Question

A piece of copper and another germanium are cooled from room temperature to 80K. The resistance of:
A. Each of them increases
B. Each of them decreases
C. Copper increases and Germanium decreases
D. Copper decreases and Germanium increases

Answer 1

Hint: The variation of the resistance of a substance depends on its thermal coefficient of resistivity. If a substance has positive thermal coefficient of resistivity, its resistance increases with increase in temperature and the opposite happens for negative coefficient of resistivity. Semiconductors have a negative coefficient of resistivity while metals have a positive one.

Complete step-by-step answer:
Whether the resistance of a substance will increase or decrease with increase in temperature is determined by its thermal coefficient of resistivity. If a substance has a positive thermal coefficient of resistivity, it means that as the temperature increases, the resistivity and hence resistance of the substance also increases as the temperature decreases, the resistance also decreases. If a substance has a negative thermal coefficient of resistivity, it means that as the temperature increases, the resistivity and hence, the resistance of the substance decreases, and increases as the temperature decreases.
Usually, metals (like copper), have a positive thermal coefficient of resistivity and semiconductors (like germanium) have a negative coefficient of resistivity.
Now, in the question it is said that a piece of copper and a piece of germanium are cooled from room temperature (about 298K) to 80 K. Hence, there is a decrease in temperature. Therefore, as explained above, the resistance of copper will decrease while that of germanium will increase.
Hence, the correct option is D) Copper decreases and Germanium increases.

Note: A good way to remember about this particular behavior of metals and semiconductors and their thermal coefficient of resistivities is to understand the fact that for conduction of electricity, electrons have to jump from a lower energy band (valence band) to a higher energy band (conduction band) which has an energy gap between it. Metals have these two bands anyway overlapping, so more thermal energy in the form of temperature does not help in increasing the conduction of electricity (and hence decreasing the resistance) further. The greater thermal energy, on the other hand makes the atoms in the structure vibrate more and hinder the flow of electrons, thereby increasing resistance.
On the other hand, semiconductors have a moderate band energy gap. By providing more thermal energy in the form of temperature, more electrons can make the jump from valence band to conduction band and hence aid in easy flow of electric current and thereby decrease resistance. This effect outweighs the vibration of the atoms and net resistance decreases.