KCET · Physics · Current Electricity

The range of electrical conductivity \((\sigma)\) and resistivity \((\rho)\) for metals, among the following, is

A \(\begin{aligned} & \rho \rightarrow 10^{-5}-10^{-6} \Omega \mathrm{~m} \\ & \sigma \rightarrow 10^5-10^{-6} \mathrm{Sm}^{-1}\end{aligned}\)
B \(\begin{aligned} & \rho \rightarrow 10^{11}-10^{19} \Omega \mathrm{~m} \\ & \sigma \rightarrow 10^{-11}-10^{-19} \mathrm{Sm}^{-1}\end{aligned}\)
C \(\begin{aligned} & \rho \rightarrow 10^2-10^8 \Omega \mathrm{~m} \\ & \sigma \rightarrow 10^{-2}-10^{-8} \mathrm{Sm}^{-1}\end{aligned}\)
D \(\begin{aligned} & \rho \rightarrow 10^{-2}-10^{-8} \Omega \mathrm{~m} \\ & \sigma \rightarrow 10^2-10^8 \mathrm{Sm}^{-1}\end{aligned}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\begin{aligned} & \rho \rightarrow 10^{-2}-10^{-8} \Omega \mathrm{~m} \\ & \sigma \rightarrow 10^2-10^8 \mathrm{Sm}^{-1}\end{aligned}\)

Step-by-step Solution

Detailed explanation

The electrical conductivity \((\sigma)\) for metals typically ranges from \(10^2\) to \(10^8 \Omega^{-1} \mathrm{~m}^{-1}\) and the resistivity (\(\rho\)) is in the range of \(10^{-2}\) to \(10^8 \Omega\) m.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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