If ' C and ' V ' represent capacity and voltage respectively then

Question:

If ' $C^{\prime}$ and ' $\mathrm{V}$ ' represent capacity and voltage respectively then what are the dimensions of $\lambda$ where $C / V=\lambda$ ?

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

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

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

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


Correct Option: 1,

Solution:

(1)

$\because v=\frac{w}{q}$ and $c=\frac{q}{v}$

dimension of $\frac{c}{v}$

$\Longrightarrow \frac{q}{v^{2}}$

$\Rightarrow \frac{q}{w^{2}} \times q^{2} \Rightarrow \frac{q^{3}}{w^{2}}$

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

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