# Voltage & Current

How would Voltage & Current relate to a garden hose? I know that the pressure of the hose is Voltage and the flow of the hose is current but I need more details about it.

Voltage is a unit used to express potential difference.The garden hose is connected to say a tap.Now,the tap releases water with pressure.As there is a difference of pressure between the ends of the hose....the water flows

But the flow of water is restricted by certain frictional forces that provide Resistance
Similarly,Ohm's Law gives us a reltion between potential difference,current and resistance

The Ohm's Law is mathematically expressed as:
$$V=IR$$

The model is more like a current in a wire if the garden hose is not an open tube. I mean if there's a 'porous media' inside the hose then the 'resistance' should be linearly propotional to the hose's length and inversely propotional to its cross section. That's exactly the Ohm's Law.

russ_watters
Mentor
You wouldn't want it open - that would make your amperage decrease through the hose. The resistance is just....the resistance. You already have it due to the roughness of the hose.

You can think of voltage as the amoutn of energy to move an electron through a resistance

and current as how many electrons are moving through the resistance.

russ_watters
Mentor
You can think of voltage as the amoutn of energy to move an electron through a resistance
No, you can't. Voltage is a pressure and is directly analagous to mechanical pressure. This is not an uncommon analogy for a teaching aid because it is exactly the same mathematically: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/watcir.html

As you can see:
pressure = voltage
volume flow rate = amperage
resistance = resistance

An open garden hose is analagous to a short to ground, so the resistance in the hose is equivalent to the resistance of a wire in a short.

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No, you can't. Voltage is a pressure and is directly analagous to mechanical pressure. This is not an uncommon analogy for a teaching aid: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/watcir.html

As you can see:
pressure = voltage
volume flow rate = amperage
resistance = resistance

He's correct. What are the units of a volt?

Then again, why do we need to make an analogy between electricity and water systems. Its totally useless. It was never worth a damn for anything other than showing there was an analogy. I never did a single circuit problem saying, soooo if I think of the pressure through the inductor..............

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russ_watters
Mentor
He's correct.
Who?
What are the units of a volt?

Then again, why do we need to make an analogy between electricity and water systems. Its totally useless. It was never worth a damn for anything other than showing there was an analogy.
I suppose that is a rhetorical question, but it is often very useful to cross back and forth between mechanical and electrical energy. It may not be as direct, but I use the concept regularly when figuring out things like fan or pump efficiency or cross-checking electrical and mechanical energy via efficiency: a joule of pump energy and a joule of electrical energy are the same thing and you can go backwards all the way from flow rate and pressure to kw and voltage and amperage.
I never did a single circuit problem saying, soooo if I think of the pressure through the inductor..............
Maybe not, but I've seen the analogy taught in both directions in school. For people who can't understand one, relating it to the other, if only for 15 minutes when first learning it, can be helpful.

And if nothing else, for a person who has to deal with both, it means only learning one set of concepts. The answer, logic, and math to the questions:
-If I add another chilled water coil (or pump) in series with this one, what will the flow be?
-If I add another resistor (or battery) in series with this one, what will the current be?
...is the same (given some other similar assumptions, of course, like constant pressure and voltage).

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Agnostic said:
You can think of voltage as the amoutn of energy to move an electron through a resistance

and current as how many electrons are moving through the resistance.

He is correct.

I suppose that is a rhetorical question, but it is often very useful to cross back and forth between mechanical and electrical energy. It may not be as direct, but I use the concept regularly when figuring out things like fan or pump efficiency or cross-checking electrical and mechanical energy via efficiency: a joule of pump energy and a joule of electrical energy are the same thing and you can go backwards all the way from flow rate and pressure to kw and voltage and amperage.

No, it is literal. The units of voltage are Joules/C. Exactly what he told you.

"the amount of energy to move an electron through a resistance".

I still stand by what I said though. This analogy business is not necessary. You apply a voltage, you have a resistance, you get a current. Thats what happens. I dont need to know anything about pumps, water, or pressure to understand whats going on, and I avoid falling into traps by drawing too close an analogy with mechanical systems. Electrons dont have turbulence, water flow in pipes do, this is the danger of analogies.

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russ_watters
Mentor
I didn't intend to be the grammar police here, but to me, what you said and what he said are not equivalent. Perhaps you correctly read what he meant, but it looks to me like what he actually said is that voltage is energy. The best I can do to reword it to be mathematically correct would make it redundant:
'You can think of voltage as the voltage [required] to move an electron through a resistance'. It still doesn't make a whole lot of sense grammatically, but at least now it is relateable to v=ir. Before, it looked to me like it was saying e=ir or p=ir.

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He said voltage is the amount of energy required to move "an electron" through a resistance. Which would be (J/C), which is exactly the units of a volt.

This analogy business is not necessary. [..] I dont need to know anything about pumps, water, or pressure to understand whats going on, and I avoid falling into traps by drawing too close an analogy with mechanical systems. Electrons dont have turbulence, water flow in pipes do, this is the danger of analogies.

Obviously the analogy isn't necessary per se, but it just so happens that the way our brains function is by making connections.

