1Which of these has the same dimensions as reactance?
Reactance and inductive reactance both have the dimensions [M L² T⁻³ A⁻²].
Induction, AC and EM wavesClass 12, Alternating Current
Dimensional formula of Reactance
[M L2 T-3 A-2]
The opposition of an inductor or a capacitor to alternating current. It has the dimension of resistance.
How to get the dimensional formula of reactance
- Start from the definition: reactance = 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 reactance with the others in the full grid.
Three questions on reactance
2What is the SI unit of reactance?
The SI unit of reactance is the ohm (Ω).
3Which one has different dimensions from the others?
Mutual inductance is [M L² T⁻² A⁻²]. The other three are all [M L² T⁻³ A⁻²].
Reactance: quick answers
What is the dimensional formula of reactance?
The dimensional formula of reactance is [M L² T⁻³ A⁻²]. It comes from reactance = electric potential / electric current.
What is the SI unit of reactance?
The SI unit of reactance is the ohm (Ω).
Which quantities have the same dimensions as reactance?
Reactance shares [M L² T⁻³ A⁻²] with electrical resistance, inductive reactance, capacitive reactance, impedance. Equal dimensions do not make them the same quantity.