Discuss Bill Compton's answer to: How to Build a 110 Volt to a Low Voltage Transformer

Let us discuss the fundamentals of transformers in a bit greater detail. 

Two coils are wound around a ferromagnetic core: one the primary coil and the remaining coil the secondary.  We apply alternating current to the primary coil, and it travels through the core to the secondary usually experiencing only hysteresis losses.  Then the secondary coil feels the magnetic field and if there is a load or other connection present current will flow from the primary to the secondary.

Depending on the ratio of turns in each coil the secondary voltage will be higher or lower than the primary.  When the field is applied to the other coil it becomes the primary and the other coil becomes the secondary.

If we apply a 60 HZ AC signal of 120 watts on the primary, we get 120 watts at 60 HZ AC on the secondary.  The difference is the voltage.

Using Ohm's Law: E=IR
Where:
E= EMF (measured in volts)
I= Inductance (curerent, measured in amperes)
R= Resistance (measured in Ohms)

For this discussion we will not discuss eddy currents and hysteresis.

We determine that to get 12 VAC 60 HZ from the secondary we will employ a 10:1 turns ratio.  We will form a primary coil of 100 turns of 22 gauge varnished transformer wire at the primary and 10 turns of 14 gauge varnished transformer wire at the secondary.

The thicker wire is necessary because of the higher current that will pass around it.