How do transformers work? A transformer is basically a primary inductor connected to a voltage $U_P$ which you want to transform. You also have an iron rod and a secondary inductor. So when there is a current $I_P$ the iron rods becomes magnetic. When you connect the  primary inductor to AC, that means that you'll have a changing current, which causes a change in flux which causes induction. My question is, is $U_S$ just the induction voltage created  by the iron rod?
 A: It's always handy to have some background information:
In Europe the mains voltage is 230 Volts, which is too much for a lamp for example, so it needs to be lowered to for example 12 Volts. This is done by using a transformer.
The primary winding is connected to the mains voltage of 230 Volts. The AC in this primary winding causes a varying magnetic flux in the iron rod (core) which on its turn creates a varying magnetic flux through the secondary winding. Because of electromagnetic induction a voltage is induced in the secondary winding. The primary winding has more turns than the secondary winding which causes the secondary voltage to be lower than the primary voltage:
$$ \dfrac{N_P}{N_S}  = \dfrac{U_P}{U_S} = \dfrac {I_S}{I_P}$$
You can see that be decreasing/increasing the number of turns in the windings you can control the voltage created by electromagnetic induction. 
Here is an illustration with an example ($U_S = 220V, U_P = 110 V$)
 You can see how simple it really is. 
A: According to ATL Transformers Ltd:

The transformer is based on two principles: first, that an electric current can produce a magnetic field (electromagnetism), and, second that a changing magnetic field within a coil of wire induces a voltage across the ends of the coil (electromagnetic induction). Changing the current in the primary coil changes the magnetic flux that is developed. The changing magnetic flux induces a voltage in the secondary coil.


The referenced article discusses Faraday's law
The Wikipedia article on magnetic core says

A magnetic core is a piece of magnetic material with a high permeability used to confine and guide magnetic fields in electrical, electromechanical and magnetic devices such as electromagnets, transformers, electric motors, inductors and magnetic assemblies. It is made of ferromagnetic metal such as iron, or ferrimagnetic compounds such as ferrites. The high permeability, relative to the surrounding air, causes the magnetic field lines to be concentrated in the core material. The magnetic field is often created by a coil of wire around the core that carries a current. The presence of the core can increase the magnetic field of a coil by a factor of several thousand over what it would be without the core

(my emphasis)

There's a useful looking article on this subject by a Dr A.M. Etamaly 
