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The specific resistance of a wire is ρ, its volume is 3m3 and its resistance is 3 ohms, then its length will be


1. 1/√ρ
2. 3/√ρ
3. √3/ρ
4. 1/ρ

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Correct Answer - Option 2 : 3/√ρ

The resistance of the wire in terms of resistivity is given as

\(R\; = \;\frac{{\rho l}}{A}\; = \;\frac{{\rho l.l}}{{A.l}}\; = \;\frac{{\rho {l^2}}}{V}\; \Rightarrow \;{l^2}\; = \;\frac{{RV}}{\rho }\; = \;\frac{9}{\rho }\; \Rightarrow \;l\; = \;\frac{3}{{\sqrt \rho }}\)

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