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# What would be a typical average speed for a dissociated electron in a household wire carrying electric current to a light bulb?

Question #62273. Asked by gmackematix. (Feb 04 06 10:21 PM)

peasypod

Are you referring to the average drift velocity (that which carries the current) or the thermal velocity? The thermal velocity is many magnitudes higher (but has nothing to do with the lightbulb turning on).

 Feb 05 06, 5:46 AM
peasypod

The drift velocity: Vd = I/(neA)

where A is the cross sectional area of the wire, n is the number density of free electrons in the wire (n = 8.48 x 10^28 m^3 for copper), I is the current and e is the electronic charge (e = 1.6 x 10^-19 C).

This gives for a 10 A wire, of cross section 3 x 10^-6 m^2 a drift velocity of Vd = 2.46 x 10^-4 m/s, or 0.246 mm/s.

This is incredibly slow, but of course the electric field travels at the (local) speed of light in the conductor, so the light bulb turns on straight away.

The rms (root mean square) thermal speed of electrons is given by
Vrms = (3kT/m)^(1/2)
where k is Boltzmann's constant, T is the temperature, and m is the electron mass...
Vrms = 1.15 x 10^5 m/s at 20 degrees C.
or rather.... 100,000 m/s...very much larger than the drift velocity.

So the drift velocity is only a tiny fraction of the average value (this is a bit different from the rms value, only by a constant, which I do not recall).

 Feb 05 06, 5:59 AM
gmackematix

It is the drift velocity I was referring to, peasy, and about a quarter of a mm per second sounds about right.
I just thought I would dispel the common myth that electrons carry the energy to the bulb and that electric current and eletrical energy travel together in a circuit.
Here is a site that attempts to address some of the dodgy terminology used by teachers in schools to convey how electicity works:
http://www.amasci.com/miscon/eleca.html

 Feb 05 06, 1:02 PM
gmackematix

Oh yes, and you'll be wanting a yay for that then won't you?
Yay peasy!

 Feb 05 06, 1:03 PM
peasypod

You can bet your booty I want a yay for that. I wasted a perfectly good envelope scribbling down those equations last night. ;)

Nice link, gmack. Do you think Ben Franklin ever concerned himself with those wrong polarities?! Nah...

 Feb 05 06, 4:40 PM

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