Question

Copper and Germanium are cooled from room temperature to $100K$. Then the resistance of
(A) Germanium decreases,Copper increases.
(B) Germanium decreases ,Copper decreases
(C) Germanium increases, Copper decreases
(D) Germanium increases, Copper increases

Answer 1

Here we are going to apply the concept of variation of resistance with temperature, properties of conductors and semiconductors and concept of resistance, conductance.

Complete step by step answer:
Resistance is defined as the restricting to the flow of electrical current through a conductor. It's important to point out that conductivity and resistivity are inversely proportional and is the property that determines final resistance. The resistance is depending on the nature of the material and by varying temperature.
Conductor resistance is a property of a conductor at a certain temperature, and it is defined as the amount of restriction/opposition there is to the flow of electric current through a conducting medium. The resistance of a conductor depends on the cross sectional area of the conductor, the length of the conductor, and its resistivity or the conductivity. It's important to point out that conductivity and resistivity are inversely proportional and is the property that determines final resistance, meaning that the more conductive something is the less resistive it is.
We can find the resistance of a conductor at a constant temperature by using,
$R = \dfrac{{\rho L}}{A}$
Where:R Is the resistance in ohms \left( \Omega \right),$$$$\rho is the resistivity of the material in ohm meters $\left( {\Omega m} \right),$ L is the length of the conductor in meters $\left( m \right),$ and A is the cross-sectional area of the conductor in meters squared $\left( {{m^2}} \right)$.
This formula tells us that the resistance of the conductor is directly proportional to $\rho \;and\;L,$ and it is inversely proportional to A. Since the resistance of some conductor, such as a piece of wire, depends on collisions within the wire itself, the resistance depends on temperature. With increasing temperature, the resistance of the wire increases since the collisions within the wire increase and the flow of current.
But for the electrical resistance of semiconductors, at absolute zero temperature, all electrons are tightly bound to their cores and the material cannot conduct electricity. Electrons must have some power to cover the band gap into the conduction band and can participate in the current leadership.
Since Copper is a conductor, the resistance and temperature is directly proportional,
$R \propto T$
And since, Germanium is a semiconductor conductor, the resistance and temperature is inversely proportional,
$R \propto \dfrac{1}{T}$
So when Copper and Germanium are cooled from room temperature to $100K.$ Then the resistance of conductor $\left( {that{\text{ }}is{\text{ }}copper} \right)$ decreases and resistance of the semiconductor (that is germanium) increases.
So, the correct Option is (C)

Note: As a student you should consolidate the relationship of temperature and resistance in an equation, so that it is easy to recollect and is very useful to this type of question. You should study some important elements for conductors, semiconductor, insulators, so that you can easily find the relations.