Which of the following is not a dimensionless | vedclass

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(C) Relative magnetic permeability $(\mu_{r} = \mu / \mu_{0})$ is the ratio of two similar quantities,so it is dimensionless.Power factor $(\cos \phi)

Vedclass · Accepted Answer

Permeability of free space $(\mu_{0})$

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(C) Relative magnetic permeability $(\mu_{r} = \mu / \mu_{0})$ is the ratio of two similar quantities,so it is dimensionless.Power factor $(\cos \phi)$ is the ratio of resistance to impedance,so it is dimensionless.Permeability of free space $(\mu_{0})$ has the $SI$ unit of $N A^{-2}$ or $T m A^{-1}$. Its dimensional formula is $[M L T^{-2} A^{-2}]$. Therefore,it is not a dimensionless quantity.Quality factor $(Q)$ is defined as the ratio of energy stored to energy dissipated per cycle,making it dimensionless.Thus,the correct option is $C$.

Which of the following is not a dimensionless quantity?

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