\(\rho=\frac{R A}{\ell}\)

Conductivity \(=\frac{1}{\text { resistivity }}=\frac{\ell}{R A}\)

\(=\frac{\ell I}{V A}(\because V=R D)\)

\( = \frac{{[{\rm{L}}][{\rm{I}}]}}{{\left[ {\frac{{\left[ {{\rm{M}}{{\rm{L}}^2}{{\rm{T}}^{ - 2}}} \right]}}{{[I][{\rm{T}}]}}} \right] \times \left[ {{{\rm{L}}^2}} \right]}}\quad \left[ {{\rm{V}} = \frac{{\rm{W}}}{{\rm{q}}} = \frac{{\rm{W}}}{{{\rm{it}}}}} \right]\)

\(=\left[M^{-1} L^{-3} T^{3}\right]\left[I^{2}\right]=\left[M^{-1} L^{-3} T^{3} I^{2}\right]\)