JEE Mains · Physics · STD 12 - Current electricity
- JEE Mains 2016
- Medium
- MCQ
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
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(M^{-1}L^{-3}T^3I^2\)
Step-by-step Solution
Detailed explanation
We know that resistivity
\(\rho=\frac{R A}{\ell}\)
Conductivity \(=\frac{1}{\text { resistivity }}=\frac{\ell}{R A}\)
\(=\frac{\ell I}{V A}(\because V=R D)\)
\( = \frac{{[{\rm{L}}][{\rm{I}}]}}{{\left[ {\frac{{\left[ {{\rm{M}}{{\rm{L}}^2}{{\rm{T}}^{ - 2}}} \right]}}{{[I][{\rm{T}}]}}} \right] \times \left[ {{{\rm{L}}^2}} \right]}}\quad \left[ {{\rm{V}} = \frac{{\rm{W}}}{{\rm{q}}} = \frac{{\rm{W}}}{{{\rm{it}}}}} \right]\)
\(=\left[M^{-1} L^{-3} T^{3}\right]\left[I^{2}\right]=\left[M^{-1} L^{-3} T^{3} I^{2}\right]\)
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