Units & Dimensions

JEE Main level, single correct, medium

77 of 149

Question 77 of 149

If R,XLandXCR,{X}_{L}\text{and}{X}_{C} represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:

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Answer: (B) RXLXc\dfrac{R}{\sqrt{{X}_{L}{X}_{c}}}

As resistance, inductive reactance and capacitive reactance have same unit ohm. So, all three have same dimension.
Thus, RXLXC\dfrac{R}{\sqrt{{X}_{L}{X}_{C}}} is dimensionless.

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