Question

Draw a plot showing the variation of resistivity of a (i) conductor and (ii) semiconductor, with the increase in temperature.

How does one explain this behaviour in terms of number density of charge carriers and the relaxation time ?

Answer 1

Showing the plot of the variation of resistivity:

(i) For Conductor

(ii) For Semiconductors

\(p = \frac {m}{ne^2r}\)

where, p = resistivity.

Conductors: For conductors, the number density n of free electrons is almost independent of temperature.

As the temperature increase, the thermal speed of electrons increases and also the amplitude of vibration of the metal ions increases, the free electrons collide more frequently with the metal ions.

The mean collision time \(\tau\) decrease.

Hence, resistivity increases.

Semiconductors: In the case of semiconductors as the temperature is increased the number of free electron increases and relaxation time decreases. The increase in number density is predominant compared to the decrease in relaxation time.

Therefore resistivity decreases with increase in temperature.

Answer 2

In conductors, average relaxation time decreases with increase in temperature, resulting in an increase in resistivity.

In semiconductors, the increase in number density (with increase in temperature) is more than the decrease in relaxation time; the net result is, therefore, a decrease in resistivity.