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I'm very new to electronics and I am going through what must be a common difficulty in grasping voltage, current, and resistance. I'll restrict my question to current as I suspect understanding that piece may shed light on voltage and resistance.

I've read a few questions here:

And they helped a bit but I'm still struggling. One specific part that's difficult for me to resolve mentally is that I am reading about the basic units of measurement, but I'm not entirely sure what is being measured. For example, a pound is measuring the force of gravity pulling on a collection of atoms. A gallon is the amount of liquid that can occupy a fixed amount of space. Electricity... I get lost on the details of what's being observed.

Many units of measurement are a fixed quantity of something that does not change (unless acted upon). For example:

  • 1 Gallon of milk
  • 16 ounces of beef
  • 30 cubic liters of air

That doesn't seem to make sense with something like current that is measuring electrons constantly in motion. Alternatively we perform measurements of something as it changes over time:

  • 35 miles per hour
  • 128 kilobits per second
  • 5,000 gallons per minute

When it comes to current, we just say "amps", not "amps per something". Well, I get that "amps" measure the flow of electrons, but what exactly does that "flow" mean? Is it the number of electrons (or the number of something else) passing through a location on a circuit in a second (or some other unit) of time? When I touch the leads of my multimeter to a wire, what exactly is it "looking at"?

I've read that volts are a measure of potential energy related to joules and coulombs (http://www.allaboutcircuits.com/vol_1/chpt_2/1.html) (more confusion but that's fine) and I believe that coulombs are measured per second. Does the per-second carry over to amps as well?

The only other thing I can think of is that amps might be more like pressure where you're measuring pounds per square inch.

I know electricity is electricity and no analogy is perfect. I'm trying to understand electricity for what it is, I'm just not sure how these measurements are actually made. Perhaps I'm overthinking, but any deeper insight would be great.

(If this has already been explained to death I apologize, I may not know the best search term to use.)


Man, as someone new to this site I'm so blown away that so many people took so much time to help me understand this. Like a lot of things I think it's going to take time and a lot more reading / experience to "sink in" but all of the answers were so helpful. I'm marking the "amps include time" answer as the one that helped me the most because it answered the core of my question "amps per what?". I'm picturing "amps" kind of like "knots" in the sense that the quantities are part of the definition of the word as opposed to being explicitly stated as they would be in another unit like "miles per hour". Not a perfect analogy but at least it helps me understand where all the hard numbers went.

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  • \$\begingroup\$ Regarding understand "a volt", see electronics.stackexchange.com/questions/73375/… \$\endgroup\$ – Phil Frost Jun 26 '13 at 3:05
  • \$\begingroup\$ Also, don't fall into the trap of thinking that electric charge is electrons. Electrons have an electric charge, and although they have "electr" in their name, they are not the only kind of electric charge. electronics.stackexchange.com/questions/72875/… \$\endgroup\$ – Phil Frost Jun 26 '13 at 3:21
  • \$\begingroup\$ Thanks Phil. That question seems like a great read. I'll be sure to go through it. As I said in my post, I'm currently currently trying to get a good grasp on current (one thing at a time right?) but some of the voltage related points in the answers have been really helpful in understanding current so I appreciate the link. \$\endgroup\$ – Cliff Pruitt Jun 26 '13 at 3:21
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    \$\begingroup\$ I bet you would enjoy reading amasci.com/miscon/whatis.html \$\endgroup\$ – Phil Frost Jun 26 '13 at 3:53
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    \$\begingroup\$ "Cubic liters"? is that something by Picasso? A litre is a measure of volume so saying cubic litres is like saying square-acres! \$\endgroup\$ – Andy aka Jun 26 '13 at 7:49
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Amps includes time...

Amps = Coulombs per second

That says more simply that...

Current = amount of charge per time interval

It's a flow rate metric. Like water... liters (volume --> amount) per minute (time)

In more depth

In practical terms, the ampere is a measure of the amount of electric charge passing a point in an electric circuit per unit time with 6.241 × 1018 electrons, or one coulomb per second constituting one ampere.

--Wikipedia Article

Probing

When I touch the leads of my multimeter to a wire, what exactly is it "looking at"?

