Question

Statement 1: The temperature dependence of resistance is usually given as $R=R_0(1+\alpha \Delta t)$. The resistance of a wire changes from 100 $\Omega$ to 150 $\Omega$ when its temperature is increased from ${27}^{o}C$ to ${227}^{o}C$. This implies that $\alpha =2.5\times {10}^{-3}{/}^{o}C$.
Statement 2: $R=R_0(1+\alpha \Delta t)$ is valid only when the change in the temperature $\Delta T$ is small and $\Delta R=(R-R_0)<<R_0$.

• A. Statement 1 is True, Statement 2 is False.
• B. Statement 1 is True, Statement 2 is True; Statement 2 is a correct explanation for Statement 1.
• C. Statement 1 is True, Statement 2 is True; Statement 2 is not the correct explanation for Statement 1.
• D. Statement 1 is False, Statement 2 is True.

Answer 1

Answer: (D)

Statement 1 is False, Statement 2 is True.

Statement 2 is correct. The statement is valid only for small $\Delta T$.

Thus for $\Delta T={200}^{\circ }C$, the above calculation is not valid.