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 |
| \[\text{=}\frac{\text{ }\!\![\!\!\text{ Dimensions}\,\text{of}\,\text{work }\!\!]\!\!\text{ }}{\text{ }\!\![\!\!\text{ Dimensions}\,\text{of}\,\text{charge }\!\!]\!\!\text{ }\,\text{ }\!\![\!\!\text{ Dimensions}\,\text{of}\,\text{current }\!\!]\!\!\text{ }}\] |
| \[=\frac{[M{{L}^{2}}{{T}^{-2}}]}{[IT]\,[I]}=[M{{L}^{2}}{{T}^{-3}}{{T}^{-2}}]\] |
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