Your Favourite Electrical Engineering College Course Question

Hello, this is my first post. I’m interested in hearing about electrical engineering assignment questions you encountered during college or sixth form that were particularly engaging, really made you think and therefore memorable. Or if you could design one such question now, what would it be?

Parents
  • One that I recently dreamed up, but was never asked, would be:

    A copper cable/wire is at it's fusing current, at UK mains frequency, and every atom provides it's conduction electron equally, how far does the electron's charge travel, in atoms, between the opposing peaks of the AC wave form? [table of values as part of exam paper] What is the peak velocity of the charge movement?

    It's somewhat surprising.

Reply
  • One that I recently dreamed up, but was never asked, would be:

    A copper cable/wire is at it's fusing current, at UK mains frequency, and every atom provides it's conduction electron equally, how far does the electron's charge travel, in atoms, between the opposing peaks of the AC wave form? [table of values as part of exam paper] What is the peak velocity of the charge movement?

    It's somewhat surprising.

Children
  • OK its not Friday, and I'm holding a mug of warm tea so I'll indulge you.

    Lets assume for argument that when we say the wire is  'at its fusing current' we use Onderdonk's formula  for reaching melting point after exactly one one second.

     this is the US version where A is in circular mils multiply mm² by 1973.5, or if you are in a hurry 2000,  to get circular mils.. 

    Then look at the answer, mutter I don't believe it and  round it off and say call it 300 amps at one second for 1mm2 to make it easy.

    is that credible ?

    1mm2 is about 17AWG.  Yeah, could be.

    300A is only 1875000000000000000000 electrons going past per second. (1.875 E 21)

    each atom of copper provides 2 electrons, and in a 1m length of copper wire 1mm2 cross-section there are (1000cubic mm ,at 9 mili-gram per cubic mm  that is 9 grams,  and at 64 grams per mol,

    Lemma 1

    Avagadros no is 6.022×1023g/Da where the Dalton is 

    1.660×10−27 kg -== mass of one atomic unit.(almost one proton. )

    each copper atom is therefore 1.062E -25 kg. 
     so our 1m of 1mm (9 grams) wire has 8.46 E+22 atoms of copper, so 

    1.693E+23 Free electrons. 

    End Lemma 1

    given 1.693E+23 Free electrons.  and the flux  (1.875 E 21)  each is doing about 1cm/second. 

    so in the half cycle period of 10msec, its moved about 100um (times pi/2)  QED

    Note that the thermal velocity of the electrons - whcih is random, when this is a mean movement in the direction of current is much more. 
    equating mv^2  to kT 

    (at room temp T=300K )  Boltzmann constant  k = 1.380649×10−23 J⋅K−1 eo energy per particle is 4.14e-21Joules

     electron mass 9.109 ×10−31 kg 

    so v squared is ~ 

    thermal velocity is ~ 6.741 E+4 m/second so about a million times faster. 


    The assumption that the  E field in any sensible wire only changes the electrons a very  gently push of the random walk  sort of way is valid. If electrons in a wire were remotely like those in a vacuum like a CRT, then there would be a square law I/V curve,  as there is for triodes.

    But in this case ohms law holds, and by more than a million to one, which is nice.

    Mike.