Question

Define resistivity of a conductor. Plot a graph showing the variation of resistivity with temperature for a metallic conductor. How does one explain such a behaviour, using the mathematical expression of the resistivity of a material?

Answer 1

We know that, R = \(p\frac{l}{A}\)

If I = 1, A = 1 ⇒ P = R

Thus, resistivity of a material is numerically equal to the resistance of the conductor having unit length and unit cross-sectional area.

The resistivity of a material is found to be dependent on the temperature. Different materials do not exhibit the same dependence on temperature. Over a limited range of temperatures, that is not too large, the resistivity of a metallic conductor is approximately given by,

PT = P₀[1 + a(T - T₀)]   .....(i)

Where ρ_T is the resistivity at a temperature T and ρ₀ is the same at a reference temperature T₀, α is called the temperature co-efficient of resistivity.

Relation (i) implies that a graph of ρ_T plotted against T would be a straight line. At temperatures much lower than 0°C, the graph, however, deviates considerably from a straight line (Fig.).

Resistivity ρ_T of metallic conductor as a function of temperature T