3-1 Energy and Power

Energy

So far we've mentioned energy a couple of times. Remember, the whole point of electric current is to carry energy from a source to a load, through a conductor. Here's a basic electric circuit:

We recognize the parts of the circuit: the source on the left, the switch at the top (here it's drawn in the open position, not allowing current to flow), and the load (in this case, a light bulb).

Let's think about the source, in this case a 2-cell battery.

When you take the cells that make up the battery out of the package, they are full of energy.

You put them into an electronic device, you use it for a while. When they're "dead," you dispose of them or recharge them, depending on the type of cell or battery you have. But what does that mean when a cell or battery is "dead?" It wasn't "alive" to begin with, after all.

Let's look at what makes up a cell like this. It's dangerous to cut into these cells, as the chemicals inside them are not particularly nice, so let's look at a cut-away view that someone else has made.

Different kinds of cells have different types of materials inside them, but they're all basically built like this. What happens is a very slow chemical change, which releases energy out of the terminals of the cell. When the chemicals are all used up, the cell can't put any more energy out, and it's no longer useful to us.

A car battery has a different structure, but it does the same thing: it provides energy to the car's electrical systems.

(The car battery in the picture is shown with "jumper cables" attached, which you can use to help start another car which has a dead car battery. Be sure to connect the jumper cables in the right order and to the right place; a car's instruction manual will have directions.)

Remember, energy has a unit of joules (J), and a symbol of E. So if you wanted to say that a load used an energy of 25 J, you would write it like this: E = 25 J

There's actually another unit of energy which is more useful to us when we're looking at larger amounts -- the type you would buy from an electricity provider to your home -- but we'll get to those later.

Power

Consider these three light bulbs. All of them are about the same brightness, but they all create light differently.

The left bulb will take in 100 J of energy in about 2.5 s (seconds). The middle one will take in the same amount of energy in about 7.7 s. The one on the right needs 11 s to take in 100 J of energy.

For all three bulbs, we can say this:

E = 100 J

But obviously there's a difference! The key is to look at a part of the bulb that talks about its power, how much energy it takes in per second. The symbol for power is P.

The number with the "W" is the power rating of the bulb, measured in watts: one watt (W) is one joule per second. So, if we want to write out the power rating of the left bulb we write it like this: P = 40 W

There is a formula that relates energy (E, in joules), power (P, in watts) and time (t, in seconds):

Example: An electric pencil sharpener takes 4.5 s to sharpen a pencil, and it takes in 228 J of energy in that time. What is the sharpener's power rating, in watts?

t = 4.5 s

E = 228 J

P = ?

P = E/t = (228 J)/(4.5 s) = 51 W

A more useful unit of power

Joules are great for short periods of time or small devices. But, here's an electricity bill from Toronto Hydro, and you won't see any joules on it:

If we zoom in on the part which actually shows how much energy was purchased, you see another unit of energy: the kilowatt-hour, abbreviated kW·h. (Sometimes the dot is left out, but it truly does belong there.)

But, what does this mean?

In order to see what a kilowatt-hour is, we have to rearrange the power formula above, to solve for energy.

Consider this:

• Watts are small, but kilowatts (kW) are 1000 times bigger.

• Seconds are small, but hours (h) are 3600 times bigger.

If an electrical device has a power rating of 1 kW, and it's being used for 1 h, the amount of energy is defined as 1 kilowatt-hour:

Example: An electric hair dryer is used for a total of 2.5 h in a month. The power rating of the hair dryer is 1600 W. How much energy did it use in that month?

Here we have to decide what units to use... the small units (joules, watts and seconds) or the big units (kilowatt-hours, kilowatts and hours)? Since the power is pretty big, let's convert that into kilowatts by dividing by 1000, then use the big units.

P = 1600 W = 1.6 kW

t = 2.5 h

E = ?

E = Pt = (1.6 kW)(2.5 h) = 4.0 kW·h

Practice

The Basics

1. What does it mean when we say that a cell or battery is "dead?"

2. A battery-powered electric fan uses 45 J of energy in 14 s. What is the fan's power rating, in watts?

3. How much energy does a spotlight use in 8.0 h, if it is rated at a power of 2.2 kW?

Extensions

1. Do some online research to see what the difference is between alkaline, carbon-zinc and lithium-ion batteries and cells.

2. Two elevators in an apartment building have two different electric motors. Elevator motor #1 uses 22.8 kW·h of energy in 11.3 h of operation, and elevator motor #2 uses 51.9 kW·h in 28.6 h of operation. Which one has the lower power rating?