Identify the temperature dependence of resistance for each material

We are comparing:

• a copper strip: this is a metal
• a germanium strip: this is a semiconductor

Copper (metal)

In metals, resistance is mainly due to collisions of free electrons with lattice vibrations.

When temperature decreases, lattice vibrations decrease, so electron scattering decreases. Hence, the resistance of a metal decreases on cooling.

Therefore, for copper: $T \downarrow \implies R_{\text{copper}} \downarrow$

Germanium (semiconductor)

In semiconductors, conduction depends strongly on the number of charge carriers.

When temperature decreases, fewer electrons have enough thermal energy to jump into the conduction band. So the number of charge carriers decreases significantly. Therefore, resistance increases on cooling.

Thus, for germanium: $T \downarrow \implies R_{\text{Ge}} \uparrow$

Compare with the options

• A: each decreases — incorrect
• B: copper increases, germanium decreases — incorrect
• C: copper decreases, germanium increases — correct
• D: each increases — incorrect

Final derived answer

The resistance of copper decreases and that of germanium increases when cooled from room temperature to $80\,K$.

So the correct option is: $\boxed{C}$

Comparison with stored correct answer

Stored correct answer: C

This matches the derived answer.