The dimensional formula of capacitance is:

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Question

(A) The capacitance $C$ is defined as the ratio of charge $Q$ to potential difference $V$,given by $C = \frac{Q}{V}$.Since $V = \frac{W}{Q}$,where $W$

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$M^{-1}L^{-2}T^4A^2$

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(A) The capacitance $C$ is defined as the ratio of charge $Q$ to potential difference $V$,given by $C = \frac{Q}{V}$.Since $V = \frac{W}{Q}$,where $W$ is work done,we can write $C = \frac{Q^2}{W}$.The dimensional formula for charge $Q$ is $[A^1T^1]$.The dimensional formula for work $W$ is $[M^1L^2T^{-2}]$.Substituting these into the formula: $C = \frac{[A^1T^1]^2}{[M^1L^2T^{-2}]} = \frac{[A^2T^2]}{[M^1L^2T^{-2}]}$.Simplifying the expression,we get $[C] = [M^{-1}L^{-2}T^4A^2]$.

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