If you are in the voltage measurement mode, you are effectively measuring the "pressure" between the two leads -- the degree to which charges in one lead seek to reach the other (but can't). The reason the charge gradient can't be neutralized depends on the circuit. In a capacitor, for example, a barrier of some kind prevents it. The existence of a voltage between two points requires that such a gradient exists.

If you are in a current measurement mode, the leads are installed in the current path (in series with) and the meter is measuring how much charge flows through them in unit time (it actually does this indirectly by applying Ohm's law).

Further reading

Bodanis, David (2005), Electric Universe, New York: Three Rivers Press, ISBN 978-0‐307‐33598‐2

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  • 1
    \$\begingroup\$ "the degree to which charges in one lead seek to reach the other (but can't)" -- Oh my. After all of the descriptions and analogies I've read, this one statement helped me come to terms with "voltage" more than any other I've read. I've always been confused about how something could have a high voltage without high current, but I guess if you only had 100 electrons that wanted very badly to move, that would be the case. And counting the number of them that move per second would be the Current. Am I (sort of) on track? Thanks! \$\endgroup\$ – Cliff Pruitt Jun 26 '13 at 1:43
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    \$\begingroup\$ @CliffPruitt even if you had a billion electrons that wanted to move very badly, but can't, you still could have no current. Volts measure electric potential. Pressure is also a potential. Height is another one. A high-pressure tank isn't necessarily discharging fluid. A stone on a mountain isn't necessarily falling. A rock need not be big to be high. A tank need not be large to contain a high pressure. \$\endgroup\$ – Phil Frost Jun 26 '13 at 3:17
  • \$\begingroup\$ Not to be a pedant, but it should read Current = charge per unit time or rate of change of charge; no need to include units when you seem to just be specifying dimensions. \$\endgroup\$ – Justin L. Jun 26 '13 at 4:37
  • \$\begingroup\$ @Justin -- Yes. Makes more sense that way. I was attempting to mirror the structure of the question, but it's better your way. Revised. \$\endgroup\$ – DrFriedParts Jun 26 '13 at 5:45
  • \$\begingroup\$ @PhilFrost Yep, understood. I was just trying to keep current in the mix, but I get that two terminals of a battery without a circuit have voltage but no current. \$\endgroup\$ – Cliff Pruitt Jun 26 '13 at 16:27
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The most fundamental unit of charge is the electron, but it's impractically small to work with. A coulomb is a larger unit of charge representing the charge of about 6,241,509,324,000,000,000 electrons. An ampere is a shorthand unit representing a flow rate of one coulomb (i.e. 6,241,509,324,000,000,000 electrons) per second, which is to say that if a wire has one ampere of direct current flowing through it, there will be about 6,241,509,324,000,000,000 more electrons entering one end and leaving the other, than vice versa.

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  • \$\begingroup\$ Thanks very much for bringing literal numbers into the picture. That really does help. I can't believe this isn't something explained in every piece of beginner literature. It seems so fundamental to know what the measurement means. \$\endgroup\$ – Cliff Pruitt Jun 26 '13 at 1:45
  • \$\begingroup\$ @Cliff: Actually it is explained. Just look up "Ampere" and you should find coulomb per second, which should lead you to look up coulomb. \$\endgroup\$ – Olin Lathrop Jun 26 '13 at 13:01
  • \$\begingroup\$ 2/3 or 1/3 electron charges are more fundamental en.wikipedia.org/wiki/Quark#Electric_charge \$\endgroup\$ – Pete Kirkham Jun 26 '13 at 13:01
  • \$\begingroup\$ @PeteKirkham: Are electric charges subdivisible? I know that charged particles are regarded as containing quarks, and if one measures the charges of various combinations of quarks and plugs them into equations, those equations will work out if one assigns to the quarks charges that are fractions of 1/3 an electron (or proton)'s charge, but I don't think it's possible to ever get a quark into a situation where its charge can be observed directly; the fact that a group of three identical quarks has a charge equal to one electron doesn't mean each quark alone would have a 1/3 charge. \$\endgroup\$ – supercat Jun 26 '13 at 16:32
  • \$\begingroup\$ 'Fundamental' and 'directly observable' aren't the same thing though. There is a wealth of evidence that the smallest directly observable charge is made up of the combination of the charges from more fundamental particles, irrespective of directly observing the particles. \$\endgroup\$ – Pete Kirkham Jun 27 '13 at 9:11
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Rather than answer your question directly (others have done that quite well), I'd like to introduce a mental model and analytical tool that should help you understand those answers. That tool is dimensional analysis.

