1Which of these has the same dimensions as electrical resistance?
Electrical resistance and impedance both have the dimensions [M L² T⁻³ A⁻²].
Current electricityClass 12, Current Electricity
Dimensional formula of Electrical resistance
[M L2 T-3 A-2]
Potential difference divided by current, from V = IR. The ohm is volt per ampere.
How to get the dimensional formula of electrical resistance
- Start from the definition: electrical resistance = 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 electrical resistance with the others in the full grid.
Three questions on electrical resistance
2What is the SI unit of electrical resistance?
The SI unit of electrical resistance is the ohm (Ω).
3Which one has different dimensions from the others?
Current density is [L⁻² A]. The other three are all [M L² T⁻³ A⁻²].
An equation that uses electrical resistance
Equation checker
Matching dimensions are necessary, not sufficient. A check cannot see pure numbers such as 1/2 or 2π, so a consistent equation can still be wrong.
Read as
V = I RV[M L2 T-3 A-1]=IR[M L2 T-3 A-1]Dimensionally consistentEvery term is [M L2 T-3 A-1]
Electrical resistance: quick answers
What is the dimensional formula of electrical resistance?
The dimensional formula of electrical resistance is [M L² T⁻³ A⁻²]. It comes from electrical resistance = electric potential / electric current.
What is the SI unit of electrical resistance?
The SI unit of electrical resistance is the ohm (Ω).
Which quantities have the same dimensions as electrical resistance?
Electrical resistance shares [M L² T⁻³ A⁻²] with reactance, inductive reactance, capacitive reactance, impedance. Equal dimensions do not make them the same quantity.