The average person already has a good degree of intuition concerning hoses, drinking straws and water pressure, but no intuition regarding electric circuits (even worse, their experience with electronics is limited to devices so highly evolved as to appear almost magical), so it is beneficial to transfer their existing understanding onto the newer field.

I think you worry too much about the traps. Sure, electric circuits additionally produce magnetism.. but then so do water hoses, if you've studied relativity! The flow of water in pipes is not normally turbulent (for that matter, electronics are not normally nonlinear) but I'm sure the manner in which viscosity causes resistance through a pipe (Poiseuille's Law) sheds insight applicable in how resistance arises in a conductor.

It also helps solve frequent confusions. For example, many people struggle to reconcile "lights turn on instantly" with "drift velocity is very small" but they understand how a hose sprays warm water as soon as it's turned on, and has to run for a while before the cold water comes out.

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This is very simple, really, if you understand the meanings of energy, work, charge, etc.

Voltage is a measure of a potential difference between two points.

for demonstration, let's say you have two points: A and B. Now, let us place a charge at point A. Now, let's turn on an electric field that tends to move this charge from point A to point B. As the electric field moves the charge from A to B it does work on the charge. This net work in moving the charge from point A to B is equal to the kinetic energy of the charge when it reaches B.

The work we do (or the amount of potential energy converted to kinetic energy) in moving a charge in an electric field is dependent on the magnitude of the charge being moved, right? But voltage is INDEPENDENT of the charge magnitude. Voltage is defined as the amount of work done when moving ONE COULOMB of charge between two points. The voltage (or potential) will depend on the points you choose but NOT on the charge itself. So, voltage is the amount of work done in moving charge between two points PER UNIT CHARGE. Therefore, V = J/C.

To find the amount of work you need to do in moving a positive charge AGAINST an electric field between two points is just W = qV, where q is the magnitude of the charge in question and V is the voltage between the two points. Or, equivalently, to find the amount of kinetic energy gained in moving a charge q between two points in an electric field is KE = qV, where V is the voltage between the two points.

I agree with agnostic 99% when he says "You can think of voltage as the amoutn of energy to move an electron through a resistance" but I would make a slight modification and I would change the phrase "an electron" to "one coulomb", since voltage isn't J/e. but it's J/C. :) This is a minor, but significant change.

And I agree with Cyrus 100% when he says using fluids analogies for electrical systems is a very very bad idea. The reason for this was demonstrated by Russ. If you do this, you will begin thinking that voltage = pressure, instead of thinking that voltage is ANALOGOUS to pressure.

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Current is the amount of charge flowing through a cross sectional area in a unit time.

However, since current can vary instantaneously, it is more proper to say that it is the derivative of charge wrt time. So, take an arbitrarily small time dt, and measure the amount of charge that flows through a given cross section in that time, dQ, and then take the ratio of the two quantities, dQ/dt, and you have current.

I dont understand why people cant just accept voltage, current, and resistance for what it is. Like I said, you apply a voltage to a resistor, and you get a current. Cause leads to effect. There is no need for any analogies here. These are the physical observations of the system. I dont have to go through analogies just to explain what I am seeing before my own eyes.

You dont need an analogy for water systems, you accepted that for what it was. Similarly, you should accept voltage, current and resistance for what it is. There is a difference in potential. The charge moves in response to that change in potential. You get current. It is what it is.

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I dont understand why people cant just accept voltage, current, and resistance for what it is. Like I said, you apply a voltage to a resistor, and you get a current. Cause leads to effect. There is no need for any analogies here. These are the physical observations of the system. I dont have to go through analogies just to explain what I am seeing before my own eyes.

You dont need an analogy for water systems, you accepted that for what it was. Similarly, you should accept voltage, current and resistance for what it is. There is a difference in potential. The charge moves in response to that change in potential. You get current. It is what it is.

lol, well, technically a resistor has no effect on the phase relationship between voltage and current. For a resistor, V and I are in phase. Therefore, one doesn't really cause the other. Now, for an inductor, for instance, voltage leads current. V = -Ldi/dt for an inductor, so, if i(t) = cost, for instance, then v(t) = -Ldi/dt = -(-Lsint) = Lsint. So, current, for an inductor, LAGS behind voltage since sint lags behind cost by 90......the opposite holds for a capacitor.

So, the cause and effect idea fails for resistors, and voltage doesn't always cause current for other electrical systems dealing with capacitors and inductors and whatnot....

'cause and effect' is just a bad phrase to use in electrical engineering.

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cabraham
What do you mean one does not cause the other?

Get a battery, plug the ends onto a resistor. You will get a flow of current through the resistor.

You just applied a voltage to the resistor. The effect is you see a current. What does phase have to do with anything? I never said an AC source.

So, current, for an inductor, LAGS behind voltage since sint lags behind cost by 90......the opposite holds for a capacitor.

Ok it lags, fine. Does that mean you get a current before you applied a voltage to the system? You dont get current and THEN see a voltage. One *has* to preceed the other.

