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, while a high resistivity indicates a material that resists the flow of electric current.

Resistivity is typically measured in ohm-meters (Ω⋅m) and is often temperature dependent. This temperature dependence is typically linear for metals and can be characterized by the equation:

ρ(T) = ρ(0)[1 + α(T - T0)]

where:

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

The temperature coefficient α is a measure of how much the resistivity changes with temperature. If α is positive, the resistivity increases with increasing temperature, which is the usual case for metals. For semiconductors and insulators, α is usually negative, meaning their resistivity decreases with increasing temperature.

The reason for this temperature dependence is due to the increase in vibrations of the atoms in the material (due to increased thermal energy with increasing temperature) which act as obstacles to the flow of current, thus increasing the resistivity. For semiconductors and insulators, the increase in thermal energy can free up more charge carriers, which can then contribute to conduction, thus decreasing the resistivity.

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