A) \[\left[ {{M}^{-1}}{{L}^{2}}{{T}^{-4}}{{I}^{2}} \right]\]
B) \[\left[ {{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{I}^{2}} \right]\]
C) \[\left[ M{{L}^{2}}{{T}^{4}}{{I}^{2}} \right]\]
D) \[\left[ M{{L}^{2}}{{T}^{-4}}{{I}^{-2}} \right]\]
Correct Answer: C
Solution :
Capacitance \[C=\frac{Ch\arg e}{Potential}=\frac{q}{V}=\frac{Q}{W/q}=\frac{{{q}^{2}}}{W}\] Dimensions of \[\text{C = }\frac{{{\text{(Dimensions}\,\text{of}\,\text{charge)}}^{\text{2}}}}{\text{Dimensions}\,\text{of}\,\text{work}}\] \[=\frac{{{[IT]}^{2}}}{[M{{L}^{2}}{{T}^{-2}}]}\] \[=\frac{[{{I}^{2}}{{T}^{2}}]}{[M{{L}^{2}}{{T}^{-2}}]}\] \[=[{{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{I}^{2}}]\]
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