# What exactly is voltage?

Bit of a strange question, but what is it? My physics teacher said it was kind of like a "push" that pushes electrons around the circuit. Can I have a more complex explanation? Any help is much appreciated.

Current is electric charges (usually electrons) moving. They don't do that by themselves for no reason, no more so than a shopping cart moves across the floor of a store by itself. In physics, we call the force that pushes charges the electromotive force, or "EMF". It is almost always expressed in units of volts, so we usually take little shortcut and say "voltage" most of the time. Technically EMF is the physical quantity and volts is one unit it can be quantified in.

EMF can be generated several ways:

1. Electromagnetic. When a conductor (like a wire) is moved sideways thru a magnetic field, there will be a voltage generated along the length of the wire. Electric generators like in power plants and the alternator in your car work on this principle.

2. Electrochemical. A chemical reaction can cause a voltage difference. Batteries work on this principle.

3. Photovoltaic. Crash photons into a semiconductor diode at the right place and you get a voltage. This is how solar cells work.

4. Electrostatic. Rub two of the right kind of materials together and one sheds electrons onto the other. Two material that exhibit this phenomenon well are a plastic comb and a cat. This is what happens when you shuffle across the right kind of carpet and then get a zap when you touch a metal object. Rubbing a balloon against your shirt does this, which then allows the balloon to "stick" to something else. In that case the EMF can't make the electrons move, but it still pulls on them, which then in turn pull on the baloon they are stuck on.

This effect can be scaled up to make vary high voltages and is the basis for how Van de Graaff generators work.

5. Thermo-electric. A temperature gradient along most conductors causes a voltage. This is called the Siebeck effect. Unfortunately you can't harness that because to use this voltage there is eventually a closed loop. Any voltage gained by a temperature rise in part of the loop is then offset by a temperature decrease in another part of the loop. The trick is to use two different materials that exhibit a different voltage as a result of the same temperature gradient (different Siebeck coefficient). Use one material going out to a heat source and a different coming back, and you do get a net voltage you can use at the same temperature.

The total voltage you get from one out and back, even with a high temperature difference is pretty small. By putting many of these out and back combinations together, you can get a useful voltage. A single out and back is called a thermocouple, and can be used to sense temperature. Many together is a thermocouple generator. Yes, those actually exist. There have been spacecraft powered on this principle with the heat source coming from the decay of a radio-isotope.

6. Thermionic. If you heat something high enough (100s of °C), then the electrons on its surface move so fast that sometimes they fly off. If they have a place to land that is colder (so they won't fly off again from there), you have a thermionic generator. This may sound far fetched, but there have also been spacecraft powered from this principle with the heat source again being radio-isotope decay.

Electron tubes use this principle in part. Instead of heating something so that electrons fly off on their own, you can heat it to almost that point so that they fly off when a little extra voltage is applied. This is the basis of the vacuum tube diode and important to most vacuum tubes. This is why these tubes had heaters and you could see them glow. It takes glowing temperatures to get to where the thermionic effect is significant.

7. Piezo-electric. Certain materials (quartz crystal for example) generate a voltage when you squeeze them. Some microphones work on this principle. The varying pressure waves in the air we call sound squish and squash a quartz crystal alternately, which causes it to make tiny voltage waves as a result. We can amplify them to eventually make signals you can record, drive loudspeakers with so you can hear them, etc.

This principle is also used in many barbecue grill igniters. A spring mechanism whacks a quartz crystal pretty hard so that it makes enough of a voltage to cause a spark.

• Thanks to all of you for some really wonderful answers! It makes complete sense now. This is only my second question on this site, and although I have a lot of experience with stackoverflow.com, this site is all very new. So thank you all once again for all of your help :) Dec 10 '12 at 17:44
• Olin answer as usual is very complete, but may miss some special cases. In an atom the electron will keep moving around and around without an emf. This can give the atom a magnetic field. Dec 10 '12 at 19:43
• This is an nice little image that's been helpful in getting a basic idea of voltage, current and resistance. Dec 13 '12 at 6:35
• @Kronos for some reason the image doesn't display Jan 25 '13 at 10:37
• @imulsion works fine for me. Jan 25 '13 at 14:24

Using a fluid analogy, Voltage is pressure, Current is Flow rate.

