Write the mathematical relation for the resistivity of a material in t

1.	Write the mathematical relation for the 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 resistivity of a metal increases and that of a semiconductor decreases with rise in temperature.
Answer» Resistivity of a material, \(p=\frac{m}{ne^2r}\) Where m is mass, e is charge on charge carrier, n is number density and τ is relaxation time. For a metallic conductor: When temperature of a metal increases, the number of collisions of electrons with ion-lattice increases, so relaxation time decreases, as resistivity \(P\,\infty \frac{1}{T},\) so resistivity of material increases with rise of temperature. For a semiconductor: When temperature increases, the covalent bonds between valence electrons of atoms of semiconductor break, so more charge carriers (electrons and holes) becomes free. In other words the number density of charge carriers increases \(P\,\infty \frac{1}{n},\) so resistivity of semiconductor decreases with the rise of temperature.

Write the mathematical relation for the 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 resistivity of a metal increases and that of a semiconductor decreases with rise in temperature.

Answer»

Resistivity of a material, \(p=\frac{m}{ne^2r}\)

Where m is mass, e is charge on charge carrier, n is number density and τ is relaxation time.

For a metallic conductor: When temperature of a metal increases, the number of collisions of electrons with ion-lattice increases, so relaxation time decreases, as

resistivity \(P\,\infty \frac{1}{T},\) so resistivity of material increases with rise of temperature.

For a semiconductor: When temperature increases, the covalent bonds between valence electrons of atoms of semiconductor break, so more charge carriers (electrons and holes) becomes free. In other words the number density of charge carriers

increases \(P\,\infty \frac{1}{n},\) so resistivity of semiconductor decreases with the rise of temperature.

Write the mathematical relation for the 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 resistivity of a metal increases and that of a semiconductor decreases with rise in temperature.

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