Temperature and Resistivity Variations

Not only resistance but specific resistance or resistivity of metallic conductors also increases With rise in temperature and vice versa.

According to the picture below the resistivities of metals vary linearly with temperature over a range of temperature, the variation becoming non-linear both at very high and at very low temperatures.

Let, for any metallic conductor,

ρ₁ =  resistivity at t₁ ^oC

ρ₂ =  resistivity at t₂ ^oC

m = slope of the linier part of the curve

Next, it is evident that

m = (ρ₂ - ρ₁ ) / (t₂ – t₁ )     or      ρ₂ = ρ₁ + m (t₂ – t₁ )  

or

ρ₂ = ρ₁ [1 + (m/ ρ₁) (t₂ – t₁) ]

The ratio of m/ ρ₁ is called the temperature coefficient of resistivity at temperature t₁⁰C. It may be defined as numerically equal to the fractional change in ρ₁ per ⁰C change in temperature from t₁ ⁰C. It is almost equal to temperature-coefficient of resistance α₁. therefore, substituting 

α₁ = m/ ρ_{1,  we get} 

ρ₂ = ρ₁ [1 + α₁ (t₂ – t₁) ] or as simple ρ_t = ρ₀(1 + α₀ t)

it has been found that although temperature is the most significant factor influencing the resistivity of metals, othes factor like pressure and tension also affect resistivity to some extent. for most metals,except lithium and calcium, increase in pressure leads to decrease in resistivity, however restivity increases with increase tension.