Besides generators and motors, one other
really handy device you can make with
induction is the transformer. Essentially
transformers are just Faraday's original
experiment in disguise.
So you take one solenoid, which is just a
coil of wire, and you pass a current
through it and that current is going to
make a magnetic field running down there.
And the advantage of having an
alternating current is that magnetic
field is also going to be also hanging
up and down. So you've got a changing
magnetic field just going to give you a
changing magnetic flux. If you have a
changing magnetic flux then you're going
to induce an electromotive force
voltage in the second coil, because the
second coil is sharing that magnetic
field. That magnetic field is going to
come out here and it's going to induce a
voltage in that second coil. Now exactly
how you place those coils doesn't matter
too much; you could have them like that
where they're basically in line with
each other. You could help a little bit
by putting a core of iron down the
middle so you can have a rod of iron
that is shared by the two of them like
that, and that way the first one will
set up a magnetic field in the iron. And
then that will be running right down
through the second one and that will
help set that changing magnetic field
for the second one. You can also put them
actually completely on top of each other
so you can wind them together. They have
to be electrically separate of course,
but you can have the coils around each
other, or you can even have them
side-by-side, up here like this, provided
that you get a piece of ferromagnetic
material and join them together like
that. And then, even then, the magnetic
field generated by this coil will create
a magnetic field that's changing inside
that coil and therefore you'll get a
voltage.
So one obvious question to ask is, why do
people build this? Because if I could
create a potential difference between
these two wires here, and I wanted to
create a potential difference between
these two wires, another obvious way of
doing that is just to connect the wires
directly. So I could connect this wire
here and that wire there, and ignore all
that coil stuff. So why not do that? And
the answer lies in here, in Faraday's law.
The electromotive force, the voltage
between those two wires, depends on the
number of loops in the coil. And also
when I make my solenoid, the strength of
the magnetic field in this solenoid
depends on the number of loops in the
coil. And so if I have a large number of
loops in say, the first coil, and a smaller
number of loops in the second coil, then
I'm going to be creating a very large
magnetic field and I'm going to be producing
a relatively small potential on the
other one. So that allows me to take a
very high voltage source and turn it
into a low voltage source. So that's a
very very handy thing. When we have 240
volts coming out of the power socket in
our houses we really want to plug that
into a very delicate device that
requires a low voltage without first
stepping it through a transformer. And
that's why most power packs and devices
have transformers built in. Conversely, if
you want to make a very large voltage, it
turns out that it's much easier to
transport electricity long distances
efficiently at high voltage, and so what
you want is a step-up transformer. So you
want a large number of loops in the
second coil and that means that the
voltage going out will be much greater
than the voltage coming in.
And the ratio of the voltages is just
exactly given by the ratio of the number
of windings of each coil. One of the
possibly surprising things about
transformers is just how efficient they
can be you, can get nearly all the power
coming out of a transformer you put in.
And that's really handy from an
efficiency point of view but it's also
really handy because it means
transformers tend not to get incredibly
hot for example as they dumped nearly all the power you're putting in. And they
don't put out large amounts of radiation.
So at a hundred percent efficiency, the
power in has to be equal to the power out and we can remember the formula for the
power in electrical circuits because
it's just the energy per unit time.
And the voltage is the energy per unit
charge and the current is the charge per
unit time and so the power is just the
voltage times the current. And so the
power in equaling the power out would be
the voltage times the current for the
first coil would be the voltage times
the current for the second coil. That's a
little bit surprising, because if you
remember back to Ohm's law you know that
the current depends pretty much only on
the voltage. Specifically the current
is just the voltage divided by the resistance. So we could write the power in terms of
just the voltages and the resistance. And
that should be a little bit concerning
because it looks like the ratio of the
voltages can be got from the ratio of
the resistances, whereas we know the
ratio the voltages come straight from
the ratio of the number of turns in the
coils. So how to resolve that? Remember
this second one only applies at a
hundred percent efficiency, whereas this
one always applies. So actually that's
telling us something very important
about how to build a transformer so that
works efficiently. You have to carefully
match the resistance of the power source
and the first coil with the load and the
second coil in order to satisfy this
equation and this equation at the same
time. That's the only way you can get a
hundred percent efficiency
and this is called impedance matching.
