Electric circuits and the hydraulic analogy: inductor-capacitor oscillator,
also known as the LC oscillator. In earlier videos, I showed how an
electronic capacitor works very much like this hydraulic capacitor -- a cylinder
separated by a flexible rubber sheet, and this electronic inductor works very much
like this hydraulic inductor, a water wheel connected to a heavy stone
flywheel. Here I have a hydraulic capacitor connected to a hydraulic
inductor. Let's see how these two circuit elements behave when connected together
like this. We start by pumping up the capacitor to some pressure, and then I'll
remove the pump and just let the circuit run. Let's see what happens.
OK, did you follow that? Let's watch it again I'll narrate it. As the flexible
rubber sheet pushes the water out, it makes the inductor spin faster and
faster. When it reaches the neutral position, there's no more force but
there's a high current, and you've got this rotating flywheel still going fast,
so it continues pushing water up through here until it has pushed the rubber
separator all the way to the other side. This is the exact opposite of the
starting position; you've got pressure built up on this side instead of this
side. It reverses and runs in the exact opposite direction until it goes back to
the original position, assuming no losses to friction. The
energy is stored in this stretched rubber sheet in this position, and when
this rubber sheet reaches the neutral position, all the energy is stored as
kinetic energy in this rotating flywheel. Now this is very much like dropping a
ball off from a tall building. It starts out with a lot of potential energy at
the top, which gets converted to kinetic energy at the bottom and no potential
energy, and then it bounces back up and the kinetic energy gets turned back into
potential energy. Now let's look at the electronic capacitor and electronic and
inductor connected in the same kind of circuit. We pump up this capacitor by
disconnecting it from the circuit and connecting a battery. When we remove
the battery, the charge remains until we reconnect the circuit, and let's see
what happens.
OK, pretty much exactly the same thing happened. This charge is built up on this
side of the capacitor starts pushing current through this inductor. The
inductor resists change just like the flywheel in the hydraulic inductor, like
this. At this point, we have the maximum current but zero voltage across
here, but we got this magnetic flux working just like the flywheel in the
hydraulic example. It's going to keep that charge flowing even though we got
no voltage here. So as it continues, this thing runs out of steam, but now this is
charged up as much as it can go in the opposite way that it was before, positive
on this side and negative on this side, and so the reverse happens. We have the
flow back and in the opposite direction from before -- which returns us to the
original starting point, assuming no losses to resistance in the wire. If you
graph the current and voltage as a function of time, you get a sine
function for the current and a cosine function for the voltage. At this
starting point, you've got maximum voltage here as you see here, and zero
current here. When this current starts flowing and when the capacitor
runs out of steam, you've got the maximum current and zero voltage, and that
current keeps on flowing and charges up this side of the capacitor. At this point,
you've got the most negative possible voltage and zero current. It reverses and
starts flowing this way and builds up magnetic flux in this inductor. At this
point, the capacitor has run out of steam but we now we've got the maximum
energy stored in this inductor with zero voltage and negative current current,
going this way. By convention, this original was considered positive
current and now it's got a negative current; that's we got a negative current
down here. And this continues until this is fully charged again; you got a maximum
voltage and a zero current. What are the period frequency of the oscillator? The
period is 2 pi times the [square root] inductance times the capacitance. So if the inductance is
one henry and the capacitance is one farad, the period is 6.28
seconds and the frequency is one over the period, in this example, about
1/6 of a Hertz, or one sixth of a cycle per second. It takes about six seconds
to complete one cycle. Now what good is an inductor-capacitor oscillator? Well for
one thing, you can use it to make a tuner for a crystal radio like this one here,
which I saved from my childhood. Turn it over and open it up, here's what you see.
You see one capacitor, this brown thing; one inductor, you can see the wire coils;
and one germanium diode, which is here; and there's a ferrite core that can
slide in and out of this inductor to increase or decrease its inductance.
There's an earphone here and a clip for the antenna here. There's no battery!
How does this thing work? Here's a schematic diagram. You have the inductor-capacitor
oscillator here, an antenna here, germanium diode, and an earphone here.
If the L-C combination is tuned to oscillate at 810 kHz, the 810 kHz radio
signals maintain an oscillating circuit here, back and forth, whereas the signals
from other nearby stations die away. The diode converts the amplitude modulated
AM radio signal to an audio signal that can be heard in the earphone.
The energy for the radio comes entirely from the transmitted radio signal,
so there's no battery needed. That results in a weak signal, so only one person at a
time can listen to this radio. In summary then, we have the hydraulic L-C oscillator
and electronic LC oscillator operating in a very similar manner.
This charge pushes the current through, builds up the magnetic flux through this
inductor, and and it continues flowing until it charges up this side, then runs in
reverse and so you can reach your starting point. The period is 2 pi times
the square root of the inductance times the capacitance.