A) \[[{{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{A}^{2}}]\]
B) \[[ML{{T}^{-3}}{{A}^{-1}}]\]
C) \[[M{{L}^{2}}{{T}^{-3}}{{A}^{-1}}]\]
D) \[[{{M}^{-1}}{{L}^{-2}}{{T}^{3}}{{A}^{-1}}]\]
Correct Answer: A
Solution :
The capacitance [C] of a conductor is defined as the ratio of charge [q] given to the rise in potential [V] of the conductor. That is \[C=\frac{q}{V}\] \[\therefore \]\[Farad=\frac{coulomb}{volt}=\frac{coulomb}{joule\text{ }/\text{ }coulomb}\] \[=\frac{coulom{{b}^{2}}}{joule}\] \[=\frac{{{(ampere-sec)}^{2}}}{newton-metre}=\frac{amper{{e}^{2}}-se{{c}^{2}}}{(kg-m\text{ }se{{c}^{-2}})\times metre}\] \[=\frac{amper{{e}^{2}}-se{{c}^{4}}}{kg-metr{{e}^{2}}}\] \[=k{{g}^{-1}}-metr{{e}^{-2}}-se{{c}^{4}}-amper{{e}^{2}}\] Hence, dimensions of capacitance are \[[{{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{A}^{2}}]\]
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