A) \[[M{{L}^{2}}{{T}^{-3}}{{I}^{-1}}]\]
B) \[[M{{L}^{2}}{{T}^{-2}}]\]
C) \[[M{{L}^{2}}{{T}^{-1}}{{I}^{-1}}]\]
D) \[[M{{L}^{2}}{{T}^{-3}}{{I}^{-2}}]\]
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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