How does an RCD know to cut the power?

It compares the current going out on the live with the current coming back on the neutral. In a healthy circuit they match exactly. If some is missing, it has found another way to earth, possibly through a person, and the device trips.

What actually happens

1. Both wires pass through one ring

   Live and neutral run through the same magnetic core. Equal currents flowing in opposite directions cancel out, so the core sees no field at all.

2. Some current goes missing

   If current leaks to earth through damaged insulation, wet equipment or a person, less returns on the neutral than went out on the live.

3. The imbalance is sensed

   The difference leaves a field in the core, which induces a current in a small sensing coil wound around it.

4. It trips

   Past the rated imbalance, typically 30 mA for socket circuits, the sensing coil releases the mechanism and both poles open, usually within a few tens of milliseconds.