Question

The physical quantity having the dimensions $\left[M^{-1}{L}^{-3}{T}^3{A}^2\right]$ is

• A. resistivity
• B. resistance
• C. electric cunductivity
• D. electromotive force

Answer 1

Answer: (C)

$\text{Explanation:-}$

We know that,

Resistivity, $\rho =\frac{m}{n{e}^{2}t}$

$\Rightarrow \rho =\frac{\left[M\right]}{\left[L^{-3}\right]\left[AT{]}^2\right[T]}$

$\Rightarrow \rho =\left[M{L}^3{A}^{-2}{T}^{-3}\right]$

Now,

Electrical conductivity, $\sigma =\frac{1}{\rho }$

$\Rightarrow \sigma =\frac{1}{\left[M{L}^3{A}^{-2}{T}^{-3}\right]}$

$\Rightarrow \sigma =\left[M^{-1}{L}^{-3}{A}^2{T}^3\right]$

$\text{Hence the correct option is C}$