The fundamental concept is that a unit a symbol that can be manipulated algebraically. I think an example is best. We know that the volume of a rectangular cuboid is its width, times its height, times its depth. Let's say we measure it to be 1 meter high, 2 meters wide, and 3 meters deep. Then:

$$ \text{volume} = 1m \cdot 2m \cdot 3m$$

If you pretend that \$m\$ is just a symbol, like the proverbial \$x\$ in algebra, then you know that:

$$ 1m \cdot 2m \cdot 3m = 6m^3$$

That is, the volume of this cuboid is six cubic meters. But we can measure volume in units other than cubic meters. In fact, any three units of length, multiplied together, is a unit of volume. Area is two units of length multiplied together, so if I multiply area by length, I get volume. So let's say I want to measure volume in some wacko unit I just made up, the acre-inch.

What's the volume of our cuboid in acre-inches? I can start with \$6m^3\$, which is \$6 \cdot m \cdot m \cdot m\$. I can then multiply it by some fractions where the numerator and denominator are equal, but in different units. These are fractions equal to 1, but multiplying by 1 doesn't change the number. It does, however, let me change the units. By the rules of algebra, any term in the numerator can cancel the same term in the denominator. So somehow, I need to get three \$m\$ in the denominator, and end up with one \$in\$ and one \$ac\$ in the numerator.

$$ \require{cancel} \frac{6 \cancel{m m} \cancel{m}}{1} \frac{1ac}{4046.86\cancel{m^2}} \frac{1in}{2.54\cancel{cm}} \frac{100\cancel{cm}}{1\cancel{m}} \approx 0.058ac \cdot in$$

Six cubic meters is equal to 0.058 acre-inches. Why would I want to measure volume in acre-inches? I have no clue, but I can. Point is, units can be manipulated algebraically.

This yields new insight into what units mean. Pick any unit, like the watt, and wikipedia will tell you something like:

$$ W = \frac{J}{s} = \frac{N\cdot m}{s} = \frac{kg\cdot m^2}{s^3} = V \cdot A $$

The elegance of SI units is that all the units are related by a factor of 1, so we don't have to write it. So what this says is one watt is equal to one joule per second. Or, one newton-meter per second. Or, one kilogram-square-meter per second-cubed. Or, one watt is one volt-amp. These are all the same thing.

See how the units relate to the electrical equations you already know, like power \$P\$ is the product of voltage \$E\$ and current \$I\$:

$$ P = I E $$

Knowing that current can be measured in amperes, and voltage is volts, then power must be measured in volt-amps. And hey, according to Wikipedia, that's a watt:

$$ W = V\cdot A$$

therefore:

$$ \frac{W}{V\cdot A} = 1 $$

Say you measure the voltage to be \$10V\$ and current to be \$10mA\$. Then:

$$ P = \frac{10\cancel{mA}}{1} \frac{10\cancel{V}}{1} \frac{\cancel{A}}{1000\cancel{mA}} \frac{W}{\cancel{V}\cdot \cancel{A}} = 0.1W $$

Here are a few more examples of dimensional analysis:

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  • \$\begingroup\$ OK, all that makes great sense. The part I get hung up on is that for all of that to work and for us to communicate between each other and mean the same thing, somewhere someone had to come up with the unit that we're measuring "one" of, correct? We can say that one "Verne" is equal to 0.025 Joules, but without some defined unit somewhere, all we would have is a formula showing a relationship and not a system of measurement. So an "ampere" applies that relationship and uses 1 joule and 1 second as the values in the otherwise open ended formula. Yes? \$\endgroup\$ – Cliff Pruitt Jun 26 '13 at 17:18
  • \$\begingroup\$ @CliffPruitt all the definitions for SI units eventually resolve to one of the seven SI base units, which have definitions based on reproducible physical phenomena. \$\endgroup\$ – Phil Frost Jun 26 '13 at 17:48
  • \$\begingroup\$ @CliffPruitt, a book I've found to be an interesting source of answers to questions about how measurements came to be quantized by the units we use today is The Science of Measurement. It covers both the history of each abstract quantity and the standardization of units to measure that quantity. One caveat is that it was written in 1974, and there has been a handful of tweaks to standards since then. \$\endgroup\$ – RBerteig Jun 26 '13 at 17:49
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When it comes to voltage, we just say "amps", not "amps per something".

