Once you convince the cover to come off, here is what you find inside.

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Under the cover

This transformer came with a rechargeable electric screwdriver. This particular transformer is rated at 3 volts and 240 milliamps. 

What you can see here are two windings. The purpose of a transformer is to convert one AC voltage to another AC voltage. In this case the transformer converts the normal 120 volt AC current in your house down to three volts. The 120 volts comes in on the primary winding on the left. Running down the middle of that winding (as well as around the outside) is an iron core. The AC current in the primary winding creates an alternating magnetic field in the iron just as it would in an electromagnet. The other winding, known as the secondary winding wraps around the same iron core. In the secondary winding the magnetic field in the core creates current. The voltage in the secondary is controlled by the ratio of the number of turns in the two windings. So if the primary and secondary windings have the same number of turns, the primary and secondary voltage will be the same. If the secondary winding has half as many turns as the primary then the voltage in the secondary will be half that of the voltage in the primary. You can see in the following figure that the primary in this particular transformer uses very fine wire while the secondary uses much thicker wire. To drop down to 3 volts, there needs to be 40 times more turns in the primary than in the secondary.