Inside the Wire (November 2025 Challenge Question)

That's correct for DC current.

Now for AC, where the electrons are going back and forth at constantly changing velocities, is the answer zero? ...or the number of electrons that pass in one half-cycle? ...or do we have to use RMS? ...does it depend on the frequency?

Good question! My guess is over a long time the net flow of electrons is zero. Instantaneous maximum determined by peak current (√2*RMS) each way.

But I could be wrong

All these questions are what made Edison campaign for DC...

I would say calculate the number of electrons in a half cycle.

I think your 10 ampere reading is probably RMS, so you have to multiply by sqrt(2) to get peak current, and then multiply by 1/pi to get the average current in that half cycle. Multiply the average current by 1/120 sec. (or 1/100 for 50 hz) to convert to charge (coulombs ). Finally, multiply by 6.24 x 10¹⁸ electrons/coulomb to convert to number of electrons.

Now, a quantum physicist will probably say that all electrons are identical, so when the electrons pass by in the other direction, you can't say they are the same ones. They could be swapping places with the electrons in the copper atoms.

Nice to see some thought went into your answer.

AC? assuming:

-modest (50/60 hz) frequencies normally associated with power transfer.

- the wire wasn't within another EMF field

The answer would be zero. Regardless of where within the phase the AC measurement started.. 20 seconds later it, the measurement would end at the same phase location.

Sorta like (?) a dual slope ADC rejecting power line AC noise..integrated over 20 seconds. The integrating period doesn't have to be sync'd to AC noise source, just has to have a total duration that is a multiple of the freq.

The answer doesn't work if the frequency of the AC is not divisible (equal number of positive and negative excursions) over the 20 second period, or at much higher frequencies where other factors become of note.

Interesting fact: If you pass 20A through a 12-gauge copper wire, the electricity is travelling at 4.54 * 10⁻⁴ m/s = 0.01787398 inches per second.

10A for 20 seconds would travel about 1/6 of an inch.

https://brainly.com/question/29801818

The electron drift velocity is 4.54 × 10^ (- 4) m/s. Electromagnetic fields of electricity travel at close to the speed of light.

The contrarian in me wonders if the motion of the core (non-valence) electrons counts in this total. I also want a better definition of the point in question. Is the point inside the conductor, a ring on the surface of the conductor, or a ring just outside of the conductor? This is an "Inside the Wire" question after all.

Only 1 electron per copper atom takes place in conduction.

Since all electrons are identical, maybe they can swap places and no one could know. It doesn't make much sense to worry if the same electron was counted twice. Electrons, like money, are fungible.

The only thing you can say for sure is that if the ammeter says 10 amperes, 10 coulombs of electrons are moving past any point in the circuit in one second.

1 electron per copper, which may mean that the number of electron passing thru can also also be dependent on the kind of material the conductor possibly be made of?

Carbon have a fewer number of electrons, which can be a limiting factor..

The current flowing through wires made of different conductive materals will be different, IFF the supply voltage is constant.

But the OP specified 10 Amperes of current. This means that wires of different sizes, different lengths, or different materials, MUST have different supply voltages, to cause that 10 Amperes.

As Rixter correctly said, copper has one electron per atom that is available for conduction. Any substance that has fewer than one, has zero, so doesn't conduct electric current under normal conditions.

May possibly be tue, unless the 10 Amperes fed into the conductor were all converted into heat... since the carbon material can simultaneously serve as the conductor and the electrical load at the same time.

The OP was/is: "How many electrons pass a given point in a conductor in 20 seconds if the conductor is carrying 10A?"

It doesn't matter how or where the energy is used, ONLY "How many electrons pass a given point in the conductor in 20 seconds if the conductor is carrying 10A"

It would be perfectly possible to connect 10 volts across the ends of a carbon conductor having a resistance of 1 Ω, and a current of 10A would result. As long as there is nothing else connected, exactly the same number of electrons that enter one end, exit the other end. Electrons can not be converted into heat, The energy carried by the moving electrons can be converted into heat, but that does not "use up" any electrons!

