Question

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

• A. $ [M{{L}^{2}}{{T}^{-3}}{{I}^{-1}}] $
• B. $ [M{{L}^{2}}{{T}^{-2}}] $
• C. $ [M{{L}^{2}}{{T}^{-1}}{{I}^{-1}}] $
• D. $ [M{{L}^{2}}{{T}^{-3}}{{I}^{-2}}] $

Answer 1

Answer: (D)

Resistance $ R=\frac{\text{potential}\,\text{difference}}{\text{current}}=\frac{V}{i}=\frac{W}{qi} $
( $ \because $ Potential difference is equal to work done per unit charge) So, Dimensions of R
$ =\,\,\frac{[Dimensions\,of\,work]}{[Dimensions\,of\,charge][Dimensions\,of\,current]} $
$ =\frac{[M{{L}^{2}}{{T}^{-2}}]}{[IT][I]}=[M{{L}^{2}}{{T}^{-3}}{{I}^{-2}}] $