Relative magnetic permeability (μr) It is the ratio of permeability of medium to the permeability of free space i.e.,
μr= As, it is a ratio of permeabilities. So, it is unitless and dimensionless quantity.
Power factor (cos‌ϕ) It is cosine of phase difference between alternating current and alternating voltage. Hence, it has only a numerical value, so it is also a unitless and dimensionless quantity.
Permeability of free space (μ0) It is the ratio of magnetising field induction (B) to magnetising field intensity (H)
i.e.
μ0= ⇒[μ0]= ...(i)
Since,
H=nl where, n = number of turns per unit length
and I = current
∴[H]=[n][I] =[L−1][A]=[AL−1] We know that, force on a current carrying conductor in magnetic field B is given as
F = IBl
where, l = length of the conductor,
B = magnetic field
and I = current.
∴B= ⇒[B]===[MT−2A−1] ∴From Eq. (i), we have
[μ0]==[MLT−2A−2] Hence, permeability of free space is not a dimensionless quantity.
Quality factor It is the ratio of energy stored to the energy dissipated per cycle.
Quality factor
=| Energy‌stored |
| Energy‌dissipated‌per‌c‌ycle |
As, it is ratio of energies so, it will be unitless and dimensionless quantity.