If C and V represent capacity and voltage res | vedclass

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(D) Given $\lambda = \frac{C}{V}$.Since $C = \frac{Q}{V}$,we have $\lambda = \frac{Q}{V^{2}}$.We know that $V = \frac{W}{Q}$,where $W$ is work and $Q$

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

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(D) Given $\lambda = \frac{C}{V}$.Since $C = \frac{Q}{V}$,we have $\lambda = \frac{Q}{V^{2}}$.We know that $V = \frac{W}{Q}$,where $W$ is work and $Q$ is charge.Substituting $V$ in the expression for $\lambda$:$\lambda = \frac{Q}{(W/Q)^{2}} = \frac{Q^{3}}{W^{2}}$.Using dimensional formulas: $[Q] = [IT]$,$[W] = [ML^{2}T^{-2}]$.$\lambda = \frac{[IT]^{3}}{[ML^{2}T^{-2}]^{2}} = \frac{[I^{3}T^{3}]}{[M^{2}L^{4}T^{-4}]}$.$\lambda = [M^{-2} L^{-4} I^{3} T^{3 - (-4)}] = [M^{-2} L^{-4} I^{3} T^{7}]$.

If $C$ and $V$ represent capacity and voltage respectively,then what are the dimensions of $\lambda,$ where $\frac{C}{V} = \lambda$?

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