Understanding concepts with analogies help can be a useful technique and hopefully this will help me better understand electricity and Electrical Engineering better.

Lets start with a simple water example:

X volume of water starts flowing from a collector (battery) through the pipe with Y pounds of pressure at Z speed when it comes across a thinner portion of pipe (resistor).

Now, perhaps my physics knowledge is off but I would image that when it hits the thinner portion of pipe, resistance increases causing the pressure and speed of the water to increase but the volume would decrease. If this is correct, does that mean that the voltage and current increase but the number of electrons (what is the mass/volume analogy for electrons?) would decrease (and therefore power)?

Additionally, since electrons actually flow from negative to positive (electron flow), in contrast to conventional flow, does that cause this analogy to break down in a true circuit (especially with numerous components)?

Thanks in advance for the help.

  • \$\begingroup\$ Electrons don't even 'flow' per-se. You can alternatively talk about hole transport which tends to move from high potential to low potential. I think an introductory EE book would cover moving charges and current pretty well \$\endgroup\$
    – HL-SDK
    Commented Dec 11, 2013 at 2:11
  • \$\begingroup\$ the volume would decrease after the small pipe, which is current limited by a resistor. \$\endgroup\$
    – Vitim.us
    Commented Dec 11, 2013 at 2:17
  • \$\begingroup\$ Welcome to EE.SE! Unfortunately you are mixing up important concepts. Current, whether water or electrons, is an amount per second rather than just a volume. Power is not related to the number of electrons but to the energy the lose as they move from high to low voltage (pressure). You really would benefit from a book on basic electronic principles. \$\endgroup\$
    – Joe Hass
    Commented Dec 11, 2013 at 3:24
  • \$\begingroup\$ @JoeHass Nowhere in my post did I confuse current with volume. I asked what the analogy for volume (mass) would be, I didn't say it was current. Furthermore, if pressure (voltage) and speed (current) were decreased, then power would also decrease (P=I*R). Nowhere did I state power = number of electrons. You would do well to read what is written first. I also own at least 5 books on Electrical Engineering. The purpose of this question is more about circuit analysis and visualizing the mechanics going on, hence the purpose of analogies. \$\endgroup\$
    – Ronald
    Commented Dec 11, 2013 at 3:50
  • \$\begingroup\$ The analogy for mass would be charge. \$\endgroup\$ Commented Dec 11, 2013 at 3:55

8 Answers 8


You need to be careful with analogies. Here are some problems in the analogy you describe:

water starts flowing from a collector (battery)

Nothing in an electric circuit really works like a collector of water. In your analogy, water is electric charge which, in metals, is carried by electrons slowly drifting. Batteries do not store charge, they are not a reservoir of charge (nor of electrons).

Batteries store energy in chemical form. A better analogy is that a primary battery is a coal-fired water pump that will deplete it's store of coal as it pumps water. A secondary battery is a bit like a pump powered by a wind-up spring, it can be run in reverse to wind up the spring. These pumps can only pump water if their outlets are connected to a circuit of pipes that eventually returns to their inlets.

does that mean that the voltage and current increase ...

Voltage isn't something you measure at one point, it's something you measure between two points - it's a difference.

If you measure the voltage at every millimeter of the circuit with respect to the batteries negative terminal you will see the voltage monotonically decreasing as you progress around the circuit‡.

The current measured at any point in the circuit‡ is the same. It neither increases nor decreases

... but the number of electrons would decrease

It isn't very useful to think of the number of electrons increasing or decreasing. Where would they go? Where would they appear from?

You measure a current† of water in litres per second. You measure a current of electricity in coulombs per second (amperes). In a steady-state system, this current is the same in all parts of a simple serial circuit - whether of pipes or of water. A constriction in a pipe cannot make n litres per second of water disappear.

If you slightly turn a gate-valve in a water pipe, the flow of water (litres per second) decreases in all parts of the circuit, including in the pump.

resistance increases causing the pressure and speed of the water to increase but the volume would decrease.

That's not how water works!