Somewhere, at some time, you hooked up a battery first. That was your cause. You wall is a voltage source. You plug something in, you will see a current through it thanks to that voltage source.

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What do you mean one does not cause the other?

Get a battery, plug the ends onto a resistor. You will get a flow of current through the resistor.

You just applied a voltage to the resistor. The effect is you see a current. What does phase have to do with anything? I never said an AC source.

Ok it lags, fine. Does that mean you get a current before you applied a voltage to the system?

voltage doesn't necessarily cause current. It's more of a chicken and egg scenario. What comes first, the chicken or the egg?

cabraham
No, its not.

You mean to tell me, you cant decide if you pluged in your circuit to a voltage supply, or it magically ran current through itself?

You *had* to plug it in at some point in time.

Charge simply wont move if there is no potential difference. The very first thing that happens in *any* circuit is that you apply a voltage to the circuit. Phase changes, etc. all happen later.

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No, its not.

You mean to tell me, you cant decide if you pluged in your circuit to a voltage supply, or it magically ran current through itself?

You *had* to plug it in at some point in time.

Charge simply wont move if there is no potential difference.

ok, perhaps you're right. But still, your post doesn't answer the OP's question, really.

But I'll concede.

MY point was voltage does not always CAUSE current.

MY point was voltage does not always CAUSE current.

I dont understand why people cant just accept voltage, current, and resistance for what it is. Like I said, you apply a voltage to a resistor, and you get a current. Cause leads to effect. There is no need for any analogies here. These are the physical observations of the system. I dont have to go through analogies just to explain what I am seeing before my own eyes.

You dont need an analogy for water systems, you accepted that for what it was. Similarly, you should accept voltage, current and resistance for what it is. There is a difference in potential. The charge moves in response to that change in potential. You get current. It is what it is.

Very well stated. In EE school, analogies are not made when studying circuit theory in the beginning. I, V, & R are defined in terms of work, time, charge, & observed behavior. Trying to make mechanical or fluid analogies is really bad.

The trouble with analogies is that they are only partially equivalent. A current in a wire is surrounded by a magnetic field. If the field is time changing, & another circuit is in proximity, induction takes place. Fluid flow does not exhibit this "transformer behavior". Likewise an antenna can receive e/m waves in the air & exhibit induced current. Pipes w/ fluid do not do this.

Attempting to relate circuits w/ fluid flow in pipes creates misconceptions & limits the students ability to move on to more advanced topics. T-lines, xfmrs, antennae, generators, motors, etc. cannot be modeled w/ fluid/pipe.

The best method is that of science. One ampere is defined as that current (flow of charge wrt time, I = dQ/dt) where 2 long parallel bars of negligible cross section exert a mutual force of 2e-7 newtons per meter of length. Alternately 1 ampere equals 6.22e18 electrons/second.

The coulomb is 1 ampere-second, or the charge on 6.22e18 electrons. A volt is 1 joule/coulomb. An ohm is 1 volt/amp. There are 4 basic units which define everything. They are mass, length, time, & charge. Charge is hard to repeatibly define, so current is used instead. A volt is a joule/coulomb = (kg*m^2)/(sec^2*coul).

These rigorous scientific definitions are sound & have withstood scrutiny for centuries. A good reference book, or web search, can expand upon these values to several, or more decimal places. I advise any & all to avoid analogies. The analogy in & of itself is not necesarily bad. But when used as a crutch it leads to misconceptions. When analyzing a complex circuit, one needs to use Kirchoff's current & voltage laws, Ohm's law, conservation of energy, Faraday, Ampere, etc. Fluids only confuse the matter.

Did I help?

The trouble with analogies is that they are only partially equivalent. A current in a wire is surrounded by a magnetic field. If the field is time changing, & another circuit is in proximity, induction takes place. Fluid flow does not exhibit this "transformer behavior".
True of course.

When trying to build understanding of the way light interacts with material, I think it is useful to distinguish: the effects common to most any emanation (e.g. 1/r^2 etc); the effects that are general wave effects; the features that are specific to electromagnetic waves; the features that are specific to the microscopic structure of the particular material; the (surprisingly few) features that can arise solely due to quantum mechanics (and of those which are due to the wave nature of the electron versus the particle nature of the photon..).

Analogously, when discussing flows of electrical charge, I consider it worthwhile to be aware of which effects are common (and share the same cause) to all conserved flows (of which water in a hose is simply the easiest for must people to visualise).

But generally the reason I think this is worth doing is primarily because afterward, when you investigate which phenomena are and are not attributable to which concepts (for example, self-inductance of a coil is mainly not attributable to inertia of the charge carriers), there is much opportunity to deepen and clarify understanding of the "essence" of different concepts. In other words, I don't think there is nearly as much point teaching the water/electricity analogy unless you are already intending to cover in detail the limitations of that analogy.

(Although I won't say there is no point, because for a lay person lacking incentive to study the abstract sophistry, such an analogy may still have a benefit in efficiently leveraging their existing knowledge into the new domain, i.e., perhaps better to have a crude approximation than to know only popular superstition about elektricity and biomagnetics.)

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