What is Voltage? Elaborated Question Explained

[martian22]

Question. What is voltage? By which I mean: what is it about an electric current that makes it current at whatever voltage it is at. To state this as a specific question: what is the difference between current of 1 amp in a circuit where the potential difference between the two ends of the circuit is 1 volt and current of 1 amp in a circuit where the potential difference is 2 volts?

Elaboration of the question. I think the bit I am confused about is the fact that voltage causes two things. It causes current, ie amps. But it also causes joules per coulomb. Is that right? If there is a circuit of 1 ohm and we put 1 volt across it we get current of 1 amp and that current has energy of 1 joule per coulomb. If we then double the voltage to 2 volts we get 2 amps but also 2 joules per coloumb. The overall power delivery is therefore 4 times as much. Ie 4 joules per second. What is it about the current that means it has got 2 joules per coulomb instead of 1 joule per coulomb? ... Maybe this is where the water pressure analogy fails. If we were producing water flow in a pipe by water pressure difference between the two ends and then we doubled the pressure. That would double the flow rate. Say we were using the water flow to power something, a wheel for example. Then we would get twice as much wheel turning work done. All this corresponds to the doubling of current in the electrical example. But what is it in the water pressure analogy that corresponds to the increase of joules per coulomb? We wouldn't get four times as much wheel turning work done. ... Sorry if this question is really stupid. I've got nothing more than school level physics. If you can keep your answer untechnical that would be great. Thank you.

 

[AUMathTutor]

Potential is sort of like potential energy. Imagine water flowing in pipes. Then...

Wires are like pipes.
Resistors are like chutes.
The battery is like a pump.

Water comes out of the "high" end of a batter, and falls through a set of pipes and chutes to get back to "ground" level, where the battery pushes the water back up to the top to start the cycle again.

Potential, in this case, would be exactly like the potential energy of the water. It's higher when you've not gone through many chutes, and it's ground once you've fallen all the way down.

I don't think the water analogy has much to do with pressure. This might be where the understanding fails.

And Ohm's law says that V = I R. So for a given resistance, the voltage and current are directly proportional.

 

[nealh149]

The plumbing analogy I've always used is as follows:

1. Wires are like pipes.
2. Voltage is water pressure.
3. Battery is a pump.
4. Resistors are like pipes with an impedance.

So if you have pipe with some high water pressure (high voltage) leading up to a tiny opening to a smaller pipe, the other end of the small pipe will have a much lower water pressure. That small pipe has and impedance and acts as a resistor and the pressure drop is equivalent to a voltage drop across a resistor in a circuit.

 

[user111_23]

This took me a while to understand too.

Voltage is the amount of work per unit of charge an electric field can do on a charge to move it from one point to another.

It is also called electric potential difference. Since charges gain more potential energy as they more towards one terminal of a battery as opposed to the other,
there is a difference in electric potential. Because of this difference, the charges naturally flow from the anode to the cathode.

The more voltage, the more work is done on the charges inside the battery. And the more work is done on the charges, the more potential energy the charge gains.

The mathematical way of expressing this is V=(delta)PE/q.

Hope I didn't confuse you.

 

[martian22]

OK, I can see that water that has been pumped up to some height will thus have potential energy. If a pump pumps water to a height of 1 metre then it gives the water 10 joules per litre. And then when the water falls that potential energy becomes (actual) kinetic energy which it yields up for our use on hitting the ground. For example if we put a wheel at ground level. Water falling from 2 metres onto our wheel will be able to yield up twice (or more?) as much energy (ie wheel turning work) per litre as water falling from 1 metre. So then I think to myself that, by analogy, voltage potential becomes the kinetic energy of the electrons that form the current. But that's not right is it? What I mean is: electrical energy isn't constituted by the kinetic energy of the electrons in the current. Is it? ... And if we are saying that electrical energy is constituted by electron pressure. I'm not sure I understand what is meant by pressure here. Is electron pressure to do with electron density? Ie more electrons per unit volume. But the density of electron flow is to do with current not with voltage. ... But now we're getting bogged down in analogies. But I don't want to know what voltage "is a bit like". I want to know what it actually is.

