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JEE Main 2023 (31 Jan, Shift 1) · Series LCR Circuit

Series LCR Circuit question from JEE Main 2023 (31 Jan, Shift 1)

Q37JEE Main 2023 · 31 JAN · SHIFT 1Easy

Series LCR Circuit

If $R, X_L$ , and $X_C$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:

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Answer: (c)

$R$ , $X_L$ and $X_C$ all have the unit ohm.
$\frac{R}{\sqrt{X_L X_C}}$ has unit $\frac{\Omega}{\sqrt{\Omega^2}} =$ dimensionless; the others have $\Omega^{-1}$ , $\Omega^3$ , $\Omega$ .
So the answer is (c).

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