1Which of these has the same dimensions as power?
Power and heat flow rate both have the dimensions [M L² T⁻³].
MechanicsClass 11, Work, Energy and Power
Dimensional formula of Power
[M L2 T-3]
Work done per unit time. One watt is one joule per second.
How to get the dimensional formula of power
- Start from the definition: power = work / time.
- 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].
- displacement = length, so displacement is [L] = [L].
- work = force × displacement, so work is [M L T-2] × [L] = [M L2 T-2].
- Put in the dimension of each part: [M L2 T-2] / [T].
- Add the powers of each base quantity: [M L2 T-3].
Quantities with the dimensions [M L² T⁻³]
Equal dimensions do not make them the same quantity. Compare power with the others in the full grid.
Three questions on power
2What is the SI unit of power?
The SI unit of power is the watt (W).
3Do power and coefficient of friction have the same dimensions?
Power is [M L² T⁻³] but coefficient of friction is [M⁰ L⁰ T⁰].
An equation that uses power
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
P = I2 RP[M L2 T-3]=I2 R[M L2 T-3]Dimensionally consistentEvery term is [M L2 T-3]
Power: quick answers
What is the dimensional formula of power?
The dimensional formula of power is [M L² T⁻³]. It comes from power = work / time.
What is the SI unit of power?
The SI unit of power is the watt (W).
Which quantities have the same dimensions as power?
Power shares [M L² T⁻³] with heat flow rate. Equal dimensions do not make them the same quantity.