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

Resistance

$$\begin{gathered} \text{R}=\frac{\text{Potential\hspace{0.17em}difference}}{\text{current}}=\frac{\text{V}}{\text{i}}=\frac{\text{W}}{\text{qi}} \\ ( Potential difference is equal to work done per unit charge) So, \\ dimensions of R \\ =\frac{\left[\text{Dimensions\hspace{0.17em}of\hspace{0.17em}work}\right]}{\left[\text{Dimensions\hspace{0.17em}of\hspace{0.17em}charge}\right]\left[\text{Dimensions\hspace{0.17em}of\hspace{0.17em}current}\right]} \\ =\frac{\left[{\text{ML}}^{\text{2}}{\text{T}}^{-2}\right]}{\left[\text{IT}\right]\left[\text{I}\right]}=\left[{\text{ML}}^{\text{2}}{\text{T}}^{-3}{\text{I}}^{-2}\right] \end{gathered}$$