The analogies I've heard are that a capacitor is like a rubber membrane in line with the water pipe, and that an inductor is like a flywheel being driven by a turbine.
I think the inductor one only makes sense if you imagine the flywheel being driven with huge buckets -- such that the voltage drop is massive if ∂V/∂t is large (with analogy to L ∂I/∂t). I'm far from convinced that is totally right though, as you can easily have arbitrarily high voltages with switched circuits and inductors, but not necessarily with turbines...
I guess a transistor is a little man twiddling a valve according to a dial in the "water model" of electricity, any through-space effects are due to leaks, and nonlinear components like MOSFETs are a bit more creatively explained. (E.g. Source: water reservoir; drain: water reservoir; gate: gate between source and drain reservoirs, driven by an utterly mad person who follows interesting rules. Oh, and inexplicably he's a bit stronger than transistor man too).
There are serious limits to the analogy. Water only ever remains inside the pipes that carry it. Anything involving the electrical energy not inside wires has no water analogue (ie the electromagnetic waves inside a transformer).
No analogy is perfect. They are intended to help illustrate a concept to gain insight. Ideally when using an analogy its limits should also be described. Luckily the very first link after the analogy is explained does just that: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/watcir3.....
Same, by the time you need to explain how transformers use electromagnetism, they probably understand the basics of V=IR which is really as far as the analogy goes.
Could a turbo-pump can be thought of as a very bad transformer? able to transform a flow mv1 at a pressure P1 to mv2 P2 where their product, power is constant (except its way more lossy).
That’s probably a good description of the main usefulness of the analogy - explaining to people who won’t actually need to apply the concepts. My conclusion (after years of doing electronics design professionally, including RF) is that to do much useful in electronics, you need to get into the habit of thinking natively in terms of voltage and current and resistance etc. so soon that the hydraulic analogy is basically not worth learning at all, since the missing things just get confusing and it becomes a distraction or blocker to advancement until you “unlearn” many of the concepts.
I mean, it’s probably worth mentioning current and voltage are “kind of” like flow, pressure etc., in a first lecture to start to get the basic idea, but then warning not to think of it as being the exactly same because that will just be confusing later.
There's a large difference between "applying the concepts" and "doing useful things in electronics". The vast majority of people barely find utility in repairing what they already own, to say nothing of tinkering or creating something new.
The water analogy, is, in my opinion, the sweet spot for people who will never own a multimeter or fire up a SPICE program. It's the level that ought to be the expectation for citizens of a technic civilization.
You can do 99.999% of practical applications of electricity with the liquid analogy, up to and including most industrial electrical stuff (remember, check valves, accumulators and whatnot are a thing).
What you can't do is design a bottom dollar power supply that uses some trick circuitry to not emit enough RF noise to matter.
Not still a good analogy, but radiation can be seen as a consequence of vacuum not being empty from the perspective of an electric field (it has a very low permittivity, but it is not zero, so it is not empty of that property) even though it is empty of mass. If your water pipes are a bit porous and the medium on which your water pipes are was not air, but a very dense fluid, radiation emanating from the porous pipes would travel at the speed of sound through the medium, and could be detected without particles of water actually travelling through the dense fluid that constitutes the medium where your hydraulic circuit is submerged.
I'm specifically talking electronics, where the usefulness runs out very quickly... As soon as you get to EMI/EMC there is no real liquid analogy (so that rules out basically any reasonably complex custom electronic design you're going to get certified to sell as a product). Parasitic effects of traces, ESR, characteristic impedance, etc. are similarly problematic (people try to come up with stuff like springs or flexible tubes for characteristic impedance but again it's just more confusing in practice). So that rules out anything decently high speed digital (like, say, routing DDR3/4). That's of course not to mention RF, antennas, transmission lines etc. where all bets are off.
Wouldn't it be easier to just say "current is how many electrons flow through a specific section of the wire in a second" and "voltage is the force that makes the electrons move"?
It's just as easy to understand without need for analogies.