My basic question is what is it about (for example) high voltage electricity that makes it high voltage as compared to low voltage. I mean what is it about the actual current itself. Are the electrons in high voltage electricity moving faster? Or are there more of them per unit volume? But it can't be any of these things because these things are to do with current. High voltage is high joules per coulomb. But how does current have high joules per coulomb?

I know I'm hopelessly confused about all this and I'm probably asking a lot for someone to deconfuse me but I'd really appreciate it if someone would! Maybe the problem is that I'm seeing the problem from a naive non-technical point of view.

 

[diazona]

It isn't actually something about the electrons themselves that makes them high or low volltage, it has more to do with there they are. The electrical potential is a field, which means that it's defined at every point in space - that is, every point in space has a number (the potential) associated with it which represents the energy of a unit charge at that point. As charges move from points of higher potential to points of lower potential, they lose energy, which is what happens as electrons flow down a wire. So a high-voltage wire is one in which the potential changes quickly as you move along the wire, and a low-voltage wire is one in which the potential changes slowly.

 

[fawk3s]

got a pretty silly question here too.
why is high voltage dangerous to a man? (signs everywhere "high voltage"). I've always understood its the current which kills you, not the voltage.
or does the voltage create a current in a man?

 

[user111_23]

got a pretty silly question here too.
why is high voltage dangerous to a man? (signs everywhere "high voltage"). I've always understood its the current which kills you, not the voltage.
or does the voltage create a current in a man?

A high voltage from i.e, a live wire, means that the charges from the wire are itching to find the shortest path to the ground, which can be you if your finger touches it.

That's how I understand it at least.

 

[Jame]

But I don't want to know what voltage "is a bit like". I want to know what it actually is.

What something "actually is" is a very hazardous question to ask when it comes to physics. But anyway, the voltage is established by an unbalanced charge distribution - there are more positive charge on one side than on the other. Since this generates an electric field, a test charge that is put between the two sides will experience a force. If you calculate the work done on this test charge when it is moved from one side to the other, you get (the negative of) the potential energy of the test charge. Since the potential energy is linearly dependent on the charge, you can set the test charge to 1 C and you get that the work done by the field on an arbitrary charge q is just W = q*U where U is the voltage, which is actually the potential energy of an imaginary unit charge that is transported between the sides.

How conduction takes place in a metal is a broad subject, you might just as well read this article: http://en.wikipedia.org/wiki/Classical_and_quantum_conductivity

got a pretty silly question here too.
why is high voltage dangerous to a man? (signs everywhere "high voltage"). I've always understood its the current which kills you, not the voltage.
or does the voltage create a current in a man?

You are right - it is the current that kills you, but it is generated by the voltage. If you touch a wire with your hands there will be a difference in potential between the wire and your hand and charges from the wire will move through your body. The higher the potential the more energy is dissipated as heat, that burns your tissue, when the electrons go through your body. I guess the current's interference with the electrical signals in the body is damaging as well.

 

[fawk3s]

A high voltage from i.e, a live wire, means that the charges from the wire are itching to find the shortest path to the ground, which can be you if your finger touches it.

That's how I understand it at least.

Yet then it would be the current which kills you. So why are there signs of "high voltage" and not "high current"?

I guess the current's interference with the electrical signals in the body is damaging as well.

I think that's what actually stops the hearth and kills you.

 

[Naty1]

But I don't want to know what voltage "is a bit like". I want to know what it actually is.

a good question..to which there is no answer...yet!

As noted, this is "hazardous" because physics can not answer 99.9% of such questions.

