crazyFlip a switch and a lamp lights up almost immediately. It is tempting to picture electrons racing all the way from the switch to the bulb. But that picture mixes up two different speeds: the drift of charge carriers and the propagation of an electromagnetic disturbance.
A wire is already full of charge carriers
A metal contains mobile electrons before a circuit is switched on. When an electric field is established, their motion gains a small average drift. This drift is superimposed on their much faster microscopic motion.
For a simple conductor, the magnitude of the current relates to drift speed through
Here, is the number of mobile carriers per unit volume, is the magnitude of each carrier’s charge, is the wire’s cross-sectional area, and is the average drift speed.
For illustration, take ampere, square millimetre, carriers per cubic metre, and coulomb. These values give a drift speed of about 0.074 millimetres per second. The assumed carrier density is representative of copper; this is a simplified model, not a universal wire speed.
The signal is a different story
Changes in the electromagnetic field propagate along the circuit much faster than the carriers drift. Their speed depends on the geometry and the materials surrounding the conductors. In an ideal transmission line, it is described by
where and are the inductance and capacitance per unit length. The signal does not propagate instantaneously, and it does not need a particular electron to travel from your switch to your lamp.
What about alternating current?
With alternating current, the average carrier motion reverses direction periodically. Energy can still be transferred to a load even though an individual carrier does not steadily travel from the power station to your home.
When someone asks how fast electricity travels, first ask: do we mean charge drift, signal propagation, or the response of the device?