If we imagine a simple circuit where a water pump is pumping water around a loop of pipe. The pipe is of uniform size apart from one place where we have a section of narrower pipe.


The resistance is greater in the narrower pipe (a greater proportion of the water is close to the pipe walls and experiencing friction)


However the pressure is lower, not higher!


It's the lower pressure that causes the water to accellerate to a higher velocity as it enters the narrow section.


When you say the volume increases, I think you mean the velocity increases. Water is relatively incompressible, it's volume doesn't change much at the pressures applying in our analogy.

The flow rate (volume per second) is unchanged.


This is one of the areas where the analogy starts to break down. The word "current" is used inconsistently. If you asked someone to measure the current in a river they might give you an answer in metres per second ("current" = average drift velocity of H2O molecules) instead of litres per second ("flow" = litres per second passing a fixed point).

This answer applies only to a simple circuit of battery and resistor connected by copper wires.

  • \$\begingroup\$ @AndrejaKo So in a pipe (with water), a certain amount of pressure will force the water through the pipe. Once it hits a narrow spot you are forcing the same amount of water through that pipe, so the speed of that water, at that point in the pipe would increase. Perhaps not the pressure or volume since the increase in speed probably attempts to maintain them. Is this not correct? \$\endgroup\$
    – Ronald
    Commented Dec 11, 2013 at 18:32
  • \$\begingroup\$ @Ronald I was going to write a thorough answer, but then I understood that I reached the point where I'd use electrical analogy to understand how water flow works. :) \$\endgroup\$
    – AndrejaKo
    Commented Dec 11, 2013 at 20:19

E=IR analogie
Electrons flow from negative to positive in the circuit,
and from positive to negative in the power source.

  • 1
    \$\begingroup\$ While I like the image, I can't vote this answer up because I feel it does not adequately attempt to answer the question. \$\endgroup\$
    – JYelton
    Commented Dec 11, 2013 at 16:19

One water analogy for capacitors I've seen somewhere long time ago is to think of a capacitor as a water tank witch is filler with water and has an elastic membrane separating it in two parts. It would look something like this:

"Empty" capacitor

Both the left and the right side of the tank are filled with water and the membrane in the middle if in relaxed position.

Now suppose we connect the tank to two water pipes connected to some system and suppose that the pressure in the right pipe is higher than the pressure in the left pipe. The higher pressure of the water on the right side would exert force on the membrane and would work to push the elastic membrane to the left in order to increase its volume.

The membrane would push some water on left side out of the tank and the volume of the water on the right side would expand to fill the the space left out by the water on the left side. At one point, the expansion of the right side water will stop, once the effects of forces from the pressure of the water on the right side and the pressure of the water on the left plus elasticity of the membrane even out.

"Full" capacitor

Our "full" tank has same amount of water in it as it had when it was empty, but the distribution is different. This is what happens when we connect the capacitor to a DC circuit. There will be some time during which the water flows though the tank and then the flow drops down to zero when the distribution of water stabilizes.

If we were to connect the ends of the tank together somehow using a pipe full of water, the membrane will push the water from the left side out and back into the right side and we'd get the first image. This is what happens when we short a charged capacitor.

Capacitor shorted

Another thing to imagine is what happens when sometimes the pressure on the left is higher and sometimes the pressure on the right is higher. In that case, the water will alternatively move from one section of the tank to another. If we measure the flow of water, we'll see that it is continuous. This is how capacitors pass AC current through them.

Sometimes, if the rate of change it high enough, the (insufficiently high) elasticity of the membrane and the diameter of the pipes will slow down the flow of the water through the tank's connections. This is how we can think about the "parasitic" side effects of a capacitor such as ESL, ESR and so on.

Few points that need to be mentioned: I always noted that we used pipes which are already filled with water to connect the tank and that the tank is already full. This is because we already have electrons inside out conductors and the there are already electrons inside of the capacitor. It' not empty and it does not need to be "filled". All the energy inside of the tank model of the capacitor is stored inside the membrane. This is same as stretching a rubber band. When released, it will try to go back into its original shape.