What is current? what is a wire? nobody REALLY knows because we do not know what charge nor mass nor time actually are. We are pretty good at describing their behavior mathematically, but not their source constituents nor their origin because so far that's beyond mathematics. Ultimately we think it all comes from nothing via a single non recurring infinite "big bang" singularity or perhaps cyclic recurring "bangs" of finite size...but the relationship between all the fundamental forces and things we "see" around us are so far hidden from our senses...and intellect.

 

[diazona]

Yet then it would be the current which kills you. So why are there signs of "high voltage" and not "high current"?

Possibly because there is no current unless you touch the wire. (Well, there's a lot of current in the wire, but that's not hurting anyone) But the voltage is always there.

 

[fawk3s]

But there can't be voltage without current (or I am very wrong here lol). Because when there's no current, there's nothing what makes the charges flow.
When you connect the powersource with Earth, then voltage is created, and also current.

I think I understand now. YOU create the voltage (it isn't there before), which creates current and kills you.
Please correct me if I am wrong. I happen to have more curiosity than knowlege.

 

[Jame]

Warning for the current and not the voltage would to have a sign saying "Watch out for high speed" warning for a steep.

Your body has a certain resistance, and according to Ohms law the current is proportional to the voltage. And there can certainly be voltage without current. One can think of voltage as the height to which you carry something before you let it go, the higher it goes the more obstacles it can pass without stopping if you let it go.

Edit: not exactly a brilliant analogy but gives a basic idea of potential difference at least.

 

[Lambduh]

There can absolutely be a voltage without a current. One example of this is simply an open circuit, ie a battery that's not hooked up to anything.

Another way to think about it is this experiment. A way to measure the energy of an electrons ejected from a sample is to put a voltage from the sample to your collector (ie a gold pin or something) through vacuum. Have this hooked up to a picoammeter so when an electron hits the gold wire you see a jump in the current. If you ground the sample and put a positive voltage on the gold wire it will accelerate electrons towards it increasing the electron's energy. However, if you put a negative voltage on the gold pin you will push the electrons away from it. If the electron has less energy than the voltage from the substrate to the pin it will never make it there because it will be stopped while making it's way through the field as it is constantly losing energy.

So think of the field caused by the voltage accelerating (or decelerating) the electron through the vacuum. That is why electric fields are in units of volts/distance such as mV/nm or whatever.

 

[negitron]

Yet then it would be the current which kills you. So why are there signs of "high voltage" and not "high current"?

Because high-current power supplies are not necessarily lethal (touch a car battery, which is typically capable of sourcing 500 amperes and report back) and it doesn't take a high current to kill you (about 100 mA through the heart is considered potentially lethal). What is required is sufficient voltage to overcome your body resistance in order to push that 100 mA through you. It may be the current which actually does the work of killing you, but without a sufficiently high voltage to push that current there's no danger.

That's why.

 

[Phrak]

The plumbing analogy I've always used is as follows:

1. Wires are like pipes.
2. Voltage is water pressure.
3. Battery is a pump.
4. Resistors are like pipes with an impedance.

3a) A battery is a voltage source and therefore like a centrifigual pump.
3b) A current source is like a constant displacement pump.

4) Resistors are like pipes with baffles and or restrictions.

5) A capacitors is a wide spot in the pipe with an elastic membrane stretched across it.
6) An inductor is like a set of vanes in the pipe connected to a flywheel.

7) A diode is a one way valve.

 

[Phrak]

But now we're getting bogged down in analogies. But I don't want to know what voltage "is a bit like". I want to know what it actually is.

By definition, voltage is the line integral of the electric field strength beteen two points

$$V = \int E \cdot dl$$

It would help to learn about electromagnetism.

 

[fawk3s]

One can think of voltage as the height to which you carry something before you let it go, the higher it goes the more obstacles it can pass without stopping if you let it go.

I thougth of voltage as the force which makes the charges flow. And when there's no charges flowing, there's nothing "pushing" them. Which means it's not currently voltage, but conserved energy.
But that's only my vision.

