In this lesson, we’re learning
about power and energy and our focus is from analytical perspective. We’ve seen how these terms relate
to mechanical processes such as pushing a stone up a hill or climbing a set of
stairs. Here, we’re going to see how to
work with power and energy in an electric circuit or an electric appliance. Let’s start off by recalling a
couple of definitions.
First, the definition of energy,
energy is the ability to do work. For example, if you were to start
at the bottom of a staircase and then climb to the top of it, that would mean you
had supplied the energy to do some amount of work against the gravitational force
pulling you down. Notice that this definition for
energy has nothing to do with how long it would take for you to get from the bottom
of the staircase to the top. In fact, that’s where power comes
Power is defined as the amount of
energy used over a certain time. So for example, if you were to
climb up these steps two times, the first time taking five seconds to do it and the
second time taking half that amount 2.5 seconds, then even though in both cases you
would use the same amount of energy, you wouldn’t use the same amount of power. In the first case when climbing the
stairs took five seconds, you would have used half as much power as you used when it
took 2.5 seconds. The waiver in this definition for
power in words often is expressed as a mathematical equation that the power 𝑃 is
equal to the amount of energy used 𝐸 divided by the time elapsed 𝑡.
Considering the units in this
expression, we know that the units of energy are joules symbolized by a capital
𝐽. By the way, that’s the same unit as
the unit for work, showing how closely energy and work are related. The base unit for time is seconds
and the unit for power we know is watts symbolized by capital 𝑊. We can see from this equation that
one watt is equal to one joule per second.
So far, all of this discussion has
had to do with a mechanical form of energy and a mechanical form of power. But of course, energy and power can
exist in electrical form as well. Just think of any electrical
appliance you might have, like a toaster or a television or a microwave. All of these and every other
electrical appliance uses some amount of energy and it uses that energy over some
time interval. Therefore, it has a power
When we think about energy and
power in an electrical context, the question may come up just what is electrical
work or what does work look like for an electrical system. To understand that, we can think
back to the basics of electricity: positive and negative charges. We know that oppositely charged
particles will attract one another and that particles with a similar charge will
repel one another. So that’s a natural tendency. Now, let’s say we try to resist
that natural tendency or work against it.
For example, let’s say we took this
positive charge here that wants to move off to the right under the repulsive
influence of this other positive charge. We’ll see we take this first charge
and instead we start to push it towards the left. If we pushed hard enough, indeed we
could close the gap between these two positive charges. If we did that, we’ll be going
against the natural inclination of these charges to push one another apart.
Going back to our picture on the
opening screen of a person pushing a stone up a hill, this is a bit like what it
would be like to push this positive charge towards the other positive charge. The charge just like the stone
wants to move in a certain direction due to the force field that it’s in. But we resist to that motion and in
fact push it the opposite way. We do work.
If we were the ones doing the work
on this positive charge, then we could say that as it gets closer to the other one,
we do positive work. And as it moves away from the other
one, we do negative work and this work is a measure of the energy that we’re putting
into the system. And if that energy for moving
charge is released over some amount of time, then we have electrical power.
One place that we may have seen
electrical power reference before is if we’ve ever gone to buy a box of light bulbs,
usually the power rating of the bulb is printed on the box. This power rating shows how much
electrical energy the bulb consumes over time and corresponds to the brightness of
the bulb. Knowing all this, let’s get some
practice now working with a few examples of electrical power and energy.
A 60-watt incandescent light
bulb is left on for 30 seconds. How much energy is supplied to
it over this time?
We have this light bulb then
that uses up 60 watts of power. If we recall that power is
equal to energy divided by time and that the units of power are watts, the units
of energy are joules, the units of time are seconds, then we can see that the
fact that this is a 60-watt bulb means that it uses up 60 joules of energy every
We can see that this way. Let’s say we rearrange this
power equation so that energy is isolated on one side by itself. When we do that, we see that
energy is equal to power times time. Substituting in for those
values, we see it’s equal to 60 watts multiplied by the time the bulb is on, 30
But look at this: power is
equal to energy divided by time, which means that one watt is equal to a joule
per second. This means we can go to our
expression for power 60 watts and rewrite it as 60 joules per second. That’s because a joule per
second is a watt. Once we’ve done that though, we
see that the units of seconds in the denominator cancel with those in the
numerator. We’re left in this expression
with the units of joules, the units of energy.
So the energy 𝐸 then is equal
to 60 joules multiplied by 30. 60 times 30 is 1800. So 1800 joules is the amount of
energy supplied to the bulb over this time. And we found that result by
multiplying the power used by the bulb times the time it was on.
Now, let’s look at a second example
of electrical energy and power.
A microwave is used for five
minutes, during which time it is supplied with 180 kilojoules of energy. What is the power of the
Okay, so we have this
microwave. And clearly, something
delicious is cooking inside. It’s being used for five
minutes. We’re told that over this span
of time, 180000 joules of energy is delivered to the microwave. The question is what’s the
power of the microwave. To see what this is, let’s
recall the relationship between power, energy, and time.
The equation connecting those
three says this. It says that the power involved
in a process is equal to the energy used divided by the time that the process
took. In this scenario, we’re given
both the energy used and the time elapsed. So we can substitute in those
values now. The power of the microwave is
equal to 180000 joules divided by five minutes.
Now, what we’ve written so far
is true. But the units in this
expression, particularly, on the right-hand side, aren’t what we want them to
be. We can recall that the base
units of energy are joules, the base units of time are seconds, and the base
units of power are watts. In other words, we can see that
one watt is equal to one joule of energy used up in one second.
When we go to calculate the
power of the microwave, we would like to get our answer in units of watts. But in order to get that, we
need to have the right-hand side in units of joules per second. We haven’t quite got there
yet. We can see that our energy is
currently in units of kilojoules not joules and our time is in minutes rather
than seconds. Here’s what we can do about
We can recall in the first
place that one kilojoule is equal to 1000 joules. That’s what the prefix kilo
refers to. And we can also recall when it
comes to time that one minute of time is equal to 60 seconds, where seconds of
course is the time unit we’re interested in. If we take this information
then and apply it to our fraction, we can write that our power is equal to the
energy of 180 times 10 to the third joules divided by the time of five times 60
And notice now that we’ve done
this conversion, we have units of joules per second, in other words watts. When we calculate all this out,
we find an answer of 600 watts. So that is the power of this
Let’s take a moment now to
summarize what we’ve learned about power and energy.
First off, as a recap, we saw that
energy is the ability to do work and it’s measured in units of joules, abbreviated
with a capital 𝐽. We further saw that power is energy
used per unit time and it’s measured in units of watts. The relationship we saw between
power and energy is that power is equal to energy divided by time. And we also saw through our
examples that it’s important to keep track of the units: joules for energy, seconds
for time, and watts for power.
And we also saw that electrical
power and energy has to do with positive and negative charges and the forces between
them, either attractive or repulsive. So just like in mechanical systems,
power and energy apply to electrical systems as well. The situations are analogous. And the equation that connects
power and energy is the same in each case.