Question

Dimension of resistivity is

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

Answer 1

Answer: (C)

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