The terminology I've seen to describe voltage is confusing. It's like there is no way to accurately state (in one or two words) that voltage is present. For example, in an open circuit, people often say that the entire supply voltage "appears" at the two open conductor ends. Does voltage "appear", does it "exist", does it "occur"? When two long wires are connected to the two battery terminals, does the voltage "propagate" down the wires? Does it "manifest"? Does it "appear"? I'd like to be able to use simple English to explain what is happening regarding the voltage.
One or two words is not really enough, if you want to state 'that there is a voltage between these two nodes'.
That can be restated as 'if you connect a DMM between these two nodes, you'll get a reading', and 'if you take some charge from one node to the other, work will be done'. This second one is the most fundamental definition, if somewhat incomprehensible without the right background.
In casual conversation, we can describe a voltage as existing, occurring, appearing (either as having been there all the time, or appearing just now), and if you hit a thesaurus, I'm sure the list could be expanded several fold. It doesn't really matter what words are used to describe existence. 'Exists' is good.
I use 'node' rather than 'wire', as in electronics, a node is essentially a point, so by definition all connections to it will have the same voltage, or potential. A wire is an extended thing, and if a wave is passing along it ...
When two long wires are connected to the two battery terminals, does the voltage "propagate" down the wires? (yes, at the speed of light) ... then it can have a different voltage at different points along it, until the waves have dissipated (wave energy radiated away, or absorbed by resistance) and the wire reaches steady state. If there's a load on the end of a pair of wires, then wire resistance will drop a little voltage along the wires due to the current flow, so people often simplify things by requiring an open circuit on the wires.
I'd like to be able to use simple English to explain what is happening regarding the voltage.
The simplicity of the English you can use depends on your audience, and which aspects you're trying to convey. I'd go for the DMM definition by default, as it's a real experiment people can do with batteries and wires, and worry about waves and charges only if people want to delve deeper.
A Voltage (electromotive force) develops as electrons are separated.
Electrons can be separated by magneto-electro-mechanical (generator) methods or electrochemical (battery) or by beta-particle decay of radioactive ☢️ materials, or tribo-electric methods triboelectric
So, you can think of voltage building up as charge is separated. Although voltage is not energy, you can assume that voltage exists because electrons are separated and, if the circuit is completed (to allow charge to recombine), energy is released (instantaneous voltage x instantaneous current integrated over time).
This is why voltage is often compared to pressure. Pressure is not energy but, releasing the pressure allows water or air to flow and do work.
Whether voltage or pressure, if you know the properties of the system, you can use the pressure or voltage value as a surrogate for the energy available. That is, if you know the size (capacity) of a capacitor, and you know the voltage, you can calculate the energy. Likewise, if you know the size of a vessel and the density of the gas compressed (and possibly other factors), you can determine the potential energy in the system.
Voltage appears at both ends of wires with no load.
But current demanded by a load will propagate like a wave at the speed of light and this time naturally depends on the length of the pair and the speed of light in the dielectric constant between the conductors. This only becomes relevant for very fast risetimes or very long distances.
It's the tension between precise and concise. Given that the study of electricity and electronics is a major branch of theoretical and applied physics, it’s a big challenge to thread that needle with a satisfying description.
Meanwhile, any explanation of electricity needs to be tailored to the audience. I’ll get into that more below.
So on both counts it's a pedagogical challenge. I get your frustration. Nevertheless, I and others do try our best.
For my part, during my time here on SE-EE, I’ve come to notice three general categories of audience:
- Beginners: physical analogs like water, pipes, flow and pressure work to explain flow of 'electricity' because they're easy to visualize. Shortly beyond that, introducing Ohm's Law (without it, impossible to grasp power) as well as Kirchhoff's Current/Voltage Law rounds out some working, attainable understanding. Here’s my attempt at exactly that: Professor said no current flows to ground
For this level, voltage 'appears' is fine.
- Engineers, engineers-in-training and serious tinkerers: the concepts of displacement current and electromagnetism, so this brings in Maxwell; for electronics, electron theory, charge, flow of charge vs. flow of electrons, some photonics, and of course semiconductors. I rely on Falstad a lot for this, especially the circuit sim. Try it yourself, here: https://www.falstad.com/circuit/
Here, charge propagates as an electromagnetic wave, emerging as voltage at the other end.
- Deep thinkers, physicists: quantum mechanical theory (or, they get referred to physics.stackexchange.) I'd like to see more 'explain it like i'm five' attempts. Here’s my go at it: Does the voltage difference have an effect on the electrons' speed?
And how to express this? "We must be clear that when it comes to atoms, language can only be used as in poetry." —Niels Bohr.
Voltage 'manifests' as a probability fits... maybe.
All the above is hugely generalized, and as always I'm open to suggestions / feedback. But that's my general playbook on this stuff.