperature coefficient of resistivity.

This formula shows that the resistivity of a material at a given temperature is equal to the resistivity at a reference temperature, multiplied by a factor that depends on the temperature difference and the temperature coefficient of resistivity.