### Video Transcript

In this video, we’re learning about
electromagnetic induction in transformers. We’ll learn what transformers are,
how they work, and how they use this phenomenon of electromagnetic induction.

As we start out, let’s recall what
electromagnetic induction is in the first place. The idea is this. If we take a loop of conducting
material, then if we change the magnetic field experienced by the cross-sectional
area of this loop, then we’ll induce current to flow in it.

One way to do this to change the
magnetic field experienced by the loop’s area is to pass a magnet through the
loop. Another way is to keep the magnet
stationary but change the size of the loop, say, by making it bigger or smaller or
even keeping it the same overall size but rotating it so that the total area exposed
to the magnetic field changes. Any and all of these methods will
have the overall impact of changing the magnetic field experienced by the loop and
therefore inducing current in it. And that process is known as
electromagnetic induction.

One of the most useful applications
of electromagnetic induction is transforming electrical power. Now the basic idea behind
electrical power transformation is this. When electricity is generated at a
power plant, it’s at a voltage, a potential difference, which is much higher than we
could safely or reasonably use in a residential context. But, in order for the electricity
to get from where it’s generated to where it’s used, the most efficient way is to
keep it at a very high potential difference. That way, the least amount of power
possible is lost in the transmission process. That means that shortly before we
use it, we’d like to be able to transform the electricity we receive from the power
plant. This transformation, as we’ll see,
relies on electromagnetic induction.

An electrical transformer looks
like this. There are three basic parts to
it. First, there’s a coil of wire known
as the primary coil. This is the wire through which
electricity is introduced to the transformer. Then, across from the primary coil
is what’s called the secondary coil. This is the coil of wire which will
have voltage induced across it and therefore current induced in it. And then, connecting these two
coils is what’s called the core. As we’ll see, the type of material
the core is made out of has a significant effect on the performance of the
transformer overall.

So here’s how the transformation
process works. First, current flows in through the
primary coil. We’ll call this current 𝐼 sub p to
show that it’s in the primary coil. This current travels around every
single one of the loops of the primary coil wrapped around the core. And then finally, it comes back out
the other side. Now, if this was all that happened
in a transformer, that would be pretty boring. And it wouldn’t really accomplish
much. But at this point, we can recall
that a loop of wire, when it carries a current, generates a magnetic field. And in particular, if we have a
loop of wire where the current is travelling in this direction as shown, then based
on what’s called a right-hand rule, the magnetic field created by this loop at the
center of the loop points straight up.

Knowing that, if we go back over to
our primary coil, which we see is wrapped around the core some number of times, we
realize that every single one of these individual loops, these windings, is itself a
loop of current. And it creates a magnetic field
that points up. The combined effect of the magnetic
field from all these individual loops is fairly strong. And overall, we have a fairly
powerful magnetic field pointing from bottom to top. Now, this is where the core
material comes in. One of the main purposes of the
core of a transformer is to channel the magnetic field lines around the core as
though they’re moving in a circuit.

This means that the field produced
within the windings of the primary coil then travels all throughout the rest of the
core and goes through the windings of the secondary coil as well. And this we can see is where
electromagnetic induction comes in. Let’s look for a moment at a single
one of these loops in the secondary coil. And we’ll look at it as though
we’re looking straight down from above onto that loop. In that case, the loop would look
to our eye like this, like a circle. And what we would see, if we could
see them, is this magnetic field line going into the screen, from our perspective,
through the center of the loop. So, whereas before there was no
magnetic field moving through this loop, now there is a field.

In other words, there’s a change in
magnetic field experienced by the area of this loop. That’s exactly the kind of effect
that through electromagnetic induction will induce the flow of current in this
loop. For reasons that we won’t get into
in this lesson, that current flows in this direction from our perspective,
counterclockwise. Of course, what we’re looking at
here is just a single loop in the many loops of the secondary coil. So this is going on for all of
those individual loops. So then, finally, this induced
current is output through the secondary coil. And it goes on to whatever its
application might be, perhaps in a residential neighborhood.

Let’s go back to 𝐼 p, the current
through the primary coil, for a moment. If this current was constant in
time, then still a magnetic field would be formed through the loops of the coil. And that field will be carried
through the core. But, after the loops of the
secondary coil had been initially exposed to this change, after that, there will be
no more change. The field lines would stay the
same. And if there is no more change in
the total magnetic field through these loops, then there’ll be no more current
induced in them. In order for a transformer to work
properly, the current in the primary coil must be alternating current, AC.

When that’s the case, it means that
the magnetic field lines in the core are constantly changing in magnitude. And when that’s happening, it means
that every single one of the windings in the secondary coil is always seeing a
different magnetic field move through it. That is, there’s a constant change
in magnetic field through the windings of the secondary coil and, therefore, will
constantly induce voltage and, therefore, current in that coil. All that to say, for a transformer,
it’s very important to work on alternating current.

We’ve said that the current going
through the primary coil is 𝐼 sub p. And let’s imagine further that we
know the voltage of that current. We’ll call that voltage 𝑉 sub
p. And let’s say it’s 500 volts. And then, if we go over to the
secondary coil, we can say the current output there is 𝐼 sub s and that the voltage
output there is 𝑉 sub s. But the question is, what is that
voltage? What is the potential difference
induced in the secondary coil? Believe it or not, we can solve for
𝑉 sub s by knowing 𝑉 sub p and also knowing the number of turns that each of the
two coils, primary and secondary, make around the core.