You have a misunderstanding.

Amperes measure current.

Volts measure potential difference. Voltage is another word for potential difference, when you are measuring it with the units of volts.

As others have answered, amps measure the flow of electrons, and an amp is equivalent to 1 cuolomb of charge passing per second.

When the current in a wire is changing, it is not uncommon to measure the rate of change in "amps per second" or A/s.

I've read that volts are a measure of potential energy related to joules and coulombs

Volts can be rewritten as watts per amp, or joules per cuolomb. Let's look at the second form, joules per cuolomb.

It means that if the potential at some point of space is held constant at 1 V, it will take 1 joule of energy to push 1 C of charge to that location.

Or it would take 1 J/s to move 1 C/s to that location; 1 Watt per amp of current flowing in to that location.

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  • \$\begingroup\$ "When it comes to voltage, we just say amps" -- Oops, I apologize for the misleading slip. I do understand that voltage measures potential energy not current. With so many terms I'm trying to understand the wrong word is coming out at the wrong time. \$\endgroup\$ – Cliff Pruitt Jun 26 '13 at 1:32
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A mechanical analogy may help sort things out.

In one mechanical analogy, force is analogous to voltage while velocity is analogous to (electric) current.

As you may know, the product of force and velocity is (mechanical) power and analogously, the product of voltage and current is (electric) power.

While force is energy per meter, voltage is energy per Coulomb (Coulomb is the unit of electric charge).

While velocity is meters per second, current is Coulombs per second.

We call force and voltage the across variables while velocity and current are the through variables.

In either case, the product of the across and through variable is energy per second which is power.

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  • \$\begingroup\$ Am I correct that although velocity specifies the speed (and direction) of a single object, voltage differs because it deals with the number of objects (electrons) and those objects always move at a fixed speed? Resistance decreases the number of electrons in motion but not their speed. Do I understand this correctly or an I entirely off base? \$\endgroup\$ – Cliff Pruitt Jun 26 '13 at 3:31
  • \$\begingroup\$ Voltage doesn't deal with number of objects; it deals with "how much" they want to move. \$\endgroup\$ – Justin L. Jun 26 '13 at 5:54
  • \$\begingroup\$ @CliffPruitt Don't think about electrons moving at the speed of light. The forces transmitted through them move at the speed of light. The electrons don't. amasci.com/miscon/speed.html \$\endgroup\$ – Phil Frost Jun 26 '13 at 13:13
  • \$\begingroup\$ @CliffPruitt, it is clear that your notions of voltage and current are not closely aligned with textbook versions. Where are you getting these ideas? \$\endgroup\$ – Alfred Centauri Jun 26 '13 at 14:31
  • \$\begingroup\$ @AlfredCentauri I have zero formal education in any of this. I'm a programmer by trade. I started off just wanting to tinker with some audio electronics and found the background interested me. Currently the material I'm reading through are the PDFs here: allaboutcircuits.com - I just don't generally do well learning things if I can't understand the "why" behind them and electricity is... confusing me. :-) \$\endgroup\$ – Cliff Pruitt Jun 26 '13 at 16:38
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Let's give a shot with a common analogy for circuits.

A circuit is like a river. Water in a river always flows "downhill" because water at the top of the hill wants to go downhill. Water will always seek a lower point.

If water always goes downhill then how is this a circuit?

Well, you can think of a "loop" river, flowing downhill -- but at one end, there is a water wheel of some sort that brings the water at the bottom back up to the top. This wheel takes low-level water, with no motivation to flow anywhere, and "pushes" it into the high level, with much motivation to flow downhill.

If we think of "height" as "potential energy", the water wheel takes water of low potential energy and puts it in a position of high potential energy -- essentially "injecting" gravitational potential energy into the water. this newly energized water wastes no time in spending that energy to go downhill once again.

This "proclivity to move downhill" is called potential which in our case is analogous to Voltage.

