Explaining how a transformer works
When an electric current passes through a long, hollow coil of wire there will be a strong magnetic field inside the coil and a weaker field outside it. The lines of the magnetic field pattern run through the coil, spread out from the end, and go round the outside and in at the other end.
These are not real lines like the ones you draw with a pencil. They are lines that we imagine, as in the sketch, to show the pattern of the magnetic field: the direction in which a sample of iron would be magnetised by the field. Where the field is strongest, the lines are most closely crowded.
With a hollow coil the lines form complete rings. If there is an iron core in the coil it becomes magnetised, and seems to make the field become much stronger while the current is on.
The iron core of a transformer is normally a complete ring with two coils wound on it. One is connected to a source of electrical power and is called the 'primary coil'; the other supplies the power to a load and is called the 'secondary coil'. The magnetisation due to the current in the primary coil runs all the way round the ring. The primary and secondary coils can be wound anywhere on the ring, because the iron carries the changes in magnetisation from one coil to the other. There is no electrical connection between the two coils. However they are connected by the magnetic field in the iron core.
When there is a steady current in the primary there is no effect in the secondary, but there is an effect in the secondary if the current in the primary is changing. A changing current in the primary induces an e.m.f. in the secondary. If the secondary is connected to a circuit then there is a current flow.
A step-down transformer of 1,200 turns on the primary coil connected to 240 V a.c. will produce 2 V a.c. across a 10-turn secondary (provided the energy losses are minimal) and so light a 2 V lamp.
A step-up transformer with 1,000 turns on the primary fed by 200 V a.c. and a 10,000-turn secondary will give a voltage of 2,000 V a.c.
The iron core is itself a crude secondary (like a coil of one turn) and changes of primary current induce little circular voltages in the core. Iron is a conductor and if the iron core were solid, the induced voltages would drive wasteful secondary currents in it (called 'eddy currents'). So the core is made of very thin sheets clamped together, with the face of each sheet coated to make it a poor conductor. The edges of the sheets can be seen by looking at the edges of a transformer core.
Chris Burtenshaw recommends the following website saying: "The following is an excellent circuit to show the magnetisation curve (B/H) of different transformer or inductor core materials."