 

[AUMathTutor]

It says high voltage because the current doesn't start flowing until it's killing you.

Like they say "Floor is slippery when wet" rather than "You're falling on the wet floor"

 

[fawk3s]

tru dat.

 

[rcgldr]

Using the water in a hose driven by gravity analogy, voltage would correspond to the height (times a constant).

Voltage is a potential. An analogy would be gravitational potential http://en.wikipedia.org/wiki/Gravitational_potential.

Since electrical and gravitational forces comply with the inverse square law, to simplify the analogy, using an infinite plate with a finite charge for the voltage reference source, the voltage is linearly related to the distance between a point and the infinite plate (see below) V = k q_plate h, similar to gravity potential from an infinite plate with finite mass P = G m_plate h.

C = Coulomb, sometimes defined as the charge of 6.24150962915265 x 10¹⁸ electron charges
h = height of a point = distance of line perpendicular from infinite plate to the point
m = meter
N = Newton
q = charge of object
s = sec
k = electrical constant = 8.9875517873681764 x 10⁹ N m² / C²

F = force between infinite plate₁ and point₂ = k q₁ q₂

W = work done by moving point charge from h_a to h_b = - k q₁ q₂ ∫ dh = - k q₁ q₂ (h_b - h_a)

The difference in potential energy between two points is -W
E_pb - E_pa = k q₁ q₂ (h_b - h_a)

V = electrical potential = E_p / q₂ => units are joules / coulomb
V_b - V_a = k q₁ (h_b - h_a)

If point a is a point on the plane, h_a = 0, and V_b = k q₁ h_b

For the case of an infinite plane, voltage is linearly porportional to height. Similarly, gravitational potential from an infinite plane is also linearly porportional to height. You could think of voltage as related to the distance from that infinite plane. Using the water in a hose driven by gravity analogy, voltage would correspond to the height (times a constant).

The concept of an "absolute" voltage depends on the reference:

For the case of an infinite plate reference, h_a = 0, V_b = k q₁ h_b
For the case of an infinitely long line or cylinder reference, h_a = 1, V_b = k q₁ ln(h_b),
For the case of a point or spherical reference, h_b = ∞, V_a = k q₁ / (h_a)

 

[nuby]

This may be incorrect.. But couldn't voltage just be considered a measurement of electrochemical attraction (electrostatic force) between ions? In a 12V battery you have "holes" or positive ions on one side, and "extra" extra electrons on the negative side... Once a conductive path is available between the two polarities the holes and electrons propagate through the conductor and neutralize.

 

[fawk3s]

You could call it potential, but is it voltage? Because by definition, voltage is the job done to move a charge from point a to b.

 

[rcgldr]

But couldn't voltage just be considered an electrostatic force

Voltage isn't a force. The electrostatic force is just that, a force.

Between an infinite plate and a point, F = k q_plate q_point
Between an infinite long wire and a point, F = k q_wire q_point / r
Between two points, F = k q₁ q₂ / r²

k = electrical constant = 8.9875517873681764 x 10⁹ N m² / C²
q = charge in C.
C = Coulomb, sometimes defined as the charge of 6.24150962915265 x 1018 electron charges
r = distance in meters
s = seconc
N = Newton = 1 kg m / s²
m = meter
J = joule = N m

Voltage is a "potential". For the inifinte plate case, where h=0 means a point on the plate, voltage = k (consant) q_plate (Coulombs) h (meters) of the infinite plate. Voltage is potential energy per unit charge, in this case the unit is J / C. The charge of the point, q_point, is ignored.

After a bazillion edits to my previous post, the affect of gravity from the Earth is similar to the infinite plate case if heights are relatively small, and using the water in a hose analogy, and using gravitational potential as voltage, then where h=0 means sea level, then P = g (9.8 m / s²) x h (meters) = (9.8 N / kg) x h (meter). P unit is potential energy per unit mass, in this case the unit is J / kg. The mass or weight of the water is ignored.

