Q 11-01-249JEE MainJEE Main 2025 (7 Apr, Shift 2)Easy
The dimension of $\sqrt{\dfrac{\mu_0}{\epsilon_0}}$ is equal to that of: ($\mu_0$ = vacuum permeability and $\epsilon_0$ = vacuum permittivity)
Answer: (D) Resistance
$L = \dfrac{\mu_0N^2A}{l}$ and $C = \dfrac{\epsilon_0A}{d}$, so $\dfrac{\mu_0}{\epsilon_0}$ has the dimensions of $\dfrac LC$.
$\dfrac LR$ and $RC$ are both times, so $\dfrac LC = \dfrac{(L/R)}{(RC)}R^2$ has the dimensions of $R^2$. Hence $\sqrt{\dfrac{\mu_0}{\epsilon_0}}$ has the dimensions of resistance (it is the impedance of free space, about $377\ \Omega$).
Solution by Sreeraj P, M.Sc Physics