Which of the following
Question:

Which of the following is not a dimensionless quantity ?

  1. Relative magnetic permeability $\left(\mu_{\mathrm{r}}\right)$

  2. Power factor

  3. Permeability of free space $\left(\mu_{0}\right)$

  4. Quality factor


Correct Option: , 3

Solution:

$\left[\mu_{r}\right]=1$ as $\mu_{\Gamma}=\frac{\mu}{\mu_{m}}$

$[$ power factor $(\cos \phi)]=1$

$\mu_{0}=\frac{\mathrm{B}_{0}}{\mathrm{H}}\left(\right.$ unit $\left.=\mathrm{NA}^{-2}\right):$ Not dimensionless

$\left[\mu_{0}\right]=\left[\mathrm{MLT}^{-2} \mathrm{~A}^{-2}\right]$

quality factor $(\mathrm{Q})=\frac{\text { Energy stored }}{\text { Energy dissipated per cycle }}$

So $\mathrm{Q}$ is unitless \& dimensionless.

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