NOTE TO THE EXPERIMENTAL:Do not connect your home-made "nail transformer" to the 120 volt source. You could burn your house down and kill yourself, and it'd likely be a slow painful death, or a fast painful death.
Transformers for high frequencies, such as radio frequencies, often have
no core, which is called an "air core." These transformers do not suffer from
saturation, as do transformers with iron cores.
We will be talking only about transformers with iron cores, here.
The basic operation of iron-cored transformers is as follows: The primary winding induces a magneting field in the nail, and the change in that magnetic field, in turn, induces voltage in the secondary winding.
One of the characteristics relating to transformers is called "saturation". As you increase the current through the primary winding, the magnetism in the nail also increases.
However, the nail can only "hold" so much magnetism.
Thus, increasing the current beyond a given ammount will not
increase the magnetic feild, any more.
That is called the saturation point.
In order to understand this, you must also understand inductance,
which I am not explaining here, yet. Have a good link?
If enough of you ask, maybe I will explain it here.
But, in short, when the transformer's core reaches the saturation point,
it then draws far more current then it normally would at that frequency
and voltage.
If you would like to submit a better introduction, summary, explanations, or other relevant informemation, feel free to email me at jesseg at suespammers dot org
History:
Around 12/22/2001, I was doing some experimenting with an old transformer,
and I collected some interesting data regarding current, voltage, saturation,
and some information on loading. (How many volts the output drops when
you add one amp of load.)
These are some of the electronic notes I took.
NOTES:
level of voltage and amperage is relative, as I adjusted the scope
for nice viewing of all scenes. In other words, just because 1 volt was
one graduation in one picture, does not mean it will be in another picture.
Also, there is no relation of amplitude between channels A and B.
This is a screenshot of xoscope, that I used. (got it from freshmeat.net)
It reads data from your soundcard, and displays it like this.
Of course you want to build in some protection when you connect your sound
card upto things as a test probe.
The green trace is a sine wave generated by the tach feedback coil
on an old dc brushtype floppy drive motor.
The red trace is same signal but amplified and clipped with some diodes.

The subject of my testing is a large transformer labed for 100v input,
one 20v, 1 amp, one 20v 7 amp, and one 20v, 8 amp outputs.
These outputs measure 20 vac RMS, when transformer is powered on 100v.
It powered a 1982 Color Scanning Sonar system, on a fishing vessel,
and was made by Furuno Electric Co. LTD., in Nishinomiya Japan.
To do these tests, I used:
A large variable transformer, which provided me
an output range of 0 to 210 volts AC;
A 125:5 current transformer;
A Digital Volt Meter, and a Digital Amp Meter;
Some clip leads;
Three resisters: one 2 ohm 50 watt, one 8 ohm 50 watt, and a portable electric
heater that was 10 ohms, and 1500 watts.
Not all devices were used in all measurements.
The blue trace is a 60 cycle hum, picked up by me holding onto the
other intput channel, but represents the phase of the AC power.
Using a current transformer, which is basically a big toriod through which
you run your large current carrying wire, I measured the current the transformer was drawing:(100vac input, drawing 35ma)

Same setup as above, but with 140vac input, drawing 840ma:
Here, I had to turn the gain way down, because the output current was
many times of that in the previous picture.
Notice how, during the top of the sine wave, the transformer saturates, and
comparatively massive ammounts of current flow.

This is the voltage-current curve for the transformer:
Volts is RMS AC input voltage, and Amps is the current that the
primary winding was drawing, according to my digital amp meter.

This is the same curve, but zoomed in on the first 300ma:

These pictures show the waveform on the 20v,1a output of the transformer,
under different conditions:
NOTE:In each case, I adjusted the scope to read at full scale, but in
reality, the higher input voltages did create proportionately
/proportionally [English buffs, which is it?] higher output
voltages. I did that since we are studying the shape, not size.
Also, I don't know why the tops of the waves are flat like they are,
but as you can see, they are same shape whether it's running on 30 or 100
volts. I suspect it's because I'm working at the end of a long power cord,
and have two computers, with switching power suplies, running.
Switching power suplies rectify the 120vac into some large filter capacitors,
so no current flows until each half cycle of the voltage exceeds that which
is stored in the filter capacitor.
Here we are feeding the transformer with 30 volts ac:

60 volts ac:

90 volts ac:

100 volts ac:

136 volts ac, about 250ma:

140 volts ac, drawing 1 amp:

144 volts ac, drawing 4 amps:

Below are three temp pictures. They were the first three I captured,
and were later re-done much better.
Normal output of transformer:

Output when transformer is slightly saturated:

Output when transformer is strongly saturated:
