A) \[\left[ M{{L}^{2}}{{T}^{3}}{{T}^{-1}} \right]\]
B) \[\left[ M{{L}^{2}}{{T}^{-2}} \right]\]
C) \[\left[ M{{L}^{2}}{{T}^{-1}}{{I}^{-1}} \right]\]
D) \[\left[ M{{L}^{2}}{{T}^{-3}}{{I}^{-2}} \right]\]
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 dons per unit charge) So, Dimensions of R\[=\frac{\left[ \text{Dimensions of work} \right]}{\left[ \text{Dimensions of charge} \right]\left[ \text{Dimensions of current} \right]}\] \[=\frac{[M{{L}^{2}}{{T}^{-2}}]}{[IT]\,[I]}=[M{{L}^{2}}{{T}^{-3}}{{I}^{-2}}]\]
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