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?

Solution

Resistivity of a material is given by,
R = $ρ \frac{l}{A}$

If, length and area is unity then,
R = $ρ$
Hence, we can say resistivity of a material is equal to the resistance of the conductor having unit length and unit area of cross-section.

Resistivity is dependent on the temperature.
$ρ_{T} = ρ_{o} [1 + α (T - T_{o})]$ .... (1)

Graph showing the variation of resistivity with temperature.

$ρ_{T}$ is the resistivity at temperature T and $ρ_{o}$ is the resistivity at a temperature T₀ . The mathematical relation (1) says that the the plot of $ρ vs . T$ should be a straight line. But, at temperature lower than 0⁰ C , the graph deviates considerably from a straight line.
$ρ_{T}$

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Current Electricity

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?

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