Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be

The correct option is [ML²T⁻³I⁻²].

To find the dimensions of electrical resistance, we can use fundamental physical relationships and Ohm's law.
According to Ohm's law, the relationship between voltage (V), current (I), and resistance (R) is:
$V=I\times R$
Therefore, resistance is given by:
$R=\frac{V}{I}$

Next, we need to express the electric potential difference (V) in terms of fundamental quantities.
Potential difference (V) is defined as work done (W) per unit charge (Q):
$V=\frac{W}{Q}$

Now, let's determine the dimensions of each term:
1. Work Done (W): Work is force times distance.
$\left[W\right]=\left[\text{Force}\right]\times \left[\text{Distance}\right]=\left[{\text{MLT}}^{-2}\right]\times \left[\text{L}\right]=\left[{\text{ML}}^2{\text{T}}^{-2}\right]$
2. Charge (Q): Electric charge is current (I) multiplied by time (T).
$\left[Q\right]=\left[\text{I}\right]\times \left[\text{T}\right]=\left[\text{IT}\right]$

Using these dimensions, we can find the dimensions of potential difference (V):
$\left[V\right]=\frac{\left[{\text{ML}}^2{\text{T}}^{-2}\right]}{\left[\text{IT}\right]}=\left[{\text{ML}}^2{\text{T}}^{-3}{\text{I}}^{-1}\right]$

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

Thus, the dimensions of electrical resistance in terms of mass M, length L, time T, and current I are [ML²T⁻³I⁻²].