Write the mathematical relation for the resistivity of a material in terms of relaxation time, number density and mass and charge of charge carriers in it. Explain, using this relation, why the resistivity of a metal increases and that of a semi-conductor decreases with rise in temperature.
CBSE DELHI - SET 1 2007
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$\rho = \frac{\text{m}}{\text{ne}^{2}\iota}$For a metal, as the temperature increases,$\iota$decreases. Hence $\rho$increases. For a semiconductor, as the temperature increases, number density of electrons in the conduction band increases. Hence $\rho$ decreases.
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