Question

A piece of copper and a piece of germanium are cooled from room temperature to 80K. Then, which one of the following is correct?
A. Resistance of each will increase
B. Resistance of each will decrease
C. Resistance of copper will decrease with that of germanium will increase
D. Resistance of copper will increase with that of germanium will decrease

Answer 1

Hint: Resistance is the opposition to the flow of current in the electrical circuit. It is measured in ohms. The resistivity of different substances vary with respect to temperature. It is based on the temperature coefficient of resistance.

Complete step by step answer:
The resistance of a conductor R is proportional to the length of the conductor l and inversely proportional to the area of cross section A. Which can be written as
$R\propto \dfrac{l}{A}$ or $R=\dfrac{\rho l}{A}$
Where, $\rho$ is known as specific resistance or electrical resistivity of the material.
If l= 1m,$A=1{{m}^{2}}$, $\rho =R$
The electrical resistivity of a material is defined as the resistance offered to current flow by a conductor of unit length having a unit area of cross section. The unit is ohm-m.
The resistivity of substances vary with temperature. For conductors, the resistance increases with increases in temperature. If $R_0$ is the resistance of a conductor at 0°C and $R_t$ is the resistance of the same conductor at t°C, then
${{R}_{t}}={{R}_{0}}\left( 1+\alpha t \right)$
Where, α is known as the temperature coefficient of resistance.
The temperature coefficient of resistance can be defined as the ratio of increase in resistance per degree rise in temperature to its resistance at 0°C. Its unit is per °C.
Metals have positive temperature coefficient, i.e., their resistance increases with increase in temperature. Whereas, insulators and semiconductors have negative temperature coefficient, i.e., their resistance decreases with increase in temperature.
In the given question, the temperature is cooled which means it is decreasing. Copper is a metal and germanium is a semiconductor. So, resistance of copper will decrease and that of germanium will increase.
Therefore, the correct answer for the given question is option (C).

Note: A material with a negative temperature of coefficient is called a thermistor. They are used in making digital thermometers and in cars to measure the oil and coolant temperatures. Alloys have low temperature coefficient.