## Friday, November 03, 2017

### Ask a Physicist: The Speed of Electricity

Electrons carry charge, but I've been told that electrons in a DC circuit actually move slower than a snail, and in an AC circuit, they don't move at all, just shifting to and fro. Then how does that make a lightbulb light up?
Nabilah,
What you've been told is correct, but I can see how it'd be confusing—after all, when you hit the light switch, the lights come on instantly! So let's explore what's going on here.

First off, it's crucial to understand that it's not the electric charge itself that makes the bulb light up—it's the motion of charges. In an incandescent light bulb, the thin wire (or filament) inside has a high voltage—a high concentration of electrons—at one end, and a low voltage at the other. Since electrons repel one another, this voltage difference pushes electrons through the filament, like water through a pipe. This is why a circuit always needs a ground, a place for the electricity to flow to; just cramming a bunch of extra electrons into the wire and charging it up won't make it light up.

 A toaster, an electric stovetop, and an incandescent light bulb all use the same principle—resistive heating—to turn the flow of electrons into heat and light. In any of these devices, when an electron flows from a high voltage to a low one, it doesn't take a smooth, direct path—it's constantly bumping into the atoms of the filament, knocking them around and imparting energy onto them in the process—almost like the frictional heating you get when you rub your hands together. Since temperature is just a measure of how fast the particles in a material are moving, this heats up the filament until it's hot enough to glow. In toasters and stovetops, the red glow we see is a side-effect of getting the coils very hot to cook our food, but in a lightbulb, it's the goal.
When the electricity only moves one direction through a wire, that's called direct current, or DC, but the fact that electronics are powered by the motion of charge underlies the answer to your question about alternating current, where the voltage in the wire is reversed dozens of times each second—with the high-voltage end switching to low, and vice versa..

If you hold a very long rope loosely in your hand, and someone reels it in very quickly, your hand is going to heat up thanks to friction—you might even get a rope burn. This is a bit like direct current flowing through a bulb filament. But imagine if, instead of reeling the rope in, they only pull the rope an inch or two, but then someone on the other side of you pulls it in the other direction, and then  the process repeats. The same piece of the rope stays in your hands, but since it's moving back and forth, it can still heat your hand up and cause that rope burn. This is alternating current, AC.

Now that we've got some groundwork laid, we can talk about the fun part of your question: the speed of electricity.

When you flip on a light switch, you're bringing two pieces of metal into contact with one another to complete a circuit, allowing electricity to flow from a high voltage to a low voltage through your lightbulb. However, in a DC circuit—thanks to the resistive bumping and jostling discussed earlier, the electrons that cross the switch when you flip it won't actually reach the light bulb for hours! So why does the bulb light up immediately when the switch is closed?

The answer lies in the fact that the wire conducting this electricity is already crammed full of electrons, which repel one another. Think of it this way: imagine you've got a hose that's a hundred feet long, hooked into a closed spigot. If the hose is already full of water, opening the valve will cause water to start flowing out the end right away! The water molecules that left the spigot when you opened it might not make it to the end of the hose for quite some time, but every drop that leaves the spigot and enters the hose is forcing another one out the end.

It's the same way with electrons—they repel one another, so pushing a few into the switch-end of the wire forces some out the bulb-end and into the light bulb's filament! (or, more likely nowadays, into the LED.) Since the repulsion that causes this push is carried by electromagnetic waves, the effect of the circuit being closed travels down the wire at close to the speed of light, and the bulb lights up almost instantly!

If you want to look at an individual electron, though, the picture is a little bit complicated. From a zoomed-out perspective, the electron is moving at what we call the drift velocity. Drift velocity depends on a number of things—the voltage, the material that your wire is made of, etc.—but it's extremely slow in most cases; in a typical wire, you might expect to see an electron move three inches per hour in the direction of current flow, because it's bumping, bouncing, and scattering off the wire's atoms.

Zoom in close enough, though, and you're in for a surprise—those sluggish electrons are actually moving at 3.5 million miles an hour! This is the velocity they're traveling at even in a wire with no current flowing through it—but they move in all directions equally often, so there's no net motion of charge until a voltage difference is introduced. Even with that voltage applied, electrons seem to move so slowly from the macro scale because they're doing a chaotic dance, bouncing around and retracing their steps thousands of times before taking another step forward.

Hopefully, this helps! Before we go—one thing we've touched on here is the similarity between electricity in wires and water in pipes. It turns out that, while it's not perfect, this analogy goes much deeper than you might expect, and provides a tremendously useful way to interpret concepts like voltage, current, and impedance. Check back next week for a deeper dive into this awesome heuristic!

—Stephen Skolnick