Power is the rate at which work is done or the rate at which energy is supplied or used. Like work and energy, power is also a scalar quantity.

The** SI unit** for power is Joules per second (**Js**^{-1}), which is defined to be a Watt (W). So 1 W = 1 J/s. There are other popular units like Kilowatt and horsepower. 1 kilowatt = 1000 Watt and 1 Horsepower = 746 Watt.

## The formula of Power – as the rate of work done or rate of energy supplied

When we define power as the rate of work done or rate of energy supplied (or used) we get the following formulas:**A) Average Power**

Average Power = Work done during some time interval / Duration of time interval ……………… (1)

Average Power = Total Energy supplied or used during some time interval / Duration of time interval ………… (2)

B)** Instantaneous Power**

The rate at which work is done might not be constant. We define instantaneous power P as the quotient in Eq. (1) as Δt approaches zero:

## Power in terms of force and velocity

In mechanics, we can also express power in terms of force and velocity.

Suppose that a force ** F** acts on an object while it undergoes a vector displacement

**Δ**. If

*s*

*F*_{||}is the component of

**tangent to the path (parallel to**

*F***Δ**

*), then the work done by the force is ΔW =*

**s***F*

_{||}Δs.

The average power is P

_{av}=(

*F*

_{||}Δs)/Δt =

*F*

_{||}(Δs/Δt) =

*F*

_{||}

*v*

_{av}……………… (a)

Instantaneous power P is the limit of this expression as Δt ->0

P =

*F*

_{||}

*v*………………(b)

where v is the magnitude of the instantaneous velocity.

We can also express Eq. (b) in terms of the scalar product:

## Power – Solve a Numerical Example

A box with a mass of 30 kg can be lifted by a light rope threaded through a smooth pulley.

(a) If the box is lifted at a constant speed from the ground to a height of 2.0 m in 4.0 s, what is the power required?

(b) If the box is lifted with a constant acceleration of 1.5 m/s2 from rest to a height of 3.0 m above the floor, what is the power required? Take g, the gravitational field strength as 10 N/kg.

Solution:

**Concepts of power from ratings of electric devices **

We may understand well its *concept from its use in electrical energy*. Electric lights and other devices are given a rating based on the power they use, as in a 60 W light bulb or a 200 W motor.

**Calculating Electrical Energy consumption & Units like KW-h**

Some electric utility providers measure energy in units of **kW⋅h**. This is a non-SI unit, but it *makes sense for energy delivery.* If power is energy/time, then energy is power × time, so kW⋅h is a valid measure of energy. If you run your 100 W light bulb for 20 h, you’ll use 100 W × 20 h = 2000 W⋅h = 2 kW⋅h of energy.