• The fluid analogy is really good. Imagine a wire as a pipe (that can't leak). Imagine a capacitor as a stretchy membrane that completely covers the pipe. A resistor is a narrowing in the pipe. An inductor is a heavy flywheel that interferes with the flow until it has spun up, and helps it along afterwards. Voilá, suddenly it's easy to visualise what might happen in specific set-ups! Like the fact that a capacitor allows water to flow only until the membrane is stretched enough to counteract the pressure, at which point the flow is blocked. Mar 15 '13 at 23:30
• To add to the analogy, if you have a spray nozzle on the end of a hose, and it is closed, the pressure at the end is the same at the spigot ( no current, so no voltage loss ). The hose has some resistance, so if you take the nozzle off, you get a lot of current, but the pressure drops very low. Let the nozzle restrict the current flow, and the pressure is higher, allowing you to spray far. Higher pressure at the source ( voltage ), or a wider hose ( less resistance ) lets you carry more volume of water over time ( current ). Oct 26 '15 at 0:04
• @RomanStarkov I really think that your explanation should be there in every introductory physics/electromagnetism book. Jan 4 '18 at 8:36
• More than that - from this "fluid analogy" it is clear that a small electrical current (like the base current) cannot directly control (steer) the flew of a larger current (collector current). Therefore, a BJT is not a current-controlled device (as can be read in some books). It is, rather, a voltage contrrolled device - described by the parameter transconductance gm=d(Ic)/d(Vbe) .
– LvW
Apr 28 '18 at 10:34
• I find this analogy really bad (disregarding the fact that it's all over the Internet). How is "flow" different from "pressure"?You're just re-iterating phrases without explaining what they mean. Jul 21 '20 at 22:38

"Voltage" is a derived quantity. It is hard to understand its Physical meaning without understanding the quantities it is derived from.

It all starts with the force between two point charges. Let the charges of the points $$\ P_1 \$$ and $$\ P_2 \$$ be $$\ q_1 \$$ and $$\ q_2 \$$. Let the distance between them be $$\ r \$$. The fundamental theorem says that, the force between these two charges are proportional with the amount of charges, and inversely proportional with square of the distance between the charges. That is:

$$\ F = k\dfrac{q_1 q_2 }{r^2} \$$

Let the location and the charge of $$\ P_1 \$$ be fixed. Now the force depends on the location and charge of $$\ P_2 \$$. So we define a vector field called "Electrostatic Field". Direction of the vector field is the same with direction of the field of the force between $$\ P_1 \$$ and $$\ P_2 \$$ when $$\ q_2 \$$ is positive unit charge. And magnitude of the field is the force per charge $$\ q_1 \$$ when $$\ q_2 \$$ is unit positive charge. That is:

$$\ \bar{E} = \lim \limits_{q_1 \to 0} \dfrac{\bar{F}}{q_1} \quad \mbox{(} q_2 \mbox{ is unit positive charge)} \$$

We make $$\ q_1 \$$ approach to zero in order to neglect some other electromagnetic effects; don't let it confuse you so much. It is something like "an aura that is able to generate some force per unite electrical charge". Its direction is the same with the direction of the force it generates, and its magnitude is proportional to the magnitude of the force.

Now we come to see that these quantities we defined are very similar to some other Physical quantities we know. For example, the force above is very similar to the force between the Earth and a space object, like the Moon. And the $$\ \bar{E} \$$ field is very similar to the gravitational field of the Earth.

