Dimensions of electrical resistance are

The correct option is [ML²T⁻³A⁻²].

To find the dimensional formula of electrical resistance ($R$), we can use Ohm's Law:
$V=I\cdot R$
Therefore, resistance is given by:
$R=\frac{V}{I}$

Here, $V$ is the potential difference (voltage) and $I$ is the electric current. The dimensional formula for current $I$ is represented by $\left[A\right]$.

Next, we determine the dimensional formula for potential difference ($V$). Potential difference is defined as work done ($W$) per unit charge ($q$):
$V=\frac{W}{q}$

We know that:
1. Work ($W$) = Force $\cdot$ Displacement. The dimensional formula for work is:
$\left[W\right]=\left[M{L}^2{T}^{-2}\right]$
2. Electric charge ($q$) = Current $\cdot$ Time. The dimensional formula for charge is:
$\left[q\right]=\left[AT\right]$

Now, substitute these into the expression for potential difference $V$:
$\left[V\right]=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[AT\right]}=\left[M{L}^2{T}^{-3}{A}^{-1}\right]$

Finally, substitute the dimensions of $V$ and $I$ back into the formula for resistance $R$:
$\left[R\right]=\frac{\left[M{L}^2{T}^{-3}{A}^{-1}\right]}{\left[A\right]}=\left[M{L}^2{T}^{-3}{A}^{-2}\right]$

Thus, the dimensional formula of electrical resistance is [ML²T⁻³A⁻²].