Tapped transformer windings and how they are referenced to ground seems to cause a lot of confusion.

I sometimes try to the use the battery arrangement mentioned above to start the explanation, as many people seem to be able to visualize this more easily with the simple one-way flow of direct current.

Take those two 1.5-volt cells and wire them in series. You now have 3 volts between the outer ends, and 1.5 volts between either end and the center tap.

Nothing you do with a ground connection will change that, but what it does do is affect the voltage between each of those three legs and ground. For the following, let's call the free negative end X, the free positive end Y, and the center tap Z.

If you took a ground rod and connected it to X, then you have referenced the negative end of the battery to ground. Point X will obviously then be at zero volts, while Y will now be at +3 volts with respect to ground. Because Z is the center-tap between the two cells, it will be +1.5V with respect to ground.

Now take the ground connection off of X and move it to Y. The positive end of the battery is now at earth potential, so X will be at -3 volts and Z will be at -1.5V with respect to ground.

Note that in in both cases we still have 1.5V between X and Z, 1.5V between Y and Z, and 3V between X and Y. All that has changed is which point is the ground reference.

Now let's move the ground connection to Z, the center-tap. X-to-Z is still 1.5V, Y-to-Z is also still 1.5V, and X-to-Y remains at 3V. This time, however, because the center-tap is grounded, X is at -1.5V with respect to earth while Y is at +1.5V.

Now move from two simple cells to the two halves of transformer winding, and you get a similar arrangement, only this time we have alternating current so the polarities are constantly changing. With the center-tap grounded, the voltages on each end are 180-degrees out of phase, so when one hot leg is positive (with respect to ground) the other is negative, and vice versa (as Virgil put it "Spin the batteries around" [Linked Image]). The current is changing direction every 120th of a second, but the polarities at the opposite ends of the winding will always be opposite. That's why you get 120V from hot to neutral/ground, and 240V between hot legs.

If you took that transformer secondary and grounded one end instead of the center tap, then you would have the hot leg running from the center tap at 120V and the other hot leg at a full 240V to ground. But because the ground refernce is now at one end of the winding, the voltages on those hot legs will be in phase, so there would be only 120V between them