alternating current

In the wires of your home the current does not flow steadily one way — it sloshes back and forth, dozens of times each second. That is alternating current. A battery gives direct current (DC, always one direction); the grid gives AC. It answers the everyday question: what kind of electricity comes out of the wall?

Precisely, AC is a current (and voltage) that varies as a sine wave, I(t) = I_0 sin(omega t), reversing direction every cycle. Its frequency f — 50 Hz across much of the world, 60 Hz in North America — is the number of full back-and-forth cycles per second, with omega = 2 pi f. Because it keeps swinging, we quote its effective value, the RMS (root-mean-square) value: for a sine wave, I_rms = I_0 / sqrt(2). Mains figures like 120 V or 230 V are RMS values; the peaks are sqrt(2) times higher.

AC is used for the grid because transformers can step its voltage up for efficient long-distance transmission and down again for safe use — and transformers only work on a changing current. The honest subtlety is that AC's average current is actually zero (it cancels over a cycle), which is exactly why we use the RMS value: it is the value that delivers the same heating power as an equivalent steady DC.