Dimensional formula of Quality factor

How to get the dimensional formula of quality factor

1. Start from the definition: quality factor = reactance / resistance.
2. velocity = length / time, so velocity is [L] / [T] = [L T^-1].
3. energy = mass × velocity², so energy is [M] × [L T^-1]² = [M L² T^-2].
4. electric charge = electric current × time, so electric charge is [A] × [T] = [T A].
5. electric potential = energy / electric charge, so electric potential is [M L² T^-2] / [T A] = [M L² T^-3 A^-1].
6. reactance = electric potential / electric current, so reactance is [M L² T^-3 A^-1] / [A] = [M L² T^-3 A^-2].
7. electrical resistance = electric potential / electric current, so electrical resistance is [M L² T^-3 A^-1] / [A] = [M L² T^-3 A^-2].
8. Put in the dimension of each part: [M L² T^-3 A^-2] / [M L² T^-3 A^-2].
9. Add the powers of each base quantity: [M⁰ L⁰ T⁰].

Quantities with the dimensions [M⁰ L⁰ T⁰]

• Angle
• Solid angle
• Coefficient of friction
• Coefficient of restitution
• Relative density
• Strain
• Poisson's ratio
• Reynolds number
• Emissivity
• Ratio of specific heats
• Sound level
• Relative permittivity
• Magnetic susceptibility
• Relative permeability
• Power factor
• Refractive index
• Magnification

Equal dimensions do not make them the same quantity. Compare quality factor with the others in the full grid.

Three questions on quality factor

Related quantities

• L Self inductance [M L² T⁻² A⁻²]
• M Mutual inductance [M L² T⁻² A⁻²]
• X Reactance [M L² T⁻³ A⁻²]
• X_L Inductive reactance [M L² T⁻³ A⁻²]
• X_C Capacitive reactance [M L² T⁻³ A⁻²]
• Z Impedance [M L² T⁻³ A⁻²]