In general, if we call the number
of windings of the primary coil 𝑁 sub p and we call the number of windings or turns
around the core of the secondary coil 𝑁 sub s, then we can write this very neat
equation. 𝑉 sub s divided by 𝑉 sub p is
equal to 𝑁 sub s divided by 𝑁 sub p. In other words, the ratio of the
potential differences is equal to the ratio of the turns. Now, in a way, this is quite
fascinating. But as we think about it, it makes
sense. The more turns that a coil makes
around the core, the more it will contribute to the magnetic field strength in the
core. And the more that magnetic field on
the core changes, the more voltage will be induced in the secondary coil.

This ratio equation tells us that
since we know 𝑉 sub p, if we would count up 𝑁 sub p and 𝑁 sub s, then we could
use all that information to solve for 𝑉 sub s. Let’s do that; let’s count up 𝑁
sub p and 𝑁 sub s. Starting out with 𝑁 sub p, we can
count these turns as one, two, three, four, five, six, seven, eight, nine,
total. So applying this equation, we have
𝑉 sub s, what we want to solve for, divided by 𝑉 sub p, 500 volts, is equal to 𝑁
sub s, what we’ll find out in a moment, divided by nine, the number of turns in the
primary coil.

Moving on to counting 𝑁 sub s,
that’s one, two, three, four, five, six, seven, eight, nine, 10, 11, 12 turns. So we fill in 12 for 𝑁 sub s in
our equation. Then if we multiply both sides by
500 volts, we find that the voltage in the secondary coil is equal to 12 divided by
nine times 500 volts. That’s the same as four-thirds
times 500 volts, which is approximately 667 volts. This change from 𝑉 sub p to 𝑉 sub
s is why this is called a transformer.

Now we might wonder, what about the
currents 𝐼 sub p and 𝐼 sub s? Can we solve for those based on the
number of turns of each coil? The answer is that we can, but the
relationship is flipped from the relationship for voltage. What we mean by that is if we take
the ratio of the number of turns in the secondary coil to that in the primary,
that’s equal to the primary current divided by the secondary current. So we have to be careful about our
subscripts here, ss and ps, and to keep them straight.

Going back to our discussion of
voltage, we can see that the primary voltage is less than the secondary voltage. When this happens, it means the
function of the transformer is to raise the voltage from the primary to the
secondary coil. When that happens, when 𝑉 sub s is
greater than 𝑉 sub p, the transformer is described as a step-up transformer. And the opposite can happen as
well. When the secondary voltage is less
than the primary voltage, the transformer is called a step-down transformer.

Before we get a bit of practice
with an example, let’s talk about the core of the transformer. From an efficiency perspective, the
core is very important. In particular, the material we
choose to make the core out of will affect just how well energy is transferred from
the primary to the secondary coil. Of all the materials we could
choose to make the core out of, we like to choose a material which is
magnetizable. That is, one which becomes a magnet
when it’s exposed to a magnetic field. And we’d also like a material that
can respond quickly to rapidly changing magnetic fields in the windings of these
coils.

A leading material for doing this
is iron. And it’s very common to make
transformer cores out of this metal. It’s a material that helps to
channel as well as amplify the magnetic field within the core. Now that we know a bit about
transformers, let’s get some practice solving a question about one.

A step-down transformer changes the
potential difference of an alternating current from 10000 volts to 250 volts. If it has 25 turns on its secondary
coil, how many turns does it have on its primary coil?

Okay, let’s say that this is our
transformer. This is our primary coil and here
is our secondary coil. We’re told that the potential
difference in the primary coil, what we we’ll call 𝑉 sub p, is equal to 10000
volts. And the potential difference in the
secondary coil, what we’ll call 𝑉 sub s, is 250 volts. We’re also told that the secondary
coil of our transformer has 25 turns. We’ll call that number 𝑁 sub
s. And if we call the number of turns
in the primary coil 𝑁 sub p, it’s that value that we want to solve for. In order to do it, we can recall a
relationship between primary and secondary voltage and number of turns. This relationship says that the
ratio of the turns primary to secondary is equal to the ratio of potential
differences primary to secondary.

In this relationship, we want to
solve for 𝑁 sub p, the number of turns in the primary coil. So to do that, we can multiply both
sides of the equation by the number of turns in the secondary coil. That means that that term, 𝑁 sub
s, cancels out on the left-hand side of our equation. We find that 𝑁 sub p is equal to
𝑉 sub p divided by 𝑉 sub s all multiplied by 𝑁 sub s. And since we know 𝑁 sub s, 𝑉 sub
p, and 𝑉 sub s, we can substitute those values into this equation now. 𝑉 sub p is 10000 volts, 𝑉 sub s
is 250 volts, and 𝑁 sub s is 25. Calculating this result, we find an
answer of 1000. That’s the number of turns that are
in the primary coil of this transformer.

Let’s take a moment now to
summarize what we’ve learned about electromagnetic induction in transformers.

In this lesson, we’ve seen that
transformers change voltage and current through the process of electromagnetic
induction. We saw that in general,
transformers have three basic components. There’s a primary coil that current
is input through. There’s a secondary coil that
current is output from. And there’s a core, typically a
solid metal material, that connects these two coils.

We saw that when it comes to the
effect a transformer has on voltage, the ratio of the primary voltage to the
secondary voltage is equal to the ratio of the number of turns in the primary coil
to the number of turns in the secondary coil. And we furthermore saw that a
transformer affects the current, that the ratio of secondary coil current to primary
coil current equals the ratio of the number of turns in the primary to the secondary
coil. Finally, we learned that a step-up
transformer increases voltage across the transformer while a step-down transformer
decreases it.