1.1.4 Power

In this lesson, you will learn what power is, why some systems are more powerful than others, and how to calculate power. You will also explore how the concept of power is applied to real-world examples to help you appreciate how important power is in understanding the world around us.

What is Power?

We can define power in two ways:

1. Power is the rate at which energy is transferred.
2. Or, power is the rate at which work is done.

If you keep in mind that work done just means energy transferred, you will realise that both of these definitions of power mean the same thing. Rate means how much something happens in a certain amount of time. Since power is the rate of energy transferred (or work done), we can think of power as how much energy is transferred in a certain amount of time. This means that how much power there is or how powerful a system is, is dependent on two things:

1. The amount of energy transferred (or work done) in a certain amount of time. If system A transfers more energy in the same amount of time as system B, system A is more powerful.
2. How much time did it take for the energy to be transferred (or for the work to be done). If system C transferred the same amount of energy as system D, but system C transferred the energy in a shorter amount of time than system D, then system C is more powerful.

From the definition of power that you have just learned, we also get watts (W) which is the unit of power. 1 watt (1 W) is the same as 1 joule per second (or 1 J/s). Watts reflect how power is the same as energy transferred (measured in joules) per time (measured in seconds).

Calculating Power

There are two formulas to calculate power shown in Equation 6 and Equation 7 below. Equation 6 is used when you are given the energy transferred, while Equation 7 is used when you are given the work done.

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

or

The formula for calculating the power of a system from energy transferred has three components:

1. \(P\) is the power of the system and has units of watts (W).
2. \(E\) is the energy transferred and has units of joules (J).
3. \(t\) is the time in which the energy was transferred. \(t\) must always have units of seconds (s) when used in this equation.

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

or

The formula for calculating the power of a system from work done has three components:

1. \(P\) is the power of the system and has units of watts (W).
2. \(W\) is the work done and has units of joules (J).
3. \(t\) is the time in which the work was done and has units of seconds (s).

Power in Everyday Life

In everyday life, when we think of systems and how powerful they are we usually talk about machines. The more powerful a machine is, the more energy it can transfer in a shorter amount of time. Below are two examples that compare the power of different machines and demonstrate what power is.

Electric Motors Lifting a Weight: Imagine two electric motors, motor A and motor B. Both motors are lifting the same weight through the same height. To lift the same weight through the same height, both motors need to do the same amount of work (or transfer the same amount of energy). However, motor A is able to lift the weight and complete the task faster than motor B. Even though both motors transferred the same amount of energy, since motor A did it faster (or in a smaller amount of time), motor A is more powerful than motor B.

Electric Kettles of Different Power Ratings: Different electric appliances can have different power ratings. A power rating indicates how much power an appliance is able to produce or the rate at which it transfers energy. If electric kettles of brand C have a higher power rating than electric kettles of brand D, the kettle of brand C can boil water faster than the kettle of brand D. Therefore, kettles of brand C are more powerful than kettles of brand D.