I also have an idea how to think about AC current carrying power, even though the electrons move back and forth.

cutting a loaf of bread

Imagine this: We have a loaf of bread and we want to cut a slice of bread from the loaf. Now let's suppose we have a sufficiently long knife. We could press the knife to the bread and then move the knife in one direction until the slice if cut. If we were to just observe this kind of motion, we could think that the depth to which we cut the slice depends on the total distance of knife's starting position. Expanding on this idea, we could claim that if we were to move knife backwards, it wouldn't be able to cut bread.

Of course, we know that we can move knife in both directions and get the same effect as shown in the following picture:

knife 2

This is where the "cutting works only if we move the knife in one direction" idea would break down. If we analyze the movement of the knife, we would be able to determine that it's not current the distance of the knife from its starting point that affects the cutting of the bread, but the length of the path the knife moved that affects the cutting.

Same idea works with AC as well. Even though the electrons move in both directions, they still do work.

  • \$\begingroup\$ I'm not sure how well that last idea turned out... :( \$\endgroup\$
    – AndrejaKo
    Commented Dec 11, 2013 at 13:28
  • \$\begingroup\$ I think this is one of the better posts. Thanks =) \$\endgroup\$
    – Ronald
    Commented Dec 12, 2013 at 1:36
  • \$\begingroup\$ Question: If I had one electron held 1 inch from a positively charge atom and I also had 100 electrons held 1 inch from 100 positively charged atoms, would they both have X voltage? I am guessing the current generated from releasing them would be different since less electrons are passing a point at a given moment in the first example versus the second example. In which case knowing the voltage can be somewhat misleading. \$\endgroup\$
    – Ronald
    Commented Dec 12, 2013 at 1:50

Water pressure isn't a terrible analogy, but your particular analogy has a few flaws. Your setup basically has a voltage source, a wire, and a resistor. The current in the wire or rather in the entire circuit is the same everywhere in the circuit (at least in this simple example because you've chosen a pressure source -- note that this would be reversed if you chose a fluid source or in EE parlance a current source). Ohms law states that V = IR (voltage = current * resistance). If you start with a known voltage (or water source) and put a load on the voltage then ohm's law will tell you what the current is. The power dissipated is found by P = I*R (or use ohm's law and substitute for I or R and find one of a few equivalent equations). You can think of pressure as voltage and flow as current, but obviously fluid dynamics get pretty complicated/tricky as do circuits. The analogy should be used for basic stuff (e.g. higher voltage yields more current for a fixed load just like more water pressure yields more flow in a fixed tube), but beyond that I'd try to avoid relying on it too heavily.


I'm going to point out why it is possible to have two conventions of the direction of current.

Which convention you choose doesn't really matter, electron flow goes from negative to positive, conventional flow see positive charges going from positive to negative. Positive charges doesn't need to exist, the absence of an electron can be perceived as a virtual positive charge.

If a electron is going in this direction ->, the space left behind is in the opposite direction <-.

I made this animation, hopefully you can see what's going on. What is the direction of this animation? it depends on what color you're looking at.

It may help to visualize covering the upper or bottom arrows with a piece of paper.

enter image description here

enter image description here

You can say the same about an Hourglass

enter image description here

Which direction it is going? It depends if you're referring to the water water or the air. Water is going down at the same time Emptiness is going up.


X volume of water starts flowing from a collector (battery) through the pipe with Y pounds of pressure at Z speed when it comes across a thinner portion of pipe (resistor).

This isn't meant to be a complete answer but rather, an extended comment which I may extend into a full answer.

For a proper use the hydraulic analogy of an electric circuit, it must be remembered that the pipes that form the closed path for water flow are filled with water. (After all, a conductor is not empty of mobile charge carriers but is instead full of them.)

Thinking carefully about this, realize that the speed of sound in water is the speed with which pressure changes propagate through the circuit.

So, it isn't productive to think in terms of "when [the volume] of water reaches the ... thinner portion...".

The flow of water may be quite slow within the pipes but pressure changes propagate much more rapidly just as, in the case of electric circuits, the flow of electrons (or whatever the relevant charge carrier is) may be quite slow but changes in voltage and current propagate near the speed of light. See transmission line.

