Question

A piece of copper and another of germanium are cooled from room temperature to 77 k, the resistance of:
A) each of them increases
B) each of them decreases
C) copper decreases and germanium increases
D) copper increases and germanium decreases

Answer 1

Hint: The resistance of metal decreases with decrease in temperature while in for the semiconductors resistance will increase with decrease in temperature because of negative temperature coefficient of resistance.

Complete answer:
A piece of copper is a metal and we know that the resistance of the metal is given by:
\[R \propto \Delta T\]
Hence, resistance of the copper will decrease on decreasing the temperature of the copper sample while the piece of germanium is a semiconductor which has a negative temperature coefficient of resistance.
i.e. \[R \propto {(\Delta T)^{ - 1}}\]
or \[R \propto \dfrac{1}{{\Delta T}}\]
As a result of it, resistance of germanium will increase with decrease in temperature.

Hence, option (C) is the correct answer.

Note: Students should have to understand the concept behind the temperature dependence of conductivity of a semiconductor.
Temperature of dependence of conductivity of a semiconductor
If the temperature of a semiconductor sample is increased, the average energy exchanged in a collision increases. More the number of valence electrons cross the gap the number of electron-hole pairs increases.
There is a very small opposing behavior due to the increase in thermal collisions. The drift speed and hence the mobility decreases and this contributes towards increasing the resistivity just like a conductor. The resultant effect is that the resistivity decreases as temperature increases. The temperature coefficient of resistivity is, therefore, negative. This behavior is opposite to that of a conductor where resistivity increases with increasing temperature.