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JEE Main 202331 JanuaryMorning Shift

Exam: JEE Main
Year: 2023
Date: 31 January
Shift: Morning Shift
Subject: Physics
Chapter: Units and Dimensions

JEE Main 2023 · 31 January · Morning Shift · Physics · Units and Dimensions

If R, X _ L and X _ C represent resistance, inductive reactance and...

If

R, {X}_{L}\text{and}{X}_{C}

represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:

Options

A $R{X}_{L}{X}_{C}$
B $\dfrac{R}{\sqrt{{X}_{L}{X}_{c}}}$
C $\dfrac{R}{{X}_{L}{X}_{c}}$
D $R\dfrac{{X}_{L}}{{X}_{c}}$

Correct answer

B. $\dfrac{R}{\sqrt{{X}_{L}{X}_{c}}}$

Step-by-step solution

As resistance, inductive reactance and capacitive reactance have same unit ohm. So, all three have same dimension.

Thus, $\dfrac{R}{\sqrt{{X}_{L}{X}_{C}}}$ is dimensionless.

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