Numford

Induction, AC and EM wavesClass 12, Alternating Current

Dimensional formula of Capacitive reactance

[M L2 T-3 A-2]

SymbolXC SI unitohm (Ω)

The opposition of a capacitor to alternating current, X_C = 1/ωC. It has the dimension of resistance.

Derivation

How to get the dimensional formula of capacitive reactance

  1. Start from the definition: capacitive reactance = 1 / (angular frequency × capacitance).
  2. angle = length / length, so angle is [L] / [L] = [M0 L0 T0].
  3. frequency = 1 / time, so frequency is 1 / [T] = [T-1].
  4. angular frequency = angle × frequency, so angular frequency is [M0 L0 T0] × [T-1] = [T-1].
  5. electric charge = electric current × time, so electric charge is [A] × [T] = [T A].
  6. velocity = length / time, so velocity is [L] / [T] = [L T-1].
  7. energy = mass × velocity2, so energy is [M] × [L T-1]2 = [M L2 T-2].
  8. Put in the dimension of each part: 1 / ([T-1] × [M-1 L-2 T4 A2]).
  9. Add the powers of each base quantity: [M L2 T-3 A-2].
Same dimensions

Quantities with the dimensions [M L² T⁻³ A⁻²]

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

Practice

Three questions on capacitive reactance

1Which of these has the same dimensions as capacitive reactance?

2What is the SI unit of capacitive reactance?

3Which one has different dimensions from the others?

Questions

Capacitive reactance: quick answers

What is the dimensional formula of capacitive reactance?

The dimensional formula of capacitive reactance is [M L² T⁻³ A⁻²]. It comes from capacitive reactance = 1 / (angular frequency × capacitance).

What is the SI unit of capacitive reactance?

The SI unit of capacitive reactance is the ohm (Ω).

Which quantities have the same dimensions as capacitive reactance?

Capacitive reactance shares [M L² T⁻³ A⁻²] with electrical resistance, reactance, inductive reactance, impedance. Equal dimensions do not make them the same quantity.

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