Question

The total resistivity of the material (conductor) is sum of thermal based, impurity based and plastic deformation based resistivities i.e., $\rho ={\rho }_t+{\rho }_c+{\rho }_p$. How does resistivity vary at low temperatures?

• A. $\rho \propto \frac{1}{T}$
• B. $\rho \propto \frac{1}{T^2}$
• C. $\rho \propto \frac{1}{T^3}$
• D. $\rho$ is independent of $T$

Answer 1

The correct option is D $\rho$ is independent of $T$

At high temperatures, the variation of resistivity with temperature is nearly linear, but at low temperatures (less than Debye temperature), the linear approximation fails to work because of the residual resistivity due to impurities. At low temperatures, thermal energy and hence thermal based resistivity is negligible. Thus resistivity is independent of temperature and depends on the amount of impurities.