Question:
In the following 'I' refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity :
In the following 'I' refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity :
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Conductivity is the reciprocal of resistivity; \(\rho=RA/l\) and \(R=V/I\).
Updated On: Nov 11, 2026
- \(\mathrm{ML^{-3}T^{-3}I^{2}}\)
- \(\mathrm{M^{-1}L^{3}T^{3}I}\)
- \(\mathrm{M^{-1}L^{-3}T^{3}I^{2}}\)
- \(\mathrm{M^{-1}L^{-3}T^{3}I}\)
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The Correct Option is C
Solution and Explanation
Conductivity \(\sigma=\frac{1}{\rho}\) and \(\rho=\frac{RA}{l}\), so \(\sigma=\frac{l}{RA}\).
\(R=\frac{V}{I}\) with \([V]=\mathrm{ML^2T^{-3}I^{-1}}\), hence \([R]=\mathrm{ML^2T^{-3}I^{-2}}\).
\([\sigma]=\frac{L}{\mathrm{ML^2T^{-3}I^{-2}}\cdot L^2}=\mathrm{M^{-1}L^{-3}T^{3}I^{2}}\).
Answer: (3) \(\mathrm{M^{-1}L^{-3}T^{3}I^{2}}\)
\(R=\frac{V}{I}\) with \([V]=\mathrm{ML^2T^{-3}I^{-1}}\), hence \([R]=\mathrm{ML^2T^{-3}I^{-2}}\).
\([\sigma]=\frac{L}{\mathrm{ML^2T^{-3}I^{-2}}\cdot L^2}=\mathrm{M^{-1}L^{-3}T^{3}I^{2}}\).
Answer: (3) \(\mathrm{M^{-1}L^{-3}T^{3}I^{2}}\)
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