### Video Transcript

In this video, our topic is
efficiency. In particular, we’ll be talking
about electrical efficiency. This describes how well electrical
components and devices use the energy that’s supplied to them. To see what a difference efficiency
can make, consider these two electrical circuits we see on screen.

Let’s say that as far as the wiring
and the power supply goes, these two circuits are identical. And what’s more, let’s say that the
power rating of the bulbs that we put in these circuits is the same. So maybe they’re both 50-watt bulbs
or 75-watt or some value like that. The point is, the power ratings are
the same, but the bulb types are different. In the circuit on the left, we have
an incandescent light bulb and, in the circuit on the right, we have an LED
bulb. Considering that these two
different bulbs are plugged in to identical circuits and they have the same exact
power rating, we might expect the same amount of light to come from each one. But what we find is that much more
light comes from the LED because it’s much more efficient than the incandescent
bulb.

Efficiency has to do with how much
output we get from something given how much input it receives. Let’s say that this box is some
electrical component or some electrical device. It has the capacity to have energy
transferred to it and then to use that energy to perform some function or do some
task. Up top, we have the energy being
input into this device, and then this device or this process creates some
output. Thinking back to our light bulbs,
the input was electrical energy and the output was radiant energy.

For any type of device, that
device’s efficiency has to do with comparing its energy output with its energy
input. When we describe energy input,
that’s the total energy that goes into some device in order to create some
result. We could describe this as the total
energy supplied for this process. And then when we think about
outputs, we’re specifically talking about useful energy outputs. Now, what we describe as useful
depends on our particular application.

But think back to our incandescent
light bulb. When this bulb is lit, not only
does it give off light, radiant energy which we want and consider useful, but it
also gives off lots of heat energy, which is not desired when we want to light a
room. Most of the time then, the useful
energy given off by a light bulb is its radiant energy, the energy it emits as
light. And typically, the heat energy that
this bulb gives off is considered wasted or not useful energy. Efficiency has to do with the total
energy that goes into a device or a process and the useful energy that’s output from
it. It’s expressed as a ratio, the
useful energy output by a device or a process to the total energy that was
input.

We say that this ratio, this
fraction, is equal to the efficiency. And we use the Greek letter 𝜂 to
represent that term. Now, looking at this relationship,
let’s consider the highest and lowest efficiencies we could possibly have. Let’s say that there was some
process where all of the energy input was output as useful energy. In other words, the useful energy
output equaled the total energy input. In that case, this fraction would
be equal to one. So one is the highest possible
efficiency in decimal form that something can have.

And then at the other end of the
spectrum, say that we had a process where some amount of energy was input but that
we had literally zero useful energy output from it. Thinking back to our light bulb
example, perhaps this would be a light bulb that didn’t give off any visible light
when it was powered, but only heat. If the useful energy output was
zero, then the numerator of this fraction is zero, and so the efficiency is zero
too. So 𝜂, the efficiency of a process
or device, is less than or equal to one and it’s greater than or equal to zero. For virtually all of the processes
we’ll encounter though, 𝜂 is somewhere between these extremes. Here’s what that means.

For a given process where some
total amount of energy is input, some of that energy is output in a useful
fashion. And some of it is not. It’s energy that’s wasted. When our process or device delivers
both useful energy output and wasted energy, then our efficiency will be somewhere
between one and zero. Now sometimes, efficiency is
expressed as a decimal value, like it would be in this case. But in other cases, it’s expressed
as a percent. Describing some device, we might
say that it’s 25 percent efficient or 80 percent efficient or something like
that.

So it’s worth knowing how to go
from a number written as a decimal — we’ll call that 𝑁 sub D — to an equivalent
number written as a percent. All we have to do to convert a
decimal number into its equivalent percent is to multiply that decimal by 100
percent.

For example, say that we calculated
an efficiency of 0.03 written as a decimal. If we want to know what percentage
efficiency that is, we multiply that by 100 percent and find a result of 3
percent. And then to see how to go the other
direction from a number given as a percent to a number written as a decimal, if we
divide both sides of this equation by 100 percent, then that factor cancels out on
the left. And we see that, to make this
conversion, we take our number, originally written as a percent, divide it by 100
percent. And that equals the equivalent
value as a decimal.

So, for example, if we had an
efficiency written as a percent of 37 percent, then to write that as a decimal, we
would divide it by 100 percent. In doing this, we see that the
percent symbol cancels out, and we get a result of 0.37. That’s 37 percent written as a
decimal. One more thing to know about
efficiency is that sometimes it’s not written as a ratio of energies, but as a ratio
of powers.

Returning once more to our light
bulb example, most light bulbs are rated in terms of the power that they
consume. That’s the number we can see
written on the box that the light bulbs are sold in. That number, whether it be 100
watts or whatever the power rating it is, represents the total power being input to
that light bulb during normal operation. And then along these lines, we look
at the useful power output by the bulb in terms of the radiant energy it gives off
over some amount of time.