Those two sentences that you wrote are precisely the hydraulic analogy. If it weren't, instead of electrons it would be charge (that can be positive or negative), or field strength (if you explain the transitory period of a capacitor or non-DC), and voltage would become not the force, but a number that applies to conservative fields that allows to calculate the capacity to do work relative to another such number...
I would say that, in general, this is a tool most useful to help people that are completely new to the concept gain an intuition about the behavior.
Based on what you've described, where would you develop the intuition about the difference in speed between the electrons and the electromotive force they are relaying? Or why you need both voltage and current to do work, or the behavior of an LCR circuit? Or an open circuit? Etc etc.
Absolutely not. You can't just throw out axioms and expect people to catch on. The utility of analogies is that you can anchor an idea in something people are familiar with.
> Water only ever remains inside the pipes that carry it.
If only! My apartment was recently destroyed by water that refused to do exactly that...
Electricity also doesn't freeze solid, expand, and break open its insulation; it doesn't evaporate and condense on cold surfaces and cling there under surface tension, it doesn't drip down.
But the analogy is still a pretty useful one for people who have lots of hands-on experience with water and not much with electricity, or vise-versa.
>> cling there under surface tension = Static charges. When a walk in wool socks on a wet carpet my socks pick up water. When I walk on a dry carpet my socks pick up electrons.
>> expand, and break open its insulation = an arc causes by too much electricity in too thin a pipe.
>> it doesn't evaporate and condense on cold surfaces = electro vapor deposition aka physical vapor deposition
Hydraulic intensifiers can act as an analog of an electrical transformer. An intensifier is a hydraulic device where a large area piston is coupled to a small area piston. They are often used in water jet cutters to produce high pressures. A jet pump[0] is another device which acts sort of like a transformer and exchanges high pressure for high flow. 'Inertance' of the water in the pipe can act in a manner similar to inductors.
> For anyone desperate enough to want to find an analogy to a light-emitting diode (LED), consider the fountain-emitting one-way value shown in Figure 2.
> Anything involving the electrical energy not inside wires has no water analogue (ie the electromagnetic waves inside a transformer)
You don't even need fancy things like transformers for energy not in the wires to be important. Even a simple DC circuit consisting of a battery in series with a light bulb mostly involves an electromagnetic field to transfer energy from the battery to the light bulb, which mostly takes place outside the wires.
The function of the wires when it comes to energy transfer is to carry moving charge which creates the magnetic part of the electromagnetic field that actually carries the transferred energy.
Here's a pretty good explanation [1]. That video was from January 2019, and not controversial.
Veritasium did a video on the topic in late 2021 that didn't really present things as well and ended up being quite controversial [2]. Other well-known YouTube channels such as EEVblog [3] and ElectroBOOM [4] responded.
There was also someone who bought a bunch of wire and did the experiment as described in the Veritasium video (although scaled down). That was discussed on HN and that discussion contains some very interesting links [5].
In particular the link to a talk by Rick Hartley in this subthread is very informative [6]. He talks about how most EMI problems in PCB designs are due to people not taking into account the the energy is not in the wires.
The thing is that KVL and KCL hold, and KVL and KCL hold for both electrons and water. You just have to not think too deeply about what motivates the electrons to move. Current is indeed the mean velocity of carriers through some area, and voltage is mmm... well it's related to the electric field. It's just not exactly fluid pressure even though it behaves as such.
The right way to think about this if you _really_ care is a bit like the way that RF engineers think about dielectric resonators. The metal motivates the fields to be guided along pairs of conductors by the motion of charge carriers within. A metal will respond in a particular way to fields, which results in new fields, and so on and so forth in a way that results in the fields propagating along in a particular way.
A propagating pulse is a bit hard to think about but you can imagine some field configuration that results in the electrons in the metal slipping a bit, and those electrons move in a way that results in new fields which contain the new wavefront of the pulse. The electrons don't keep moving -- they move on average the distance of the mean free path and give their energy to the lattice as heat. This is why the drift velocity is just a meaningless number. The fields propagate at around c and the conductors guide them.
