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 $(\cos \phi)]=1$
$\mu_{0}=\frac{ B _{0}}{ H }\left(\right.$ unit $\left.= NA ^{-2}\right):$
Not dimensionless
$\left[\mu_{0}\right]=\left[ MLT ^{-2} A ^{-2}\right]$
quality factor $( Q )=\frac{\text { Energystored }}{\text { Energy dissipated per cycle }}$
So $Q$ is unitless & dimensionless.