Q 11-01-131JEE MainJEE Main 2023 (31 Jan, Shift 1)Easy
If $R$, $X_L$ and $X_C$ represent resistance, inductive reactance and capacitive reactance, then which of the following is dimensionless?
Answer: (B) $\dfrac{R}{\sqrt{X_LX_C}}$
$R$, $X_L$ and $X_C$ all have the dimensions of resistance. $\sqrt{X_LX_C}$ is also a resistance, so $\dfrac{R}{\sqrt{X_LX_C}}$ is dimensionless. The other combinations have dimensions of $R^3$, $R^{-1}$ and $R$.
Solution by Sreeraj P, M.Sc Physics