JEE MAIN - Physics (2023 - 31st January Morning Shift - No. 11)
If $$\mathrm{R}, \mathrm{X}_{\mathrm{L}}$$, and $$\mathrm{X}_{\mathrm{C}}$$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless :
$$\frac{R}{X_{L} X_{C}}$$
$$R X_{L} X_{C}$$
$$\frac{R}{\sqrt{X_{L} X_{C}}}$$
$$R \frac{X_{L}}{X_{C}}$$
Explanation
$R=$ Resistance
$$ \begin{aligned} & {\left[X_{L}\right]=[R]} \\\\ & {\left[X_{C}\right]=[R]} \end{aligned} $$
So, $\frac{R}{\sqrt{X_{L} X_{C}}}$ is dimensionless.
$$ \begin{aligned} & {\left[X_{L}\right]=[R]} \\\\ & {\left[X_{C}\right]=[R]} \end{aligned} $$
So, $\frac{R}{\sqrt{X_{L} X_{C}}}$ is dimensionless.
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