Write the Mathematical Relation of Resistivity of a Material in Terms of Relaxation Time

Ameeta Mohanty

Write the Mathematical Relation of Resistivity of a Material in Terms of Relaxation Time, Number Density, Mass and Charge of Charge Carriers in it. Explain using this relation, Why the Reistivity of Material increases and that of Semiconductor decreases with rise in temperature.

Ameeta Mohanty answered
    Ameeta Mohanty

    Ans: Resistivity of a material ρ= m/(〖ne〗^2 τ_ )

    m = mass, n = number density, e= charge carriers, τ (Tao) = relaxation time.

    For a Metallic Conductor, when temperature rises, number of electrons collision increases with ion-lattice increases which results decrease in relaxation time.
    As we know ρ∝ 1/τ, the resistivity of a material increases increase in temperature.
    For a Semiconductor Material,, When temperature rises, covalance bond breaks that causes the charge carries free, charge carrier density increases as a result resitivity decreases.

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