It would be equally possible to connect 10 volts across the ends of 2 copper wires having a total resistance of 0.1Ω, leading to a motor having an effective resistance of 0.9Ω, and a current of 10A would result. Here, part of the energy carried by the electrons is converted into heat, and part of it is converted into some form of motion, but it is a simple series circuit, and whatever current flows in one part of the circuit, must flow in all parts of the circuit. Again, no electrons are converted into any other form; they're electrons when they enter the circuit, and they're still electrons when they exit the circuit.

Of course the electrons that exit the circuit aren't the same ones that entered the circuit.

I believe that 10 Amperes of current as it passes thru a conductor can possibly be exhausted at a rate of 1ampere / coulomb, by which the time the current passed thru the heated carbon pile as the heated conductor material...

The amount of time in my view may also be affected by the conversion of electricity into heat since heat is also developed as the 10A current passes thru the carbon pile material..

This isn't a matter of belief or view! It's a matter of well-established scientific facts!

In a single wire (which could be copper or any other conductive material, including carbon) or a simple series circuit, where electrons enter at one end and exit at the other (and only at the ends), the current is the same at all points within the length of that conductor. There is no ability to store any electrons or "use up" any electrons, so the number of electrons entering the circuit MUST be the same number as the number of electrons exiting the circuit.

The terms "Volt, Ampere, Watt, Ohm, Coulomb, second, and Joule" all have very specific and very precise definitions, and very simple equations relate all of them to each other. Most students who have understood high-school physics know those equations.

Unfortunately, the term "electricity" isn't so well defined! Electric energy (the energy of moving electrons) is commonly converted into heat, but that conversion does NOT change the electron into anything different.

A moving vehicle loses energy when you apply the brakes, but even when it has stopped completely, it is still the same vehicle!

Unless of course you have an access to a quantum level electro-scope,

Yes as I had observed and experienced electrons are so microscopically tiny that its reflections can only get represented by reflections of light while using an electron microscope and observable during a cell plating processes..

To illustrate why there is no storage of electrons in the wire, 2 coulombs placed 1m apart repel with a force about 10^10 newton, or 10^6 tonnef.

Yet about 10^5 coulombs (1 Faraday) are required to deposit 1 gm-equivalent of a substance in electrolysis.

The width of a point is infinitesimally small. This is far less than the 2.28*10^-10 meters of a copper atom. So why don't the non-valence electrons count in this total?

I'm just clarifying my contrarian perspective.

...because they are held in place by the structure of the material, commonly crystal structure.

I see that you do not wish to play my little "contrarian" game. Pity. I was hoping someone might, because it ultimately leads to some useful revelations. IMHO.

If the transition threshold for "counting" electron motion is smaller than a copper atomic nucleus, then the current magnitude becomes a negligible part of total electron motion. Remember, all electrons are constantly in motion. The spherical shape of any S orbital identifies the volume where that electron can be found 90% of the time. The "1S" orbital is the smallest for any atom, but it is vastly larger than the nucleus of the atom. This perspective reinforces the observation that, despite a drift of electrons occurring, the conductor does not ionize.

Lastly, suppose the transition threshold for counting electron motion is a geometric "point" and not a "disk" intersecting the conductor. In that case, the current density along with possible skin effects are the relevant metrics.

I have no idea what "useful revelations" you may be referring to.

As you correctly point out, the nucleus of any atom is vastly smaller than the diameter of any electron's path, but that has no effect on the number of electrons drifting with the current. It seems to me that you are unnecessarily complicating a simple question.

You can't observe the number of electrons passing through a single point, if you mean a geometric point. A rigorous statement of the OP's question would say something like "...passing through a single cross-section of the wire..."

I think that's correct for AC too. The problem asks how many electrons pass a given point in a given time -the fact that in AC the electrons pass at different moments of time in opposite directions doesn't mean you don't count them (regardless of the direction and if they are the same electrons or not), so the answer is not zero. Although the AC current is variable in time, its value is defined so that it will cause the same effect as a DC one. If you have a resistive load, a 10A current passing that load will cause the same power consumption, no matter it's DC or AC, so the number of electrons will be the same (a constant value in DC but the same average value in AC).

Yahtzee!