Transformers can be represented by paddle wheels and gearboxes and such. They come free with inductance (inertia.)
The pedagogical failure of this analogy is how it suggests that the energy is stored in the potential and kinetic energy of the fluid (the electron density) rather than in the fields. Then you end up with this drift velocity nonsense which is essentially a holdover from the Drude model which is only predictive by luck.
At my engineering undergrad, the mechanical, computer, and electrical engineers had effectively the same curriculum through our sophomore year. One of the big class combos was Electrical Systems, Mechanical Systems, and Fluid & Thermodynamic systems where you work through from the laws of thermodynamics to how they apply in each of the areas. It was mind blowing when you realize how much of the underlying reasoning - and therefore resulting formulas - are nearly identical.
It led to many EEs getting a certificate in fluid & thermo because the extra couple classes counted as tech electives and the math was the same.
> One of the big class combos was Electrical Systems, Mechanical Systems, and Fluid & Thermodynamic systems where you work through from the laws of thermodynamics to how they apply in each of the areas.
I would love to find a book with this type of presentation. Do you happen to remember which textbooks were used for this class?
It doesn't approach it from a thermodynamic perspective, but the following paper summarises the duality between electrics, hydraulics, acoustics and mechanics:
SchÖnfeld, J. C. (1954). Analogy of hydraulic, mechanical, acoustic and electric systems. Applied Scientific Research, Section B, 3(1), 417–450. doi:10.1007/bf02919918
Yes. At my university this course was called "Systems theory". Electrical networks, mechanical systems, hydraulic networks were shown to have laws that have the same shape. They also only gave the course after letting you struggle with electricity, mechanics, fuild mechanics, ... for a few years. I guess to make you appreciate it more (which I did!)
I recently got into electronics/electricity and I have been trying to put together a course for myself, mostly for the kind of work that involves fixing things (power supplies, small house appliances, and so on) but also for having a good understanding for how things work. Of course the field is huge and there’s all sorts of applications out there. I’m a long time software dev and I’ve delved into all sorts of software-oriented subjects over the years, so I’m hoping I can apply some of this knowledge, at least from a troubleshooting/analysis perspective. But oh boy is this difficult due to electromagnetism and not being able to really visualize these things (not without an oscilloscope I suppose).
A close family member was an EE/technician and they ran a repair service for appliances for many decades - anything and everything, TVs, radios, kitchen appliances, industrial machinery, and so on. Sadly they passed away and I don’t know anyone personally I can ask about where to begin and how to approach this.
Any recommendations for curriculum? I started with Make: Electronics 3rd Ed and a half dozen or so online resources, like the Khan Academy series and some other undergraduate level videos on circuit analysis and such. I really like the electricity misconceptions site as well.
Except the wifi has it's own wifi that has it's own interference that is having it's own echo. Go too low down the frequency hole and you get so lost :-)
For fixing things, a couple of good books on home repair will do you a lot better than deep theory (both because safely manipulating high voltages in a home setting doesn't require the underlying physics so much as following the rules and because if you apply the theory too strictly, you run the risk of getting tripped up, possibly dangerously so, by somebody failing to do something to code).
On the other hand, the underlying theory is very useful for if you do encounter something off code, because something off code will be doing something, and you as the homeowner are stuck figuring out what.
Did you know - a boost switching regulator was used to pump water up to the top of a garden in Victorian times. The regulator uses the water pipe analogy to electricity, except electricity hadn't really been invented then. The system uses an inductor (a long straight pipe, where the water has momentum), and a switch (a flap that closes and opens regularly), with a diode (one-way valve) and a capacitor (a container with a pressurised air cavity). https://en.wikipedia.org/wiki/Hydraulic_ram
Check out Spintronics, it's a game/kit for building mechanical analogs for electric circuits. It's coming out sometime this year from the same team that made Turing Tumble.
I bought it and explained to my kids (7 and 3) that it's "daddy's game" and they can watch me play it but can't play it without me. My 7 year old daughter helped me up through about the first 1/3rd of the game but then quickly it became too hard.
