The speed of electric currents

People think that electricity moves at the speed of light.  Well, the influence of electric fields moves at the speed of light.  The surprising truth is that actual electrons carrying current in wires move slowly in DC systems, and scarcely move at all in AC systems.

Consider a 0 gauge aluminum wire carrying 100 amperes DC.  Aluminum has an atomic weight of 26.98 and a density of 2.70, with 3 valence electrons available to conduct current.  This means that 1 cc of aluminum has almost exactly 0.1 moles of atoms and about 1.8056*10²³ conduction-band electrons in it.

A 0 gauge wire has a cross-sectional area of 0.535 cm², so each cm of wire has about 9.66*10²² conduction-band electrons in it.  100 amperes is 100 coulombs/second, and there are 6.2419*10¹⁸ electrons in a coulomb, so a 100-amp current means there are 6.2419*10²⁰ electrons moving across any given cross-section per second.  Dividing this number by 9.66*10²² electrons per centimeter of wire yields an electron speed of just 6.46*10^-3 cm/sec, less than 100 micrometers per second!

A micrometer is small for a human, but big for an atom; the electrons are moving more than fast enough to run into many atoms per second, thus generating heat.  But the contrast between the speed of electric potential waves and the actual speed of the electrons is something that people have difficulty grasping.

Labels: electricity, physics, science

  ¶ 7/17/2021 02:31:00 PM