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Question 12

Consider four conducting materials copper, tungsten, mercury and aluminium with resistivity $$\rho_C$$, $$\rho_T$$, $$\rho_M$$ and $$\rho_A$$ respectively. Then:

We begin by recalling the definition of resistivity. For any homogeneous conductor we have the relation

$$R=\rho\,\frac{\ell}{A},$$

where $$R$$ is the resistance of the specimen, $$\ell$$ its length, $$A$$ its cross-sectional area and $$\rho$$ the material‐dependent constant called resistivity. A smaller value of $$\rho$$ therefore corresponds to a better electrical conductor, while a larger value corresponds to a poorer conductor.

The standard tabulated resistivities at room temperature (≈ 20 °C) for the four materials mentioned in the question are:

$$\rho_C \;( \text{copper}) \approx 1.72\times10^{-8}\;\Omega\text{m},$$

$$\rho_A \;( \text{aluminium}) \approx 2.8\times10^{-8}\;\Omega\text{m},$$

$$\rho_T \;( \text{tungsten}) \approx 5.6\times10^{-8}\;\Omega\text{m},$$

$$\rho_M \;( \text{mercury}) \approx 9.5\times10^{-7}\;\Omega\text{m}.$$

Now we arrange these values in descending order (largest first):

$$\rho_M \;>\;\rho_T \;>\;\rho_A \;>\;\rho_C.$$

Next we compare this true order with each option supplied in the problem statement.

A. $$\rho_C > \rho_A > \rho_T$$ contradicts the numerical data because $$\rho_C$$ is the smallest, not the largest.

C. $$\rho_A > \rho_T > \rho_C$$ is also wrong because $$\rho_T$$ is greater than $$\rho_A$$, not the other way round.

D. $$\rho_A > \rho_M > \rho_C$$ is incorrect because $$\rho_M$$ is the largest of all; it cannot be less than $$\rho_A$$.

B. $$\rho_M > \rho_A > \rho_C$$ does not mention tungsten, but it is completely consistent with the accurate ordering of the three quantities that do appear, namely $$\rho_M > \rho_A$$ and $$\rho_A > \rho_C$$. Because the other three options are plainly false, Option B is the only statement that matches the established numerical hierarchy.

Hence, the correct answer is Option B.

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