Physics

# A quantity $X$ is given by $\epsilon_0 L\dfrac {\Delta V}{\Delta t}$, where $\epsilon_0$ is the permittivity of fee space, $L$ is 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
Dimensional formula for $\epsilon_0 = [M^{-1} L^{-3} T^{4} I^{2}]$
Dimensional formula for $L = [L]$
Dimensional formula for $\Delta V = [M L^2 T^{-3} I^{-1}]$
Dimensional formula for $\Delta t = [T^{1}]$
Therefore, dimensional formula for $X$ is: $\dfrac{ [M^{-1} L^{-3} T^{4} I^{2}] [L] [M L^2 T^{-3} I^{-1}] }{ [T^{1}] }=[I]$
Therefore, its the same as that of current.

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