Then the idea of defining electrical potential arises which is similar to the potential of a space object with respect to the Earth. Potential of a point in the space around Earth is energy per unit mass to bring an object (which has unit mass) from infinity to that point. When we define it in Electrostatics, the potential of the point $$\ P_2 \$$ becomes:

$$\ V_2 = - \int \limits_{\infty}^{P_2} \bar{E} d\bar{\ell} \$$

Then, the potential difference between two independent points ($$\ P_2 \$$ and $$\ P_3 \$$) in the space within the $$\ \bar{E} \$$ field (caused by $$\ q_1 \$$) is:

$$\ V_2 - V_3 = \left(-\int \limits_{\infty}^{P_2} \bar{E} d\bar{\ell}\right) - \left(-\int \limits_{\infty}^{P_3} \bar{E} d\bar{\ell}\right) = \int \limits_{P_3}^{P_2} \bar{E} d\bar{\ell}\$$

Note that electric field is curl-free, which means it can always be represented as gradient of a scalar field ($$\ \bar{E} = - \bar{\nabla} V \$$). These line integrals are independent of path.

So, this is the definition of the potential field. A point will always have a potential even if there is no charge on it. Think it as of "the energy needed to bring a unit charge to there from infinity". Potential difference between two points is similar; it is the energy needed to carry a unit charge from one point to another. Or think it on a more concrete example like for celestial bodies. Potential difference between 100km height and 200km height above Earth's surface is nothing but differences of potential energies between two 1kg objects at the given heights.

When we come to real world, potential of a point is some of all individual potentials caused by the charges around (theory of superposition applies).

A voltage appears whenever there is an imbalance of electrical charge (i.e. electrons). Since like charges repel and opposite charges attract, any collection of electrically charged particles creates some kind of force on each other. If there is an imbalance of negative to positive, a kind of "pressure" or "push" is formed. In conducting materials, electrons are free to flow through the material, as opposed to being fixed in atoms, and will therefore flow to the point of least "pressure".

Some complicating considerations:

• Electricity and chemistry are closely connected. In a battery, for example, a chemical imbalance creates an electrical imbalance (voltage) across the terminals, by forcing charged particles to one side. Chemistry also affects electrical conditions in other ways.
• Current (I) is the flow of electrons, however, electrons (since they are negative) flow in the opposite direction of the "current". The current is then the conceptual flow of positive charge, even though the actual flow is negative, but in the other direction. This demonstrates that a negative "push" is the exact same as a positive "pull".
• This is the only answer that answers the question. While the others talk about how voltage is created or what it does, this answers what voltage is.
– Rob
Jul 5 '14 at 12:48
• @Craig Like the other responses, your answer has nothing to do with the question or my response which was about voltage, not current from a year ago.
– Rob
Aug 10 '15 at 13:27
• @Craig, I'm afraid you've misunderstood the pedantic hair that you're trying to split :-). While there is indeed an important distinction between the drift velocity of electrons in a conductor and the speed at which an electric wave propagates, the fact remains that you cannot have voltage or current without moving electrons around. Your insistence that current is NOT the flow of electrons is incorrect. Aug 10 '15 at 18:23
• @DaveTweed Electromagnetic induction... :-) I'm honestly interested in understanding the phenomenon (not trying to just argue), and I sincerely don't buy the argument that "current is moving electrons." Current is a moving electric charge, we agree on that, right? But in an AC circuit, the electrons literally don't go anywhere, they sort of wiggle in place (because the direction of the current switches 50 or 60 times/second, and electron drift is slow). I believe the actual energy is in the EM wave, and the electrons carry/guide that wave. The electrons themselves aren't the energy wave... Aug 10 '15 at 19:39
• This is the best answer I've seen so far and the only one that really explains it in the right way. Thanks a lot man. Apr 20 '20 at 8:59

A definition I've heard is:

Voltage is the potential (for charge) to do work.

In other words, voltage is the energy given to a unit of charge, i.e., $V = {dE \over dQ}$, where $E$ is energy and $Q$ is charge.

The quickie, first approximation, rule-of-thumb answer: voltage is electrical pressure.

