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.


ANSWER

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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