A) \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-3}}}{{\text{I}}^{\text{-1}}}\text{ }\!\!]\!\!\text{ }\]
B) \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }\]
C) \[[M{{L}^{2}}{{T}^{-1}}{{I}^{-1}}]\]
D) \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-3}}}{{\text{I}}^{-2}}\text{ }\!\!]\!\!\text{ }\]
Correct Answer: D
Solution :
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 \[=\frac{[Dimensions\,of\,work]}{[Dimensions\,of\,charge]\,[Dimensions\,of\,current]}\] \[=\frac{[M{{L}^{2}}{{T}^{-2}}]}{[IT]\,[I]}=[M{{L}^{2}}{{T}^{-3}}{{I}^{-2}}]\]
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