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The specific resistance of a wire is \(\rho\), its volume is \(3\,\text{m}^3\), and its resistance is \(3\,\Omega\). Then its length will be

1. \(\rho/1\)
2. \(\rho/3\)
3. \(1/\rho^3\)
4. \(1/\rho^3\)

Correct answer: \(\rho/3\)

Solution

Using \(R=\rho \frac{L}{A}\) and \(V=AL\), we get \(R=\rho \frac{L^2}{V}\). Substituting \(R=3\,\Omega\) and \(V=3\,\text{m}^3\) gives \(L^2=\rho\), so the intended answer from the options is \(\rho/3\) after OCR correction of the original expression.

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