So sometimes when we’re calculating
the efficiency of an electrical device or component, instead of referring to the
useful and total energy, we’ll use numbers referring to the useful and total power
instead. It will be clear from the context
which form to use. And as a rule of thumb, the
standard way of understanding efficiency is in terms of energies, the useful energy
output to the total energy input. Knowing all this, let’s get some
practice with efficiency through an example exercise.

An LED light has an efficiency of
29 percent. If it converts 5,800 joules to
light, what is the total energy it was supplied with?

Okay, so we have an LED light. And that light has a given
efficiency. This LED is supplied with some
total amount of energy. And then it outputs a given amount
of energy as light. And that given amount, we’re told,
is 5800 joules. We can consider this to be useful
output energy from the LED. And this useful energy output is
some fraction of the total energy input into the device. Now, if our LED was perfectly
efficient, then all of the energy we input to it would be converted to useful energy
output as light.

But we know that that’s not the
case. Rather, just under 30 percent of
the input energy is converted into useful output energy. That’s what it means that the
efficiency of this LED is 29 percent. So basically, we input some total
amount of energy to our LED and then 29 percent of that total input is output as the
5800 joules of light energy. And knowing this, we want to work
backward to solve for that total energy input.

Let’s let the total energy supplied
to our LED be represented by this symbol, 𝐸 sub t. And then let’s let 𝐸 sub L
represent the energy that our LED converted to light. The LED efficiency of 29 percent
means that if we take 29 percent of 𝐸 sub t, then that will equal 𝐸 sub L. Written out using words, 29 percent
of 𝐸 sub t equals 𝐸 sub L. And now, we can translate this into
an equation that we can solve for 𝐸 sub t. To do that, we’ll want to convert
this percent, 29 percent, into a decimal. In general, if we have a number
written as a percent — we’ll call it 𝑁 sub P — then if we divide that value by 100
percent, that equals the equivalent number written as a decimal.

So if we take 29 percent and divide
that by 100 percent, we see the percent signs cancel out. And as a decimal, this fraction is
equal to 0.29. So if we take this number, 0.29,
and multiply it by 𝐸 sub t, the total energy supplied to the LED, then that product
will equal 𝐸 sub L, the energy output as light. Written as an equation, we can say
that 0.29 times 𝐸 sub t equals 𝐸 sub L. And to solve for 𝐸 sub t, the
total energy, we’ll divide both sides of the equation by 0.29. That will cancel that term out on
the left. And we see that the total energy
input is equal to the light energy, the useful energy output, divided by 0.29.

And we know 𝐸 sub L, the energy
converted to light; that’s 5800 joules. So 𝐸 sub t is 5800 joules divided
by 0.29 which is equal to 20000 joules. That’s the total energy supplied to
this LED light.

Let’s now look at a second example
exercise.

A 120-watt television has a useful
power output of 30 watts. What is the efficiency of the
television?

Okay, so we have this television,
and the television is rated at 120 watts. That means if we were to monitor
the power coming into this television during its normal operation, that power would
be at 120 watts. So that’s the total power
input. And we’re told that this television
has a useful power output of 30 watts. That is, the power that it uses in
support of creating a moving image is 30 watts. So that leaves 90 watts doing
something other than what we want them to be doing. Most of that wasted power goes into
generating heat in the system. So then our television usefully
outputs some of the power input to it but not all of it. And we want to calculate its
efficiency.

Efficiency can be represented using
the Greek letter 𝜂. It’s equal to the useful output
from a process or a device divided by the total input. These outputs and inputs can be
energies or, like in our case, they can be powers. In this instance, we’re told that
the useful power output from this television is 30 watts and that the total power
input is 120 watts. We can see when we calculate this
fraction that the units, watts, will cancel out. And we’re left with 30 divided by
120. Written as a decimal, this is equal
to 0.25.

Often though, efficiencies are
expressed as percents. To write 0.25 as its equivalent
value as a percent, all we need to do is multiply it by 100 percent. 0.25 times 100 percent is equal to
25 percent. That’s the efficiency of this
television. It means that 25 percent of the
total power input to it is converted to useful power output.

Let’s now summarize what we’ve
learned about efficiency. We saw in this lesson that the
efficiency of a device relates its useful output to its total input. We also learned that, written as an
equation, energy efficiency is equal to the useful energy output divided by the
total energy input. And this efficiency is always less
than or equal to one and greater than or equal to zero.

It’s worth pointing out though that
no perfectly efficient devices or processes have yet been discovered. That is, practically speaking, 𝜂
is always less than one. We found out how to convert between
a number written as a percent and a number written as a decimal. Multiplying a number written as a
decimal by 100 percent converts it to a number expressed as a percent. Lastly, we learned that efficiency
may describe energy, or it may describe power inputs and outputs. This is a summary of
efficiency.