JEE Main · 2025 · 07 Apr 2025 · Shift 2 · Units & Measurement

The quantity $\sqrt{{\mu }_0/{ϵ}_0}$ is the characteristic impedance of free space. Since an inductance carries a factor of ${\mu }_0$ and a capacitance a factor of ${ϵ}_0$, the combination $\sqrt{{\mu }_0/{ϵ}_0}$ shares the dimensions of $\sqrt{L/C}$; and because $\omega L$ and $1/(\omega C)$ are both resistances, $\sqrt{L/C}$ has the dimension of resistance. Hence $\sqrt{{\mu }_0/{ϵ}_0}$ has the dimension of resistance.