If ‘C’ and ‘V’ represent capacity and voltage respectively then what are the dimensions of $λ$ where C / V= $λ$ ?

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$[M^{- 2} L^{- 4} I^{3} T^{7}]$

$[M^{- 1} L^{- 3} I^{- 2} T^{- 7}]$

$[M^{- 3} L^{- 4} I^{3} T^{7}]$

$[M^{- 2} L^{- 3} I^{2} T^{6}]$

answer is A.

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Detailed Solution

$\begin{array}{l} Voltage, V = \frac{W}{Q} = \frac{[M L^{2} T^{- 2}]}{[I T]} = [M L^{2} T^{- 3} I^{- 1}] \\ Capacitance, C = \frac{Q}{V} = \frac{[I T]}{[M L^{2} T^{- 3} /^{- 1}]} = [M^{- 1} L^{- 2} T^{4} I^{2}] \\ So, λ = \frac{C}{V} = \frac{[M^{- 1} L^{- 2} T^{4} l^{2}]}{[M L^{2} T^{- 3} I^{- 1}]} = [M^{- 2} L^{- 4} T^{7} I^{3}] \end{array}$