Power transformersAny transformer used in the 60-Hz utility line, intended to provide a certain rms ac volt-age for the operation of electrical circuits, is a power transformer. Power transformersexist in sizes ranging from smaller than a tennis ball to as big as a room.At the generating plantThe largest transformers are employed right at the place where electricity is generated.Not surprisingly, high-energy power plants have bigger transformers that develophigher voltages than low-energy, local power plants. These transformers must be ableto handle not only huge voltages, but large currents as well. Their primaries and secon-daries must withstand a product EI of volt-amperes that is equal to the power P ulti-mately delivered by the transmission line.When electrical energy must be sent over long distances, extremely high voltagesare used. This is because, for a given amount of power ultimately dissipated by theloads, the current is lower when the voltage is higher. Lower current translates into re-duced loss in the transmission line.Recall the formula PEI, where P is the power in watts, E is the voltage in volts,and I is the current in amperes. If you can make the voltage 10 times larger, for a givenpower level, then the current is reduced to 1/10 as much. The ohmic losses in the wiresare proportional to the square of the current; remember that PI 2R, where P is thepower in watts, I is the current in amperes, and R is the resistance in ohms.Engineers can’t do much about the wire resistance or the power consumed by theloads, but they can adjust the voltage, and thereby the current. Increasing the voltage10 times will cut the current to 0.1 its previous value. This will render the I 2R loss (0.1)20.01 (1 percent!) as much as before.For this reason, regional power plants have massive transformers capable of gener-ating hundreds of thousands of volts. A few can produce 1,000,000 V rms. A transmis-sion line that carries this much voltage requires gigantic insulators, sometimes severalmeters long, and tall, sturdy towers.334 Transformers and impedance matching18-8Schematic symbols for autotransformers. At A, air coreand at B, ferromagnetic core. The unit at A steps downand the one at B steps up.