Temperature dependence of resistance for copper , $(Cu)$

Copper is a metal. For metals, in the moderate temperature range around room temperature, resistance varies approximately linearly with temperature:

$R = R_0[1+\alpha (T-T_0)]$

where $\alpha>0$ is the temperature coefficient of resistance.

Hence, as temperature increases from $300\,K$ to $400\,K$, the resistance of $Cu$ increases linearly.

Temperature dependence of resistance for undoped silicon , $(Si)$

Undoped silicon is an intrinsic semiconductor. In a semiconductor, as temperature increases, the number of charge carriers increases rapidly.

The conductivity of an intrinsic semiconductor is approximately:

$\sigma \propto e^{-E_g/(2kT)}$

Therefore resistance behaves oppositely:

$R \propto e^{E_g/(2kT)}$

As $T$ increases, the exponent $\dfrac{E_g}{2kT}$ decreases, so resistance decreases exponentially with temperature.

Check the options

• A: Linear increase for $Cu$, exponential decrease for $Si$ — Correct
• B: Linear decrease for $Cu$, linear decrease for $Si$ — Incorrect
• C: Linear increase for $Cu$, linear increase for $Si$ — Incorrect
• D: Linear increase for $Cu$, exponential increase for $Si$ — Incorrect

Final answer

The best description is:

$\boxed{A}$

Comparison with stored correct answer

Stored correct answer = A.

My derived answer = A.

So, they agree.