The dimensional formula of capacitance is _____. Take $Q$ as the dimension formula of charge

M^{1} L^{- 2} T^{- 2} Q^{- 2}

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M^{1} L^{2} T^{- 2} Q^{- 2}

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M^{1} L^{- 2} T^{2} Q^{2}

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M^{- 1} L^{- 2} T^{2} Q^{2}

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Solution

The correct option is D $M^{- 1} L^{- 2} T^{2} Q^{2}$
We know that Capacitance is given as:
$C = \frac{Q}{V}$

The voltage is defined as the work done per unit charge.
$V = \frac{W}{Q}$

$⟹ C = \frac{Q^{2}}{W}$
$C = \frac{[Q^{2}]}{[M L^{2} T^{- 2}]} = [M^{- 1} L^{- 2} T^{2} Q^{2}]$

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Find the dimensional formulae of the capacitance C

Some of the equations containing these quantities are

Q = It, U = VIt, Q = CV and V = RI;

Where 'I' denote the electric current, 't' is time and 'U' is energy.

Energy has the dimension of Force x displacement

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