# The Speed of Electricity

Say you had a longing desire to flick on a switch connected by a very long wire to a light bulb far far away (because reasons). Would there be a delay before the bulb lit up? Could you run to the light bulb before the ‘electricity’ got there? No? How about if you flew in your private jet? We’ll see…

Unfortunately describing electricity in terms of how fast it travels isn’t particularly scientific. There are many ‘electricities’. Which ‘electricity’ do you mean? Electricity in general refers to the phenomena that involve electric charge. The rate of flow of electric charge is called the electric current (I talked about this a little in Resistance Is Futile), and can, in simple terms, be described by the equation below:

Yes, I’m sorry for omitting the deltas or d’s. t is time, Q is charge, I is current (because reasons again). It’s interesting actually, because the Q represents ‘quantity of electricity’ before they called it charge. I comes from ‘intensité de courant’ or French for ‘current intensity’. When you think of this you realise that science isn’t based around only English (or is it? *teehee*).

Essentially, current is defined by the amount of charge that passes by a point in one second. The more charge there is, the higher the current, and the faster the charge moves, also the higher the current.

So the speed of electricity is the current, right? Done. Piece of cake.

Well… you see, current doesn’t measure the ‘speed’ of charge, but more the amount of flowing charge. It means that we can’t express current in m/s. What we could consider, on the other hand, is the physical speed of the actual things that carry the charge. Often these charge carriers are electrons, but they can be other particles as well (like ions).

Wait, did you say electrons? I’ve heard of those before (from this post hopefully)!

One issue with using the speed of an electron is that they are constantly colliding with each other and with other particles in a wire, and they change direction all the time. However, if there’s a current, we know that the electrons must have net movement in one direction along the wire. The speed of this movement is known as the drift velocity.

The speed of electricity gotta be drift velocity then. Tell me that’s right?

The thing is, if we take a look at the speed of an electron in a wire for example (this is called the drift velocity), it is ridiculously low. It can be calculated using this formula:

Q and I you met earlier. n is the number of conducting electrons per cubic metre of the wire (this is usually the constant for one material). A is the cross-sectional area of the wire. With a current of 1 A, and a copper wire of diameter 2 mm, the electrons move at about 8.4 cm/h. I know I don’t have great time management but I’m pretty certain that it doesn’t take an hour to turn my lamp on.

The reason why the speed of electricity is not the drift velocity is because in a circuit, the electrons don’t actually need to physically travel from the switch to the bulb in order to make it light on. Electrons only need to transfer a wave across the circuit to carry a signal, by knocking forward other electrons. Thus the speed at which a signal travels is really the speed of the wave. This wave is an electromagnetic wave, and we all know they have one special property – they travel at the speed of light!

Okay, not quite. They travel at the speed of light in vacuum, but in wires the speed can vary from 50% to 99% of the speed of light, depending on the material. That’s still ludicrously fast though.

So the answer is no, your private jet cannot beat electricity in a drag race. Even if you tried. Like, really hard.

Yanhao