17.2 Transformers

Transformers

One of the real-world applications of Faraday's Law is in a transformer .

Eskom generates electricity at around 22 000 V. When you plug in a toaster, the mains voltage is 220 V. A transformer is used to step-down the high voltage to the lower voltage that is used as mains voltage.

Transformer

A transformer is an electrical device that uses the principle of induction between the primary coil andthe secondary coil to either step-up or step-down the voltage.

The essential features of a transformer are two coils of wire, called the primary coil and the secondary coil, which are wound arounddifferent sections of the same iron core.

When an alternating voltage is applied to the primary coil it creates an alternating current in that coil, which induces analternating magnetic field in the iron core. The changing magnetic flux through the secondary coil induces an emf, which creates a current in this secondary coil.

The circuit symbol for a transformer is:

By choosing the number of coils in the secondary solenoid relative to the number of coils in the primary solenoid, we can choose how much bigger or smaller the induced secondary current is by comparison to the current in the primary solenoid (so by how much the current is stepped up or down.)

This ability to transform voltage and current levels according to a simple ratio, determinedby the ratio of input and output coil turns is a very useful property of transformers and accounts for the name. We can derive a mathematical relationship by using Faraday's law.

Assume that an alternating voltage $V_p$ is applied to the primary coil (which has $N_p$ turns) of a transformer. The current that results from this voltage generates a changing magnetic flux ${\phi }_p$ . We can then describe the emf in the primary coil by:

Similarly, for the secondary coil,

If we assume that the primary and secondary windings are perfectly coupled, then:

which means that:

A transformer designed to output more voltage than it takes in across the input coil is called a step-up transformer. A step-up transformer has more windings on the secondary coil thanon the primary coil. This means that:

Similarly, a transformer designed to output less than it takes in across the input coil is called a step-down transformer. A step-down transformer has more windings on the primary coil thanon the primary coil. This means that:

We use a step-up transformer to increase the voltage from the primary coil to the secondary coil. It is used at power stations to increase the voltage for the transmission lines. A step-down transformer decreases the voltage from the primary coil to the secondary coil. It is particularly used to decrease the voltage from the transmission lines to a voltage which can be used in factories and in homes.

Transformer technology has made long-range electric power distribution practical. Without the ability to efficiently stepvoltage up and down, it would be cost-prohibitive to construct power systems for anything but close-range (within a few kilometres) use.

As useful as transformers are, they only work with AC, not DC. This is because the phenomenon of mutual inductance relies on changing magnetic fields, and direct current (DC) can only produce steady magnetic fields, transformers simply will notwork with direct current.

Of course, direct current may be interrupted (pulsed) through the primary winding of a transformerto create a changing magnetic field (as is done in automotive ignition systems to produce high-voltage spark plug power from alow-voltage DC battery), but pulsed DC is not that different from AC. Perhaps more than any other reason, this is why AC finds suchwidespread application in power systems.

Real-world applications

Transformers are very important in the supply of electricity nationally. In order to reduce energy losses due to heating,electrical energy is transported from power stations along power lines at high voltage and low current. Transformers are used tostep the voltage up from the power station to the power lines, and step it down from the power lines to buildings where it is needed.

Transformers

1. Draw a sketch of the main features of a transformer
2. Use Faraday's Law to explain how a transformer works in words and pictures.
3. Use the equation for Faraday's Law to derive an expression involving the ratios of the voltages and the number of windings in the primary and secondary coils.
4. If we have $N_p$ = 100 and $N_s$ = 50, and we connect the primary winding to a 230 V, 50Hz supply, then calculate the voltage on the secondary winding.
5. State the difference between a step-up and a step-down transformer in both structure and function.
6. Give an example of the use of transformers.