 

[user111_23]

By definition, voltage is the line integral of the electric field strength beteen two points

$$V = \int E \cdot dl$$

It would help to learn about electromagnetism.

I don't know calculus that well (I'm a freshman in high school), but isn't that just "El" or Ed? (Electric field times distance)

 

[nuby]

Ok, how about ... Voltage is the measurement of (potential) work done per coulomb of charge... which is caused by the electrostatic force.

 

[rcgldr]

Ok, how about ... Voltage is the measurement of (potential) work done per coulomb of charge... which is caused by the electrostatic force.

In this case energy would be a better term than work.

Voltage is electrial potential energy per unit charge, example unit would be Joule / Coulomb. The charge of the reference object is considered, but not the charge of the target object.

Gravitational potential is mechanical potential energy / unit mass, example unit would be Joule / kilogram. The gravity of the reference object is considered, but not the gravity of the target object.

The concept is to decribe the potential of a point in a field, without having an acutal object interacting with the reference object. Height from an infinite plate, or a relatively small height from the surface of the Earth (times a constant) is a reasonable analogy to "potential". Using gravitational potential as an example, imagine 2 tubes, one has a 1 foot diameter and is filled with water, the other has a 10 foot diameter and is filled with mercury. The gravitational potential at 30 feet above sea level for the fluid in both tubes is the same.

 

[Jame]

I thougth of voltage as the force which makes the charges flow. And when there's no charges flowing, there's nothing "pushing" them. Which means it's not currently voltage, but conserved energy.
But that's only my vision.

Then you've almost got it - except that voltage is what you call conserved energy.

 

[Lambduh]

I don't know calculus that well (I'm a freshman in high school), but isn't that just "El" or Ed? (Electric field times distance)

As long as the field is a constant, yes.

 

[rcgldr]

voltage is what you call conserved energy.

Voltage is potential energy per unit charge, it's not potential energy. It's not useful for predicting the amount of work done unless the current (charge flow / unit time) or associated capacitance is included.

Back to my previous analogy, a 1 gram weight at 30 meters above sea level has the same gravitational potential as a 1 kilo-gram weight, but the potential energies are not the same.

Similarly, a 1 micro farad capacitor and a 1 farad capacitor might have the same potential, 12 volts, but the 1 farad capacitor has a lot more potential energy stored in it.

 

[rcgldr]

$$\Delta V = \int_a^b \vec{E} \cdot d\vec{s}$$

I don't know calculus that well (I'm a freshman in high school), but isn't that just "Es" or Ed? (Electric field times distance)

It's a dot product between the vector E and the small distance moved by the vector$\Delta s$. Only a change in the direction of the field matters, movement perpendicualr to the field doesn't change the voltage.

$$\Delta V = \int_a^b \vec{E} \cdot d\vec{s} = \int_a^b E cos(\theta) ds = \int_{r_a}^{r_b} E dr$$

where r is the distance from the field source to a point in the field.

For a point source
$$E = k q / r^2$$
$$\Delta V = k q \int_{r_a}^{r_b} dr / r^2 = - k q (\frac{1}{r_b} - \frac{1}{r_a})$$

For an infinite line source
$$E = k q / r$$
$$\Delta V = k q \int_{r_a}^{r_b} dr / r = k q (ln(r_b) - ln(r_a))$$

For an infinite plate source
$$E = k q$$
$$\Delta V = k q \int_{r_a}^{r_b} dr = k q ((r_b) - (r_a))$$

Since change in potential energy from point a to b = - work done moving from point a to point b

$$\Delta E_p = E_{pa} - E_{pb}$$

[tex]\Delta V = V_a - V_b[/itex]

 

[AUMathTutor]

Jeff Reid:

A clear and elegant exposition of the relevant facts.

(if you already know what you're talking about, and have studied the things before, and already know the answer to the question being asked, ...)