A) \[\left[ M{{L}^{2}}{{T}^{-3}}{{I}^{-1}} \right]\]
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 \[R=\frac{Potential\text{ }difference}{Current}=\frac{V}{i}=\frac{W}{qi}\] (\[\because \] Potential difference is equal to the work done per unit charge) So, dimensions of R \[=\,\,\,\frac{\left[ Dimensions\,\,of\,\,work \right]}{\left[ Dimensions\,\,of\,\,ch\arg e \right]\left[ Dimensions\,\,of\,\,current \right]}\]\[=\,\,\,\frac{\left[ M{{L}^{2}}{{T}^{-2}} \right]}{\left[ IT \right]\left[ I \right]}=\left[ M{{L}^{2}}{{T}^{-3}}{{I}^{-2}} \right]\]
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