A cell or a battery pushes charge round a circuit in one direction only. Its potential difference is direct: one terminal is always positive. The current is direct current (d.c.).

The mains supply is different. Its potential difference keeps swapping direction, so the current flows one way, then the other, many times a second. That is alternating current (a.c.).

The flat line is a 6 V d.c. supply. The wave is an a.c. supply with a peak of 10 V. One complete cycle (peak to the next peak) is the period, here 20 ms. The frequency is the number of cycles each second:

frequency = 1 ÷ period
f = 1 ÷ T

Frequency in hertz (Hz), period in seconds (s).

1. T = 20 ms = 0.020 s
2. f = 1 ÷ 0.020
3. f = 50 Hz

Change milliseconds to seconds before you divide: 1 ÷ 20 gives 0.05, not 50.

In the UK the mains is an a.c. supply with a frequency of 50 Hz and a potential difference of about 230 V.

Most appliances join to it with a three-core cable. Each wire has its own colour and its own job:

• Live wire (brown): carries the alternating potential difference from the supply. It is at about 230 V. The fuse and the switch go in this wire.
• Neutral wire (blue): completes the circuit. It is at, or close to, 0 V.
• Earth wire (green and yellow stripes): a safety wire joined to any metal case. It is at 0 V and only carries a current if something goes wrong.

So the potential difference between the live wire and the neutral or earth wire is about 230 V.

Your body is at, or close to, 0 V because you are in contact with the ground. Touch the live wire and there is a potential difference of about 230 V across you: a current flows through your body to earth. That is an electric shock, and it can kill.

That is still true when an appliance is switched off. The switch breaks the circuit further along, but the live wire between the socket and the switch is still connected to the supply, so it is still at 230 V.

If a fault makes a metal case live, the earth wire gives the current an easy path to the ground. The large current melts the fuse in the live wire, which cuts off the supply before anyone touches the case.

Any connection between the live wire and earth is dangerous, whether that connection is a person, a damp wall or a metal pipe.