But expanding on that: Voltage is not like pressure, not exactly. Instead, it's a math/physics concept called "potentials." Voltage is more like altitude in a gravity field, where each electron or proton is like a boulder. Altitude isn't pressure or weight or force. If a boulder is at the top of a hill, the boulder at a high-potential location. This means the boulder is storing potential energy (PE), and will release this energy as kinetic energy (KE) if it's allowed to move downhill (move to a low-potential location.) Lifted to the same voltage (altitude,) larger boulders would have higher PE.

More precise: voltage is electric Potential. It isn't force (it's not like the boulder's down-force or weight, nor is it like the amount of force upon an electric charge in an electrical field.) Also voltage is not potential energy, since if we take away the boulder, then the gravity, altitude, and potential still exists. Potentials are part of the field itself. Patterns of voltage can hang in empty space.

Voltage is a way of describing/visualizing/measuring electric fields.

To describe e-fields, we can draw flux-lines between opposite electric charges. Or instead, we can draw the pattern of voltage, the iso-potential surfaces, drawing them perpendicular to the flux lines. Wherever we find some electric lines-of-force, we'll also find voltage.

What is voltage not? What are typical misconceptions? Here's a big one: "voltage is a kind of potential energy." Nope, wrong. Instead voltage is the math-concept "Potentials," which aren't energy, nor are they "potential to do something." Here's another miscon: "voltage is the potential energy per unit charge." Nope, wrong. That's just the physics definition of the Volt unit, linking it with Joule and Coulomb units. Actually it goes the other way: the amount of energy (amount of work done in moving a charge across a certain voltage-difference) is found by multiplying charge by change in voltage! Electrical energy is determined by voltage! But Voltage itself needs no moving charge nor potential-energy stored, since voltage is a way to describe a field in empty space. The test-charges used to describe voltage are imaginary infinitesimal charges. Another miscon: "voltage appears on the surface of wires." Wrong, voltage actually extends into the space around wires. Half-way between your 9V battery terminals you'll find a 4.5V potential, hanging alone in empty space! But typical voltmeters won't detect the space-voltage, since that requires a voltmeter with infinite Z(inp), or at lest a few hundred gigohms. Normal 10Meg DMM voltmeters draw significant current, will short out any pure e-fields, so they must be touched to conductor surfaces in order to measure voltage.

What is voltage? It's a stack of invisible membranes which fill the space between charged capacitor plates. Voltage is the pattern of concentric onion-layers which surround any charged object, with the onion-layers running perpendicular to the flux-lines of the electric field. So, 'stacks of voltage-layers' is one way of describing an electric field. The other more familiar way is to use 'lines of force.'

• With regard to the pressure analogy, it's useful to recognize that while there is a concept of absolute voltage (as with pressure), in many cases far more meaningful to think in terms of relative voltage. For example, a typical pipe organ may be said to operate with a pressure of 7mm Hg. One could in theory use a barometer to measure the pressure inside as 764mm Hg, and the pressure outside as 757MM Hz, and conclude that the pipes saw a pressure difference of 7mmHg, but it would be easier and more accurate to measure the difference in pressure between the inside and outside. With voltage... Dec 13 '12 at 16:25
• ...the difference between the "baseline" and the typical differential voltages people deal with are usually many orders of magnitude larger. Think about trying to measure a man's stature by measuring the distance from the center of the earth to to of his head, and from the center of the earth to bottom of his feed, and subtracting. Measuring absolute voltage would be even worse than that. Dec 13 '12 at 16:27
• I just want to thank all of you once again for some really amazing answers - I never thought I would get a silver badge for such a simple question! :) Dec 13 '12 at 17:47

Actually we can't.

Electrostatic force is proportional to the potential gradient, but not directly to potential. Force on a one coulomb of charge is proportional to the potential gradient:

$$\ F= Q \times {d[V]\over dl } \$$

Actually, 1 V means if you have 1 joule of electrical energy, it will be transferred into mechanical energy on a +1 coulomb charge [so it will accelerate, or increase its 1/2mV^2 by 1 J]. It's actually analogous to energy.