Power — Work, Energy and Power

1. What Is Power?

Power tells us how fast work is done or how quickly energy is used. Two people may do the same work, but the one who finishes faster has more power.

In simple words: Power = speed of doing work.

1.1. Power and Effort

Doing a lot of work slowly means low power. Doing the same work quickly means high power.

Example: Climbing stairs faster means using more power.

2. Mathematical Definition of Power

The formula for power is:

\( P = \dfrac{W}{t} \)

where:

\( P \) = power
\( W \) = work done
\( t \) = time taken

2.1. Understanding the Formula

If work increases, power increases. If time increases, power decreases.

For the same work, doing it in less time means more power.

3. Relation Between Power and Energy

Since work is energy transfer, we can also write:

\( P = \dfrac{E}{t} \)

This shows that power also tells us how fast energy is being used.

3.1. Examples

An electric bulb uses electrical energy quickly → higher power rating.
A mobile charger uses energy slowly → lower power rating.

4. Units of Power

The SI unit of power is the Watt (W).

1 Watt = 1 Joule of work done in 1 second.

4.1. Larger Units

kilowatt (kW) = 1000 W
megawatt (MW) = 1,000,000 W

4.2. Beyond Common Units: Horsepower

Machines and automobiles often use horsepower (hp):

1 hp ≈ 746 W

5. Average Power

When work is not done at a constant rate, we talk about average power:

\( P_{avg} = \dfrac{W_{total}}{t_{total}} \)

5.1. Example

If a machine uses 300 J of energy in 10 seconds:

\( P = \dfrac{300}{10} = 30 \text{ W} \)

6. Instantaneous Power

Instantaneous power describes how much power is being used at a specific moment.

It is given by:

\( P = Fv \)