Consider a water pump connected to water filled pipe and imagine that the pipe offers essentially zero friction. This means that the water flows through with essentially zero pressure provided by the pump.

Now, imagine that the pipe is suddenly constricted at some point along the path such that, to maintain the same flow of water, a pressure P must be present across the constriction (the constriction is analogous to a resistor).

Note that a pressure P will appear across the pump almost immediately since the change in pressure will propagate away from the constriction to the pump at the speed of sound of the water in the pipe.

As an aside, I've noticed that the hydraulic analogy of a capacitor has been introduced in another answer.

So, to be complete, the hydraulic analogy of an inductor might be something like an impeller inside the pipe with some moment of inertia. The water flowing past the impeller must exert a pressure to start the impeller rotating but, once rotating at the appropriate rpm, no pressure is required to maintain the rotation. If the water flow begins to decrease, the impeller will act to create a pressure that opposes the increase.


Let's fix the physics in your simple water example:

X volume of water starts flowing from a collector (battery) through the pipe with Y pounds of pressure at Z mass flow rate when it comes across a thinner portion of pipe (resistor).

When it hits a portion of pipe with baffles (thin pipes only offer a very small resistance in subsonic flows), resistance increases causing a measurable change in pressure between input and output (and a net force on the pipe) and mass flow rate of the water will remain the same. This does that mean that the voltage across a resistor will increase with resistance but the rate of flow of electrons/current stays the same.

Additionally, since electrons actually flow from negative to positive (electron flow), in contrast to conventional flow, does that cause this analogy to break down in a true circuit (especially with numerous components)?

No, the analogy can work either considering current flow or electron flow as long as you're consistent. Mass flow of liquid is analogous to flow of charge, whether considered as conventional current, or as electron flow.

Your original description included velocity increasing and pressure decreasing in a cataract. This is known as Bernoulli's principle. If you want to have Bernoulli's principle as part of your analogy - conservation of energy means lower pressure for higher speed in an inviscid fluid - then you need to work in a electrical domain which is physically similar. You need no viscosity, and for there to be a transfer of energy between potential energy and the kinetic energy of the flow. Viscosity is the effect which causes the resistance to flow in a pipe (the fluid touching the walls is stationary, energy is lost by vortices and shearing), and you need a model where the speed of the electrons is high enough for their kinetic energy to be significant. Perhaps something like an electron gun will have enough velocity to show a transfer between PE and KE with no resistive effects.

  • 1
    \$\begingroup\$ Your analogy only holds if the pipe is initially empty because you talk about "when water hits the thinner portion". A better analogy would assume that the pipe starts full and the pressure in the fat parts of the pipe is the same at any point in a given fat pipe, just like the voltage is the same everywhere on an ideal wire. The Bernoulli effect is not a good analogy either...moving electrons through a solid is more like moving water through a pipe packed full of sand. \$\endgroup\$
    – Joe Hass
    Commented Dec 11, 2013 at 14:25
  • \$\begingroup\$ @JoeHass the analogy holds for the steady state. The use of 'hits' is from the OP; I took it to mean any given point volime in the flow. Thin pipes offer a small resistance, sand or baffles are better analogy so I've updated that. The OP mentioned Bernoulli as part of the analogy; I agree that it isn't appropriate for a resistive model for the reasons I give. \$\endgroup\$ Commented Dec 11, 2013 at 15:53
  • \$\begingroup\$ Pete, I don't see the word "Bernoulli" anywhere but in your answer and the comments below it. \$\endgroup\$
    – Joe Hass
    Commented Dec 11, 2013 at 19:11
  • \$\begingroup\$ @JoeHass Read the OP. He is talking about a flow hitting a thinner portion of the pipe, the velocity increasing and the static pressure decreasing. That is Bernoulli's principle. It is not a good analogy for electric resistance. I have edited to make in clear that Bernoulli's principle came from the OP. \$\endgroup\$ Commented Dec 11, 2013 at 22:53
  • \$\begingroup\$ @PeteKirkham so the effect (or concept really) of resistance on pressure and current in a circuit differs than that of the water? Which would explain the confusion. I always found the resistor affecting voltage, rather than current, kind of weird. Thanks. \$\endgroup\$
    – Ronald
    Commented Dec 12, 2013 at 0:07

Water is a great analogy for understanding the basics and even for generally intuiting more complicated stuff.