It does a good job of introducing concepts slowly but they are in fact hard concepts if you're new to them. It is actually a bit of a challenge for adults too.
Mechanically, the game is good but a bit finicky to set each piece in place. That means the time between "I think I know what to do" and testing it out is a bit too long. Overall, I find it pretty fun though. (I also backed the spintronics kickstarter)
Thanks for that, this looks indeed like a fantastic educational game (previous discussion [0]). Seems there is a similar game to building "computers" [1] as well.
A hydraulic cylinder connecting the systems would work. It maps voltage (pressure) between two disconnected systems through a ratio of windings (piston area). It only creates flow when there is a change in voltage (pressure) and current (flow), and if the circuit is open on the induced side then the transfer of energy is limited to the capacitance (compressibility) in the circuit.
Acoustics is a more direct parallel, and even uses the same unit- the acoustic Ohm. The hydraulic Ohm also exists, but is not really used.
Helmholtz resonators[1] are used to provide capacitive acoustic impedance in a gas system. Archetypically a beautiful hollow copper sphere. Ported subwoofers use the same formulas, as do some types of automotive exhaust. Exhausts use a long pipe and cylindrical section to form a low-pass filter, which transforms the individual exhaust bursts of an engine into a smooth continuous flow. Two stroke exhausts[2] are band-pass filters that improve compression by putting backpressure on the engine at the correct time.
Electrics, Acoustics, Hydraulics, Mechanics, ... They are all mathematical duals of each other. Just the terminology is different in each field (pun?). James Clerk Maxwell, who wrote down the fundamental equations for electromagnetism, also worked in acoustics.
Thank you. Stuyding the hydraulic version really helped prepare me to understand the electrical version. I've been wanting to understand how boost converters work for a while, so this was super useful and interesting!
Just the other day I was thinking about experimenting with some hydraulic or pneumatic cylinders, and I saw photo of a dual input cylinder with couples of pipes going in and out interconnected with a power source and a three position valve to hold or release pressure coming from either of two ports.
I looked at the photo and the description and suddenly realized I was looking at a XOR’d MOSFET low side switch circuit made of pipes and valves.
Funny that sometimes the water analogy also works the other way around.
It can get you into trouble in real (high pressure, specifically) hydraulic circuits, since hydraulic pumps/actuators are almost always flow (current) sources instead of voltage/pressure sources. It's almost a fundamental rule, since liquids are so incompressible. A hydraulic reservoir under a very high pressure will only provide a tiny amount of flow before the pressure drops to zero.
The opposite is also true; if the flow out of a pump is blocked then the pressure will immediately climb extremely high and usually break things. Once you get into the weeds with transistors etc you obviously also have to worry a lot more about currents, but with hydraulics it's always about the flow.
Unfortunately, water isn't as simple as electricity.
Pipes almost always end up having turbulent flow inside, in which case, pressure drop is proportional to flow rate squared. Whereas for electricity, voltage drop is always proportional to current. This leads to problems when trying to use circuit analogies when trying to solve for pressure drop in a system of pipes.
If you force enough current through a wire, the Lorenz force can cause it to pinch in on itself and disintegrate. Copper wires aren't so simple at high currents, high voltages, or high frequencies.
Whereas for electricity, voltage drop is always proportional to current.
The water metaphor works fine for many DC circuit comparisons, up to and including basic transistor operation. Meanwhile, at AC, your statement above doesn't hold up much better than the water analogy would. Lots of additional terms come into play... skin effect, radiative losses, displacement current and phasor relationships, even quantum effects.
Every once in a while, a huge Internet argument springs up among people who don't understand that the Ohm and Kirchoff laws represent the steady-state map and not the time-variant territory. Do a search on eevblog for "Lewin," for instance. (Actually that's terrible advice. Don't do that, and forget I said anything.)
While this is true, these analogies do have limits of applicability, like all models have. They are only valid down to a specific point of abstraction and only within certain bounds.
