# Inductor-Capacitor LC Oscillator: Hydraulic Analogy (fun)

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.

## 6 thoughts on “Inductor-Capacitor LC Oscillator: Hydraulic Analogy (fun)”

1. Nunzio Turtulici says:

Very nice and very clear video. I'm learning a bit of electronics and your video did help, thanks

2. Oussama Chemrouk says:

Loved your work, clearly too much effort is put to it.

Although I stopped learning electronics since I started med school, I still find your video very interesting to watch with some nostalgia brought with it. Thanks <3

3. AKUJU says:

Dude where have you been all my life! I've been looking for water flow analogies to help me understand circuits better! Mechanical engineering major transitioning to robotics.

4. Lukie Kelen says:

What would happen if you couple an inductor and a capacitor magnetically where inductor is the primary and capacitor is the secondary? They are coupled using soft iron core.

5. Hrishikesh Kulkarni says:

This guy says Wheel just the way Stewie from Famlily Guy says "cool Whip" https://www.youtube.com/watch?v=7ZmqJQ-nc_s

6. Squidward says:

Great video sir , I finally understood it.