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Electric field accelerates electrons in wire.

Because of at least inertia, when the electric field (voltage) is applied, electrons will not instantly have some maximum speed, but will continuously accelerate to maximum value that can be calculated by Ohm’s law.

I am wondering: if electrons need time to achieve some speed, will the current (amplitude speed of electrons) decrease with high-frequency AC voltage applied?

Say, for 100V (DC) electrons need 1ms to accelerate to maximum speed. So, if we apply, for example 251 Hz AC square-waved source, the voltage will be decreased before 1 ms, and will be applied to opposite direction, damping electrons. So they will not accelerate to maximum, and, hence the resulting current will be decreased?

I actually forget about Ohm’s law for AC voltage, and yes, current inversely depends on frequency, so higher frequency, lower current, but I want to know is my understanding correct. I want to understand the fundamentals of the phenomenon. People in comments started to answer kinda “it is not because of inertia, it is because of inductance”, the same as to state, for example, that ballon inflates not because outside air atoms will bump it insides, but because of “pressure”, although it is the same, just a bit more fundamental explanation.

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  • $\begingroup$ Can you briefly describe how Ohm's law can be used to calculate the maximum speed of electrons in a conductor? $\endgroup$
    – M. Enns
    Commented Feb 3, 2022 at 16:22
  • $\begingroup$ "will the current (amplitude speed of electrons) decrease with high ac voltage applied?" Is this a typo? Because you say current decreases with increasing voltage here. Also, I don't think amplitude or speed is the definition of current. $\endgroup$
    – DKNguyen
    Commented Feb 3, 2022 at 16:38
  • $\begingroup$ Well all else being equal, you're actually right about current decreasing with increasing frequency. But not really because of the concepts you put forth (which i find a bit confusing TBH). All wires have a self inductance....it doesn't need to be wrapped in a coil shape to be an inductor...and an inductor has an increasing impedance as a function of frequency. By ohms law, impedance goes up, voltage is constant, then current must go down. $\endgroup$
    – Kyle B
    Commented Feb 3, 2022 at 17:17
  • $\begingroup$ I would caution about imagining the motion of electrons to visualize what's going on in a circuit. The magic is actually in the electromagnetic fields surrounding the wires. Just like waves on a pond can have different amplitudes and speeds, but the water molecules themselves barely move. $\endgroup$
    – Kyle B
    Commented Feb 3, 2022 at 17:20
  • $\begingroup$ @M.Enns current by definition is amount of electrons that pass through area of conductor per time. Increasing currency can mean only two things: there came more electrons to the wire (from nowhere), electrons are started to move faster. Hence, higher current, higher net speed $\endgroup$
    – Stdugnd4ikbd
    Commented Feb 4, 2022 at 9:39

2 Answers 2

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It could be instructive to work out yourself the ac response of the Drude model or its simplified version (see my own posts here and here). The key point is that electron acceleration by the electric field is already taken into account in the electron mobility/conductance $$ \sigma_0 = \frac{nq^2\tau}{m}, $$
since the electrons are constantly reaccelerated by the field after being scattered from the lattice (impurities and phonons). In particular, the ac conductance is predicted to be $$ \sigma(\omega)=\frac{\sigma_0}{1-i\omega\tau}= \frac{\sigma_0}{1+\omega^2\tau^2} + \frac{i\omega\sigma_0}{1+\omega^2\tau^2} $$ As one can see, the conductance has an imaginary part, characterizing the current retardation in respect to the electric field. Moreover, it decreases in magnitude at higher frequencies - that is, the cvurrent decreases with increasing the frequency, as $$ \mathbf{j}(\omega)=\sigma(\omega)\mathbf{E}(\omega) $$

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  • $\begingroup$ Also as for Joule-Lentz law, does it show how much heat will be produced by wire at some moment $t$, or it shows the total summary heat from produced from 0 to $t$? $\endgroup$
    – Stdugnd4ikbd
    Commented Feb 4, 2022 at 10:45
  • $\begingroup$ Joule's law works for ac current as well, but one usually averages over the period of the ac oscillations when reporting the values. See here. Note that $220$V in a power socket is also root mean square value rather than the amplitude. $\endgroup$
    – Roger V.
    Commented Feb 4, 2022 at 10:48
  • $\begingroup$ I asked generally, about DC $\endgroup$
    – Stdugnd4ikbd
    Commented Feb 4, 2022 at 11:03
  • $\begingroup$ DC means direct current (постоянный ток), which is frequency-independent... perhaps I don't quite understand what you are asking. Or do you means that the bias has both constanta nd ac component? $\endgroup$
    – Roger V.
    Commented Feb 4, 2022 at 11:05
  • $\begingroup$ You probably, missed my first comment to Your answer, it was not about the topic, it was about Joule-Lentz law $\endgroup$
    – Stdugnd4ikbd
    Commented Feb 4, 2022 at 11:30
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In the classical theory the free electrons are in thermal equilibrium with the atoms of a conductor, and are bouncing at random at a very high speed from one atom to another. An electric field will cause an acceleration between each bounce and cause a very small drift. The mean free time between collisions is small compared with the period of most achievable frequencies.

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  • $\begingroup$ Well, actually if there was no resistance, even for a constant voltage the current will be constantly increasing, but electrons will constantly accelerate due to external elect field (voltage) applied (at least if to talk about generator as the source) $\endgroup$
    – Stdugnd4ikbd
    Commented Feb 4, 2022 at 10:03
  • $\begingroup$ In real conductor, electrons are still constantly accelerated by voltage, but every time, some part of the incoming kinetic energy will be lose due to bumping in obstacles, i.e. on heating (that is described by Joule-Lentz law) $\endgroup$
    – Stdugnd4ikbd
    Commented Feb 4, 2022 at 10:06
  • $\begingroup$ If to consider a single electron, obviously, the distance that it can move freely before bumping in something is tiny, but there are more than one electron, and if to consider the whole picture, I think my assumption will make sense $\endgroup$
    – Stdugnd4ikbd
    Commented Feb 4, 2022 at 10:09

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