A) \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{-3}}{{\text{I}}^{\text{-1}}}\text{ }\!\!]\!\!\text{ }\]
B) \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{-2}}\text{ }\!\!]\!\!\text{ }\]
C) \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{-1}}{{\text{I}}^{-1}}\text{ }\!\!]\!\!\text{ }\]
D) \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{-3}}{{\text{I}}^{-2}}\text{ }\!\!]\!\!\text{ }\]
Correct Answer: D
Solution :
Resistance \[R=\frac{potential\text{ }difference}{current}=\frac{V}{i}=\frac{W}{qi}\] (\[\because \] Potential difference is equal to work done per unit charge) So, Dimensions of R \[=\frac{\left[ Dimensions\text{ }of\text{ }work \right]}{\left[ Dimensions\text{ }of\text{ }charge \right]\text{ }\left[ Dimensions\text{ }of\text{ }current \right]}\] \[=\frac{[M{{L}^{2}}{{T}^{-2}}]}{[IT][I]}=[M{{L}^{2}}{{T}^{-3}}{{I}^{-2}}]\]
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