Question

Define resistivity of a conductor. How does the resistivity of a conductor depend upon the following:

Hint:

Resistivity depends on the material properties such as the number of free electrons and their ability to move (relaxation time).

Answer 1

Resistivity \( \rho \) is the property of a material that quantifies how strongly it resists the flow of electric current. It is given by the formula: \[ \rho = \frac{m}{ne^2\tau}, \] where: - \( m \) is the mass of the electron, - \( e \) is the charge of the electron, - \( n \) is the number density of free electrons in the conductor, - \( \tau \) is the relaxation time. (a) Resistivity is inversely proportional to the number density of free electrons: \[ \rho \propto \frac{1}{n}. \] (b) Resistivity is directly proportional to the relaxation time \( \tau \): \[ \rho \propto \frac{1}{\tau}. \]