1Which of these has the same dimensions as impedance?
Impedance and inductive reactance both have the dimensions [M L² T⁻³ A⁻²].
Induction, AC and EM wavesClass 12, Alternating Current
Dimensional formula of Impedance
[M L2 T-3 A-2]
The total opposition of a circuit to alternating current, in ohm.
How to get the dimensional formula of impedance
- Start from the definition: impedance = electric potential / electric current.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- energy = mass × velocity2, so energy is [M] × [L T-1]2 = [M L2 T-2].
- electric charge = electric current × time, so electric charge is [A] × [T] = [T A].
- electric potential = energy / electric charge, so electric potential is [M L2 T-2] / [T A] = [M L2 T-3 A-1].
- Put in the dimension of each part: [M L2 T-3 A-1] / [A].
- Add the powers of each base quantity: [M L2 T-3 A-2].
Quantities with the dimensions [M L² T⁻³ A⁻²]
Equal dimensions do not make them the same quantity. Compare impedance with the others in the full grid.
Three questions on impedance
2What is the SI unit of impedance?
The SI unit of impedance is the ohm (Ω).
3Which one has different dimensions from the others?
Power factor is [M⁰ L⁰ T⁰]. The other three are all [M L² T⁻³ A⁻²].
Impedance: quick answers
What is the dimensional formula of impedance?
The dimensional formula of impedance is [M L² T⁻³ A⁻²]. It comes from impedance = electric potential / electric current.
What is the SI unit of impedance?
The SI unit of impedance is the ohm (Ω).
Which quantities have the same dimensions as impedance?
Impedance shares [M L² T⁻³ A⁻²] with electrical resistance, reactance, inductive reactance, capacitive reactance. Equal dimensions do not make them the same quantity.