You just have to be aware of the limits of your analogies, to use them as a tool, an educational one in this context.
You can think of a capacitor as sort of like a rubber membrane stretched across the pipe. It allows some water to flow as it distends but then stops. When distended like that, it has some reverse pressure that wants to flow back.
An inductor would be something like a propeller/impeller attached to a flywheel.
I've been recently learning all about hobby electronics recently (circuit design, microcontrollers, basic components so far), so I want to give a beginner's perspective, and honestly this water pressure /flow analogy is actually really distracting and misleading as soon as you get past the basics of circuits and components.
If you're an educator please reconsider using these analogies that fall apart later on becuase in more complex concepts but the analogy may stick on in your students head when it doesn't apply. Or at least heavily stress that these are analogies and not to expect that this "water circuit" analogy will hold forever.
I don't know how hard it is to find these days, but I stumbled across a book called "There are no elections" ages ago that I found very helpful. As a student of American high schools familiar with both the water analogy and the basic electron flow theory we get in school, that book does a good job of upending both by presenting a sort of third model that, while tongue-in-cheek, fits the observations the first two models explain. Then it's sort of goes on to show how those models are all lacking because there are other things we know about electricity that don't fit any of them.
This Falstad animated circuit simulation has been the best at conceptually understanding what's going on in circuits:
https://falstad.com/circuit
Click on the 'Circuits' menu to see dozens of example circuits.
One issue with the hydraulic/fluid analogy is the "empty pipe" misconception - we forget or don't know that in electrical circuits, the circuit is a closed loop. An example of this misconception is that beginners sometimes think the current "wears out" as it goes along the wire. The Falstad simulation shows a line of moving dots that move faster or slower depending on the current - a little more like a train moving in a pipe - which helps counter this misconception, although it, too, isn't perfect. As a next level, I like showing animations/simulations that show the role of charge on the 'outside' of the wire in steering current flow, as well as magnetic fields surrounding the wire.
A "closed" circuit is just an open circuit plus a pump (electron pump or water pump).
Open circuits work fine if there is a powerful source of electricity (like a a radio) and a sink (like the Earth), and same for water (an icy comet crashing into a cliff, making a waterfall).
An open water circuit is full of stationary water.
Those are exceptional. I remember gaining really nice math and physics intuition from his "applets" years ago. Yes, those started as Java applets if anyone still remembers those.
I'm pretty sure this is the one that I found while in undergrad physics. That diagram helped me gain a level of visual understanding that I hadn't obtained from hobby DC circuit tinkering. I remember feeling very grateful to exist during a time when an interactive web app could show me what would have taken N hours in an electronics lab to see in years prior. Many thanks Paul Falstad.
There are also some very interesting analogies with mechanical and thermo dynamical* systems.
What i find even more interesting, is that those analogies are no lucky coincidence.
The rules of dynamical systems apply on a higher level. The differential equations governing those systems do not care, how the concepts of inertia, capacitance or resistance are realised in a real world system. Those are implementation details.
Neither do physical principles, like the principle of least action, which 'govern' those differential equations.
*Fun fact: Classical thermals systems do not have an inductive element. That's why there are no oscillations in thermal systems. You need two kinds of energy storage for that, so that the energy can switch between them.
These water circuit analogs to electric circuits remind me of Eric Laithwaite's water analogs. Several videos showing the analogs in action on youtube in The Circle of Magnetism. For example: https://www.youtube.com/watch?v=0tJfqMYHaQw
I've had my head buried in law too long because when I saw this headline I didn't think about electricity; I figured somebody had come up with a boneheaded way to explain a legal theory.
Anyway.
The water analogy is pretty good, but it's important to not get too wrapped up in it. In some very fundamental ways, electricity is not like water, and believing it is will trip you up when you get into more complicated circuits or try to take what you've learned about DC and apply it to alternating current. It's a great place to start though.
