Dimensions of resistance in an electrical circuit, in terms of dimension of mass $M$, of length $L$, of time…

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
  1. $M L^2 T^{-2}$
  2. $M L^2 T^{-1} I^{-1}$
  3. $M L^2 T^{-3} I^{-2}$
  4. $M L^2 T^{-3} I^{-1}$

Solution

We know that $\begin{aligned} R & =\frac{V}{I}=\frac{\left[M L^2 T^{-2}\right]}{\left[I^2 T\right]} \\ & =\left[M L^2 T^{-3} I^{-2}\right] \end{aligned}$

Asked in: NEET 2007

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