Physics

# A quantity X is given by $\varepsilon_oL\dfrac{\Delta V}{\Delta L}$ where $\varepsilon_o$ is the permittivity of free space. L is a length, $\Delta V$ is a potential difference and $\Delta t$ is a time interval. The dimensional formula for X is the same as that of.

Current

##### SOLUTION
Given,

$X=\epsilon_0 L\dfrac{\Delta V}{\Delta L}$

Dimensional formula for $\epsilon_0=[M^{-1}L^{-3}T^3I^2]$

Dimensional formula for $L=[L]$

Dimensional formula for $\Delta V=[ML^2T^{-3}I^{-1}]$

Dimensional formula for $\Delta t=[T^{-1}]$

$\therefore$ Dimensional formula for $X=\dfrac{[M^{-1}L^{-3}T^4I^2][L][ML^2T^{-3}I^{-1}]}{[T^1]}=[I]$

So, the dimensional formula of $X$ is same as that of current.

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