After getting one's head wrapped around those, I found that Kirchoff's loop and junction rules were great, because they make intuitive sense (junction because matter is not created or destroyed, and loop because the value of a thing has to be equal to itself, so no matter what path you take around the circuit, when you return to a point of origin it must be true that the point of origin has the same voltage at the end of the path as it did at the beginning).
76 comments
[ 2.7 ms ] story [ 147 ms ] threadI guess a transistor is a little man twiddling a valve according to a dial in the "water model" of electricity, any through-space effects are due to leaks, and nonlinear components like MOSFETs are a bit more creatively explained. (E.g. Source: water reservoir; drain: water reservoir; gate: gate between source and drain reservoirs, driven by an utterly mad person who follows interesting rules. Oh, and inexplicably he's a bit stronger than transistor man too).
Still, I think the water analogy is over used
I mean, it’s probably worth mentioning current and voltage are “kind of” like flow, pressure etc., in a first lecture to start to get the basic idea, but then warning not to think of it as being the exactly same because that will just be confusing later.
The water analogy, is, in my opinion, the sweet spot for people who will never own a multimeter or fire up a SPICE program. It's the level that ought to be the expectation for citizens of a technic civilization.
What you can't do is design a bottom dollar power supply that uses some trick circuitry to not emit enough RF noise to matter.
All radio/wifi and everything involving fiber optics or magnets. That's probably slightly more than 00.001% of applications.
It's just as easy to understand without need for analogies.
Based on what you've described, where would you develop the intuition about the difference in speed between the electrons and the electromotive force they are relaying? Or why you need both voltage and current to do work, or the behavior of an LCR circuit? Or an open circuit? Etc etc.
If only! My apartment was recently destroyed by water that refused to do exactly that...
Electricity also doesn't freeze solid, expand, and break open its insulation; it doesn't evaporate and condense on cold surfaces and cling there under surface tension, it doesn't drip down.
But the analogy is still a pretty useful one for people who have lots of hands-on experience with water and not much with electricity, or vise-versa.
>> expand, and break open its insulation = an arc causes by too much electricity in too thin a pipe.
>> it doesn't evaporate and condense on cold surfaces = electro vapor deposition aka physical vapor deposition
Arcing (or shorting in general) would probably be more akin to water's tendency to find the lowest point.
[0]https://en.wikipedia.org/wiki/Injector#/media/File:Ejector_o...
If that were the case I wouldn't be paying twelve hundred bucks and counting to fix the plumbing in my mom's house.
You don't even need fancy things like transformers for energy not in the wires to be important. Even a simple DC circuit consisting of a battery in series with a light bulb mostly involves an electromagnetic field to transfer energy from the battery to the light bulb, which mostly takes place outside the wires.
The function of the wires when it comes to energy transfer is to carry moving charge which creates the magnetic part of the electromagnetic field that actually carries the transferred energy.
Here's a pretty good explanation [1]. That video was from January 2019, and not controversial. Veritasium did a video on the topic in late 2021 that didn't really present things as well and ended up being quite controversial [2]. Other well-known YouTube channels such as EEVblog [3] and ElectroBOOM [4] responded.
There was also someone who bought a bunch of wire and did the experiment as described in the Veritasium video (although scaled down). That was discussed on HN and that discussion contains some very interesting links [5].
In particular the link to a talk by Rick Hartley in this subthread is very informative [6]. He talks about how most EMI problems in PCB designs are due to people not taking into account the the energy is not in the wires.
[1] https://www.youtube.com/watch?v=C7tQJ42nGno
[2] https://www.youtube.com/watch?v=bHIhgxav9LY
[3] https://www.youtube.com/watch?v=VQsoG45Y_00
[4] https://www.youtube.com/watch?v=iph500cPK28
[5] https://news.ycombinator.com/item?id=29598860
[6] https://news.ycombinator.com/item?id=29601273
The right way to think about this if you _really_ care is a bit like the way that RF engineers think about dielectric resonators. The metal motivates the fields to be guided along pairs of conductors by the motion of charge carriers within. A metal will respond in a particular way to fields, which results in new fields, and so on and so forth in a way that results in the fields propagating along in a particular way.
