Question

A piece of copper and another piece of germanium are cooled from room temperature to $80\text{K}$. The resistance of

• A. each of them increases.
• B. each of them decreases.
• C. copper increases and for germanium decreases.
• D. copper decreases and for germanium increases.

Answer 1

The correct option is D copper decreases and for germanium increases.

Resistance varies with temperature and for small changes in temperature the formula is $$R=R_o(1+\alpha \Delta T)$$Here,
$R_0$ is the original resistance of the material.

$\alpha$ is called temperature coefficient of resistance.

$\alpha$ is $\text{+ve}$ for conductors and it is $\text{-ve}$ for semiconductors.

If we decrease temperature then $\Delta T$will be $\text{-ve}$.

Therefore, for copper which is conductor as $T\downarrow$ then $R\downarrow$.

For germanium which is semiconductor, resistance will increase with decrease in temperature.

Why this question? To introduce the concept that " Number of free electrons in semiconductor is very less as compared to that in conductor at room temperature. When temperature increases, electrons get detach from binding of nucleus due to thermal energy and become free. This increased free electrons are responsible for increased conductivity in semiconductor as temperature increases."