Question

In which of the following substances the resistance decreases with the increase in temperature?
(A) Carbon
(B) Constantan
(C) Copper
(D) Silver

Answer 1

Hint Increasing temperature increases the mobility of the electrons that either decreases the resistance or increases it. These two effects depend on the concentration of the free electrons in the substance and the forbidden energy gap between valence and conduction band.

Complete step-by-step solution
Constantan is an alloy of nickel and copper, which is highly resistive. That implies that the forbidden energy gap between valence and conduction band of constantan is very high. So that it is not possible for an electron in valence band to jump to the conduction band, with increasing temperature. Hence, resistivity of constantan does not decrease with increase in temperature.

Copper and silver are metals and are good conductors. So the concentration of free electrons is high in them. After increasing temperature, the electrons in them start to move randomly, making frequent collisions, resulting in an increase of resistance.

But in the case of carbon, the forbidden energy gap is very small. After increasing temperature, electrons in the valence band can get sufficient energy to make a jump to the conduction band, resulting in increasing conductivity or decreasing resistance.

Hence, option A is the correct option

Note To answer this question, you must keep all things in mind. It is not possible to answer this question keeping only one aspect in mind. Semiconductors show such property of decreasing resistance when temperature is increased.