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 \[R=\frac{potential\,\,difference}{current}=\frac{V}{i}=\frac{W}{qi}\] \[(\because \]Potential difference is equal to work done per unit charge) So, Dimensions of\[R\] \[=\frac{\text{ }\!\![\!\!\text{ Dimensions}\,\,\text{of}\,\,\text{work }\!\!]\!\!\text{ }}{\text{ }\!\![\!\!\text{ Dimensions}\,\,\text{of}\,\,\text{charge }\!\!]\!\!\text{ }\!\![\!\!\text{ Dimensions}\,\,\text{of}\,\,\text{current }\!\!]\!\!\text{ }}\]\[=\frac{[M{{L}^{2}}{{T}^{-2}}]}{[IT][I]}=[M{{L}^{2}}{{T}^{-3}}{{I}^{-2}}]\]
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