Water is like charge. Pipes are like wires. The rate of flow of the water though a cross section of a pipe is like current.

I like to think of voltage as the height of the water above the floor. The floor is "ground".

Water will flow from a higher spot to a lower spot. Only differences in height really matter for determining rate of flow. The bigger the difference in the heights, the more pressure that will be behind the flowing water.

If you have a very fat pipe, you can quickly move a lot of water even with very little height difference driving it. Think the Hudson River. It is so wide that it can carry billions of gallons of water past a point per hour even though the height difference is only a few feet. This is like a wire with very low resistance, you can have a large flow of current though it even with a small voltage across it.

As the pipe gets narrower, you need more pressure to keep the rate of flow constant. Think of a straw connected to a bucket at the top of the Empire State Building. Even though there is a huge height differential, the amount of water flowing though the straw is small.

There is a balance between pipe size and pressure. As resistance in a wire goes up, you need more voltage to maintain the same amount of current flowing though it.

If the pipe becomes blocked then there will be no flow at all until the pressure gets so high that it blasts out the blockage. No current will flow across an insulator, unless the voltage gets higher than the breakdown voltage.

You can even model other components.

Water will flow into a pressure tank as long as the pressure in the pipe is greater than the pressure in the tank. As the pressure in the tank builds, the water will flow in more slowly until it stops when they have reached the same pressure. At that point, you can close the valve (switch) going into the tank and it will hold that pressure indefinitely (unless is has a leak). When you open the valve, the water will push out - and the pressure will drop as more water comes out of the tank until it is at them same pressure as the pipe it is connected to. Larger tanks take longer to fill and longer to empty than smaller ones. (The pressure in the tank is like the charge stored in a capacitor.)

If you insert a turbine into a pipe of running water, initially the blades will block the water from flowing. As the turbine blades spin up, more and more water will be allowed to pass though until the blades are spinning at the same speed as the water flowing across them and the flow rate will be what it was when you started. If you then drop the pressure of the water, the momentum of the turbine will keep it spinning and it will start to pump water across it, generating pressure like a pump. As the blades slow down, the pressure will drop until they are stopped and there is no pressure difference across the turbine. (The turbine is an inductor and momentum of the spinning blades is the magnetic field.)

You could even model a transistor as a pilot valve. The flow of a small amount of water in a small pipe can control a much larger flow in a big pipe.

I've always wanted to actually build some demo circuits using these analogies. You should be able to make an LRC oscillator that would actually work just like its electronic cousin, except that you could see what was happening.

If you are just getting started learning this stuff, here is a book that changed my life...


It is for High School kids and easy to follow. It actually really explains what is going on without analogies. The analogies are great, and I often use them in my mind when thinking about this stuff - but there are times that they fail and knowing what the electrons are doing and why makes everything make sense.

  • \$\begingroup\$ -1 for furthering the misconception that charge is stored in a capacitor. The capacitor stores energy. Unlike a water tank the capacitor as two terminals and exactly the same amount of charge leaves one terminal as enters the other. \$\endgroup\$
    – Joe Hass
    Commented Dec 11, 2013 at 11:49
  • \$\begingroup\$ Granted. Maybe a more useful analogy might be a membrane pressure tank with taps on both ends. The energy in this case is stored in the stretching of the rubber membrane by a pressure difference between the two taps. Bigger tank (more capacitance) can store more energy for a given pressure difference (voltage). More pressure difference stores more energy than smaller pressure difference. Could even stretch the analogy by pointing out that there is a maximum pressure difference (voltage) that will burst (breakdown) the membrane (dielectric) and allow the water (current) to flow though. \$\endgroup\$
    – bigjosh
    Commented Jan 3, 2014 at 6:28

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