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I am currently studying Practical Electronics for Inventors, Fourth Edition, by Scherz and Monk. Chapter 2.5.1 How the Shape of a Conductor Affects Resistance presents the following image:

enter image description here

I wanted to check the authors' calculations for drift velocity, since there has been some issues[2][3] related to their electron drift velocity calculations in prior sections of the textbook.

My understanding is that the drift velocity of electrons is calculated as

$$\dfrac{\text{current density}}{\text{free electron concentration} \times \text{electron charge}}$$

But, as far as I can tell, we are not provided with the free electron concentration in this case, so how does one calculate the drift velocity (to verify that the authors' calculations are correct)?

I would greatly appreciate it if people would please take the time to clarify this.

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  • \$\begingroup\$ omnicalculator.com/physics/… \$\endgroup\$
    – G36
    Commented Jan 29, 2020 at 18:48
  • \$\begingroup\$ @G36 Doesn't this assume that you already know the free electron concentration (in order to calculate the drift velocity)? Also, I'm not sure how we take the values we have here and apply it to their "number density", since it is set to a variable multiple of \$10^{28} \text{carriers}/m^3\$ as default? \$\endgroup\$ Commented Jan 29, 2020 at 19:17
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    \$\begingroup\$ Yes, this is what we normally do we, use a number between 8.4.....8.5 as a ballpark number. In fact, in EE we never does such calculations. So why even bother about it? \$\endgroup\$
    – G36
    Commented Jan 29, 2020 at 19:25
  • \$\begingroup\$ @G36 Ahh, that actually produces a value that is approximately what the authors got: omnicalculator.com/physics/… !!! So it seems that you are correct about the 8.4-8.5 value. This is what I was looking for. Thanks! Do you want to post an answer? I will then accept it, so that we can close this question. \$\endgroup\$ Commented Jan 29, 2020 at 19:49
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    \$\begingroup\$ Also, you should check this onedrive.live.com/… \$\endgroup\$
    – G36
    Commented Jan 29, 2020 at 20:22

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It might be off, it might not, why bother?

The Drude model of conductivity is so inaccurate, so lacking in good correlation with reality, that it's really a waste of time to get pedantic about exactly what the drift velocity is. Just let the big, or small, numbers wash over you in a hand waving way, 'coo, I didn't realise average electron drift velocity was that slow!'

If you want to check the book's calculations, then the electronic concentration is the same as the atomic concentration, as atoms in a metal donate one electron each to the conduction band. Wikipedia will give you the density and the atomic weight for any metal to allow you to calculate the atomic concentration.

If you want a model to make circuit theory a bit more intuitive, then the hydraulic model goes a long way, you can even build a DC-DC boost converter (water hammer, hydraulic ram) with it!

If you want to understand how conductivity works quantitatively, then you need quantum mechanics.

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    \$\begingroup\$ It's not about the value being accurate; it's about the textbook being consistent with its calculations and how it teaches to calculate values. \$\endgroup\$ Commented Jan 29, 2020 at 7:33
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    \$\begingroup\$ To be clear: I want to understand how things are calculated; I am not satisfied with just accepting things without thought and moving on. This is not how learning is done. \$\endgroup\$ Commented Jan 29, 2020 at 19:55

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