Dimension of resistance can be worked out by using Ohm's law

You know V = IR or R = V/I....(1)

The dimensional formalism of equation (1) can be written as follows

[R] = [V]/[I] = [W/q]/[I] { since potential refers to work done(W) per unit charge }

So [R] = [w]/[qI] = [W]/[I^{2}T] { [I] = [q]/[T] where T stands for time }

thus [R] = [ML^{2}T^{-2}]/[A^{2}T] { dimension of current is taken as [A] }

= **[M**^{1}L^{2}T^{1}A^{-2}] (ans)