1Which of these has the same dimensions as inductive reactance?
Inductive reactance and reactance both have the dimensions [M L² T⁻³ A⁻²].
Induction, AC and EM wavesClass 12, Alternating Current
Dimensional formula of Inductive reactance
[M L2 T-3 A-2]
The opposition of an inductor to alternating current, X_L = ωL. It has the dimension of resistance.
How to get the dimensional formula of inductive reactance
- Start from the definition: inductive reactance = angular frequency × self inductance.
- angle = length / length, so angle is [L] / [L] = [M0 L0 T0].
- frequency = 1 / time, so frequency is 1 / [T] = [T-1].
- angular frequency = angle × frequency, so angular frequency is [M0 L0 T0] × [T-1] = [T-1].
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- acceleration = velocity / time, so acceleration is [L T-1] / [T] = [L T-2].
- force = mass × acceleration, so force is [M] × [L T-2] = [M L T-2].
- Put in the dimension of each part: [T-1] × [M L2 T-2 A-2].
- 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 inductive reactance with the others in the full grid.
Three questions on inductive reactance
2What is the SI unit of inductive reactance?
The SI unit of inductive reactance is the ohm (Ω).
3Which one has different dimensions from the others?
Quality factor is [M⁰ L⁰ T⁰]. The other three are all [M L² T⁻³ A⁻²].
Inductive reactance: quick answers
What is the dimensional formula of inductive reactance?
The dimensional formula of inductive reactance is [M L² T⁻³ A⁻²]. It comes from inductive reactance = angular frequency × self inductance.
What is the SI unit of inductive reactance?
The SI unit of inductive reactance is the ohm (Ω).
Which quantities have the same dimensions as inductive reactance?
Inductive reactance shares [M L² T⁻³ A⁻²] with electrical resistance, reactance, capacitive reactance, impedance. Equal dimensions do not make them the same quantity.