A propagating pulse is a bit hard to think about but you can imagine some field configuration that results in the electrons in the metal slipping a bit, and those electrons move in a way that results in new fields which contain the new wavefront of the pulse. The electrons don't keep moving -- they move on average the distance of the mean free path and give their energy to the lattice as heat. This is why the drift velocity is just a meaningless number. The fields propagate at around c and the conductors guide them.
The pedagogical failure of this analogy is how it suggests that the energy is stored in the potential and kinetic energy of the fluid (the electron density) rather than in the fields. Then you end up with this drift velocity nonsense which is essentially a holdover from the Drude model which is only predictive by luck.
https://en.wikipedia.org/wiki/Hydraulic_analogy
https://i.redd.it/42ah3br6r2251.jpg
It led to many EEs getting a certificate in fluid & thermo because the extra couple classes counted as tech electives and the math was the same.
I would love to find a book with this type of presentation. Do you happen to remember which textbooks were used for this class?
SchÖnfeld, J. C. (1954). Analogy of hydraulic, mechanical, acoustic and electric systems. Applied Scientific Research, Section B, 3(1), 417–450. doi:10.1007/bf02919918
I recently got into electronics/electricity and I have been trying to put together a course for myself, mostly for the kind of work that involves fixing things (power supplies, small house appliances, and so on) but also for having a good understanding for how things work. Of course the field is huge and there’s all sorts of applications out there. I’m a long time software dev and I’ve delved into all sorts of software-oriented subjects over the years, so I’m hoping I can apply some of this knowledge, at least from a troubleshooting/analysis perspective. But oh boy is this difficult due to electromagnetism and not being able to really visualize these things (not without an oscilloscope I suppose).
A close family member was an EE/technician and they ran a repair service for appliances for many decades - anything and everything, TVs, radios, kitchen appliances, industrial machinery, and so on. Sadly they passed away and I don’t know anyone personally I can ask about where to begin and how to approach this.
Any recommendations for curriculum? I started with Make: Electronics 3rd Ed and a half dozen or so online resources, like the Khan Academy series and some other undergraduate level videos on circuit analysis and such. I really like the electricity misconceptions site as well.
On the other hand, the underlying theory is very useful for if you do encounter something off code, because something off code will be doing something, and you as the homeowner are stuck figuring out what.
Did you know - a boost switching regulator was used to pump water up to the top of a garden in Victorian times. The regulator uses the water pipe analogy to electricity, except electricity hadn't really been invented then. The system uses an inductor (a long straight pipe, where the water has momentum), and a switch (a flap that closes and opens regularly), with a diode (one-way valve) and a capacitor (a container with a pressurised air cavity). https://en.wikipedia.org/wiki/Hydraulic_ram
https://www.kickstarter.com/projects/upperstory/spintronics-...
My 9 year old brother found it quickly too hard though.
It does a good job of introducing concepts slowly but they are in fact hard concepts if you're new to them. It is actually a bit of a challenge for adults too.
Mechanically, the game is good but a bit finicky to set each piece in place. That means the time between "I think I know what to do" and testing it out is a bit too long. Overall, I find it pretty fun though. (I also backed the spintronics kickstarter)
[0] https://news.ycombinator.com/item?id=27222457
[1] https://www.turingtumble.com/
How would you model mutual inductance in other circuits?
Helmholtz resonators[1] are used to provide capacitive acoustic impedance in a gas system. Archetypically a beautiful hollow copper sphere. Ported subwoofers use the same formulas, as do some types of automotive exhaust. Exhausts use a long pipe and cylindrical section to form a low-pass filter, which transforms the individual exhaust bursts of an engine into a smooth continuous flow. Two stroke exhausts[2] are band-pass filters that improve compression by putting backpressure on the engine at the correct time.
[1]: https://en.wikipedia.org/wiki/Helmholtz_resonance
[2]: https://en.wikipedia.org/wiki/Expansion_chamber#/media/File:...
https://acousticstoday.org/past-issues/james-clerk-maxwell-a...
