Question

Which of the following is not a dimensionless quantity ?

• A. Relative magnetic permeability $\left({\mu }_r\right)$
• B. Power factor
• C. Permeability of free space $\left({\mu }_0\right)$
• D. Quality factor

Answer 1

Answer: (C)

$\left[{\mu }_r\right]=1\text{ as }{\mu }_r=\frac{\mu }{{\mu }_m}$
$[$ power factor $(\cos \varphi )]=1$
${\mu }_0=\frac{B_0}{H}($ unit $=N{A}^{-2}):$
Not dimensionless
$\left[{\mu }_0\right]=\left[ML{T}^{-2}{A}^{-2}\right]$
quality factor $(Q)=\frac{\text{ Energystored }}{\text{ Energy dissipated per cycle }}$
So $Q$ is unitless & dimensionless.