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# Solve this following

Question:

If ' $C^{\prime}$ and ' $V^{\prime}$ represent capacity and voltage respectively then what are the dimensions of

$\lambda$, where $\frac{\mathrm{C}}{\mathrm{V}}=\lambda$ ?

1. $\left[\mathrm{M}^{-2} \mathrm{~L}^{-3} \mathrm{I}^{2} \mathrm{~T}^{6}\right]$

2. $\left[\mathrm{M}^{-3} \mathrm{~L}^{-4} \mathbf{I}^{3} \mathrm{~T}^{7}\right]$

3. $\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{I}^{-2} \mathrm{~T}^{-7}\right]$

4. $\left[\mathrm{M}^{-2} \mathrm{~L}^{-4} \mathrm{I}^{3} \mathrm{~T}^{7}\right]$

Correct Option: , 4

Solution:

$\lambda=\frac{\mathrm{C}}{\mathrm{V}}=\frac{\mathrm{Q} / \mathrm{V}}{\mathrm{V}}=\frac{\mathrm{Q}}{\mathrm{V}^{2}}$

$\mathrm{V}=\frac{\text { work }}{\mathrm{Q}}$

$\lambda=\frac{\mathrm{Q}^{3}}{(\text { work })^{2}}=\frac{(\mathrm{It})^{3}}{(\text { F.s })^{2}}$

$=\frac{\left[\mathrm{I}^{3} \mathrm{~T}^{3}\right]}{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]^{2}}=\left[\mathrm{M}^{-2} \mathrm{~L}^{-4} \mathrm{I}^{3} \mathrm{~T}^{7}\right]$