The current of the river is...well..Current. How would you measure the current of a river?

I would say ... "take a stopwatch and time how many liters of water pass through a certain mark in the river in one second". That sounds like a reasonable way to quantify a current. Liters per second.

In a circuit, your water is charge. Instead of timing how many liters of water pass through a point on a wire after a second, you could measure how many units of charge pass through a specific point on a wire per second.

Just like saying "cubic decimeters" is a mouthful and we give it a convenient unit -- "liter", we give "charge per second" a convenient name as well -- "amps".

We do this a lot -- "miles per gallon" turns into "mileage", "kilograms times meters per second per second" turns into "newton", "joules per second" turns into "watts".


If gravity is not doing it for you, consider water in pipes and water pressure.

I have pressurized water in one end and unpressurized water at the other. The water will move from the pressurized side to the unpressurized side. Pressure is a measure of the force of all the water molecules wanting to get away from eachother. Water molecules have a comfortable distance and pressurization the act of pushing those water molecules closer and closer past that comfortable point.

You might remember that electrons repel each other. When you have a "high voltage", you really have "high electron pressure" -- stuffing electrons waaay too close together for their own comfort.

Note that this analogy is actually very literal -- voltage really can be seen as literally electron pressure!

Just like putting too much air into a balloon ... things that are stuffed too close together will want to "get away", and there is a real force.

Now, back to our water pipes -- water will want to rush from the pressurized end to the unpressurized end.

Think carefully about the pipe. When we let the water rush...what is actually rushing? Is it the water molecules? Imagine a single water molecule in the pressurized end, and letting the pressure "go". That molecule won't rush to the other end. It'll just stay in place while the pressure equalizes.

So what is actually moving?

The pressure moves.

Let's say you have a little display at every inch on the pipe that measured the pressure at that exact point. At first, all the ones on the left are high; all the ones on the right are low.

When you let the pressure go...you see these displays start changing. The "highness" starts moving to the right.

Let's say at one display says "50" for pressure, and then the next display to the right says "20". One second later, the first display now says "40" and the second says "30". You can see this as 10 "pressure" units moving to the right at a rate of 10 pressure units per second. This is current - 10.

Now I'm playing a little loose with dimensions and sort of hand-waving away some of the the differences between Potential and charge, but the basic principle is the same.

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  • \$\begingroup\$ Ok, but now you have to explain how gravity works. \$\endgroup\$ – Pete Kirkham Jun 26 '13 at 13:03
  • \$\begingroup\$ What we call "current" (in the context of Ohm's Law) isn't defined as electrons moving, it's not electrons per second as you've indicated. It's charge moving. It's coulombs per second. Electrons in low-power DC circuits move through copper on the order of cenitmeters per hour. The charges move as a wave at astronomically faster speeds. Actual electron drift (centimeters per hour) is also technically a current (it's a flow of electrons, after all) but it isn't what people talk about when they're talking about voltage and resistance. \$\endgroup\$ – Adam Lawrence Jun 26 '13 at 18:37
  • \$\begingroup\$ @Pete I'm moving the "intuition" requirement from electric potential (which is hard) to gravity, which people have a much higher intuitive grasp of typically. it's hard to imagine charge having potentials and moving away from high potentials; it's easy to imagine water being high and flowing downhill and saying that they are analogous \$\endgroup\$ – Justin L. Jun 26 '13 at 19:17
  • \$\begingroup\$ @Justin Yes, it's much easier to understand gravity because gravity is something we have first hand natural contact with. On the other hand, something "in my gut" keeps nagging at me telling me that it's not the same and it's the "what is it really?" that I keep trying to understand. I think I'm somewhat in the same position as a child that's learning to multiply and is troubled because he doesn't fully understand trigonometry. \$\endgroup\$ – Cliff Pruitt Jun 26 '13 at 19:27
  • \$\begingroup\$ @Madmanguruman I think I obviously need a better understanding of charge I always assumed that something received a charge due to an excess or deficiency in the number of it's electrons. If the electrons aren't moving, I don't think I understand what is causing the charge. (Don't feel compelled to answer. I'm a little on overload anyway.) \$\endgroup\$ – Cliff Pruitt Jun 26 '13 at 19:29

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