## Illustration 31.3: Transformers

Windings on transformer: Np = | Ns=

A transformer is connected to an outlet. The graph shows the input voltage (the voltage across the primary) and output voltage (the voltage across the secondary) as a function of time. Restart.

A transformer works by induction. A changing voltage in the primary coil (connected to the outlet) causes a changing current in the primary coil. The changing magnetic flux in the primary coil induces an emf (voltage) in the secondary coil. If you think about a coil of wire, the induced emf depends on the rate of change of the magnetic flux through the coil and the number of windings in the coil. Try changing the number of windings on the primary and secondary. How does the ratio of peak voltages depend on the windings? You should find that the ratio of the voltages is equal to the ratio of the coils. If the number of windings on the primary is greater than on the secondary, it is called a step-down transformer, but if the number of windings on the primary is smaller than on the secondary, it is a step-up transformer.

Both the step-up and step-down transformers conserve energy. For ideal transformers (no heat losses), energy conservation means that the average power (IrmsVrms) is the same in the primary and secondary. Since the ratio of the number of windings is equal to the ratio of the voltages, for a step-down transformer with 200 turns on the primary and 20 turns on the secondary, 2 A coming into the transformer would yield 20 A out of the secondary. Conversely, for a step-up transformer, less current would be available at the secondary.

The facts that the power is the same in the primary and secondary and that transformers are easy to construct (coils wound around iron cores) are the reasons we use alternating current (instead of DC). Power companies can deliver a large amount of power either with high voltages and low current or with low voltages and high current. For the same amount of power, the lower-current option is preferable because of resistive heat losses on power lines. Consider the following two ways to deliver power over a 10-Ω power line and notice that the power from the plant is the same in both cases.

1. V = 10,000 V at the power plant and 2 A through the line. The total power dissipated is given by I2R = 40 W (and the voltage drop between the power plant and the user is 20 V).
2. V = 1000 V at the power plant and 20 A through the line. In comparison, the total power dissipated is 4000 W (and the voltage drop is 200 V).

It is clearly better to choose the high voltage, low current route, and so power plants produce electricity at high voltages (around 20 kV). This is stepped up with transformers to a couple of hundred kV (e.g., 300,000 V) for cross-country transmission and then stepped back down in cities and at your house. It is not nearly as easy or as efficient to step up and down DC, which makes AC cheaper to transport over wires.

Illustration authored by Anne J. Cox.
Script authored by Morten Brydensholt and modified by Anne J. Cox.

Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.