Question

Dimension of resistivity is

• A. $M L^{2} T ^{-2} I ^{-1}$
• B. $ML ^{3} T ^{-3} I ^{-2}$
• C. $ML ^{3} T ^{-2} I ^{-1}$
• D. $ML ^{2} T ^{-2} I ^{-2}$

Answer 1

Answer: (C)

By definition
$R = \rho \frac{l}{A}$
$\Rightarrow \quad\rho = \frac{RA}{l} = \frac{\frac{V}{I}A}{l} = \frac{VA}{Il}$
$\therefore \,\left[\rho\right] = \frac{\left[V\right]\left[A\right]}{\left[I\right]\left[l\right]}$
$= \frac{ML^{2}T^{-2}L^{2}}{IL} = \left[ML^{3}T^{-2}I^{-1}\right]$