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Q. $[ML^{3}T^{-3}A^{-2}]$ is the dimensional formula of

UP CPMTUP CPMT 2012

Solution:

Resistances $=\frac{\text{Potential difference}}{\text{Current}}$
$=\frac{\left[ML^{2}T^{-3}A^{-1}\right]}{\left[A\right]}=\left[ML^{2}T^{-3}A^{-2}\right]$
Resistivity $=\frac{\text{Resistance $\times$ Area}}{\text{Length}}$
$=\frac{\left[ML^{2}T^{-3}A^{-2}\left[L^{2}\right]\right]}{\left[L\right]}=\left[ML^{3}T^{-3}A^{-2}\right]$
Conductance $=\frac{1}{\text{Resistivity}}=\left[M^{-1}L^{-3}T^{3}A^{2}\right]$
$\therefore \left[ML^{3}T^{-3}A^{-2}\right]$ is the dimensional formula of resistivity.