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(D) Step $1$: Analyze Statement $I$. The resistivity of a conductor is given by $\rho(T) = \rho_0 [1 + \alpha(T - T_0)]$. Since $\alpha > 0$ for condu

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Statement $I$ is false but Statement $II$ is true.

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(D) Step $1$: Analyze Statement $I$. The resistivity of a conductor is given by $\rho(T) = \rho_0 [1 + \alpha(T - T_0)]$. Since $\alpha > 0$ for conductors, resistivity increases with temperature. Thus, Statement $I$ is false.Step $2$: Analyze Statement $II$. For semiconductors, the number of charge carriers increases exponentially with temperature, which dominates the decrease in relaxation time. Thus, resistivity decreases as temperature increases. Statement $II$ is true.Step $3$: Conclusion. Statement $I$ is false and Statement $II$ is true.

Given below are two statements:
Statement $I$: The resistivity of a conductor is independent of its temperature.
Statement $II$: The resistivity of a semiconductor decreases with an increase in temperature.
Select the correct option.

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Given below are two statements:Statement $I$: The resistivity of a conductor is independent of its temperature.Statement $II$: The resistivity of a semiconductor decreases with an increase in temperature.Select the correct option.