I looked at the photo and the description and suddenly realized I was looking at a XOR’d MOSFET low side switch circuit made of pipes and valves.
Funny that sometimes the water analogy also works the other way around.
The opposite is also true; if the flow out of a pump is blocked then the pressure will immediately climb extremely high and usually break things. Once you get into the weeds with transistors etc you obviously also have to worry a lot more about currents, but with hydraulics it's always about the flow.
Pipes almost always end up having turbulent flow inside, in which case, pressure drop is proportional to flow rate squared. Whereas for electricity, voltage drop is always proportional to current. This leads to problems when trying to use circuit analogies when trying to solve for pressure drop in a system of pipes.
The water metaphor works fine for many DC circuit comparisons, up to and including basic transistor operation. Meanwhile, at AC, your statement above doesn't hold up much better than the water analogy would. Lots of additional terms come into play... skin effect, radiative losses, displacement current and phasor relationships, even quantum effects.
Every once in a while, a huge Internet argument springs up among people who don't understand that the Ohm and Kirchoff laws represent the steady-state map and not the time-variant territory. Do a search on eevblog for "Lewin," for instance. (Actually that's terrible advice. Don't do that, and forget I said anything.)
That's how modelling works.
An inductor would be something like a propeller/impeller attached to a flywheel.
If you're an educator please reconsider using these analogies that fall apart later on becuase in more complex concepts but the analogy may stick on in your students head when it doesn't apply. Or at least heavily stress that these are analogies and not to expect that this "water circuit" analogy will hold forever.
Click on the 'Circuits' menu to see dozens of example circuits.
One issue with the hydraulic/fluid analogy is the "empty pipe" misconception - we forget or don't know that in electrical circuits, the circuit is a closed loop. An example of this misconception is that beginners sometimes think the current "wears out" as it goes along the wire. The Falstad simulation shows a line of moving dots that move faster or slower depending on the current - a little more like a train moving in a pipe - which helps counter this misconception, although it, too, isn't perfect. As a next level, I like showing animations/simulations that show the role of charge on the 'outside' of the wire in steering current flow, as well as magnetic fields surrounding the wire.
Open circuits work fine if there is a powerful source of electricity (like a a radio) and a sink (like the Earth), and same for water (an icy comet crashing into a cliff, making a waterfall).
An open water circuit is full of stationary water.
Here are math and physics ones: https://falstad.com/mathphysics.html
I like the 2D vector field one https://falstad.com/vector (2d) and the 3d one https://falstad.com/vector3d.
Antenna simulator: https://falstad.com/antenna
Waveguide is awesome too https://falstad.com/embox/guide.html. Don't forget to pick various modes in the little square at the bottom.
If Paul Falstad comes around these parts, thank you for creating and sharing those!
behold! the MONIAC
https://www.rbnz.govt.nz/research-and-publications/videos/ma...
What i find even more interesting, is that those analogies are no lucky coincidence. The rules of dynamical systems apply on a higher level. The differential equations governing those systems do not care, how the concepts of inertia, capacitance or resistance are realised in a real world system. Those are implementation details. Neither do physical principles, like the principle of least action, which 'govern' those differential equations.
*Fun fact: Classical thermals systems do not have an inductive element. That's why there are no oscillations in thermal systems. You need two kinds of energy storage for that, so that the energy can switch between them.
Anyway.
The water analogy is pretty good, but it's important to not get too wrapped up in it. In some very fundamental ways, electricity is not like water, and believing it is will trip you up when you get into more complicated circuits or try to take what you've learned about DC and apply it to alternating current. It's a great place to start though.
After getting one's head wrapped around those, I found that Kirchoff's loop and junction rules were great, because they make intuitive sense (junction because matter is not created or destroyed, and loop because the value of a thing has to be equal to itself, so no matter what path you take around the circuit, when you return to a point of origin it must be true that the point of origin has the same voltage at the end of the path as it did at the beginning).