Transformer

Transformer diagram

Fig. 1: The green dotted line around the iron core shows how the alternating magnetic field is transported from the primary coil to the secondary coil. Wikimedia, CC-BY-SA 3.0

There are three main parts that make up all transformers:

• The primary coil - this is connected to the first alternating current (AC) circuit and the voltage across it is equal to the incoming voltage from the circuit. This voltage is called \(V_p\), with the subscript referring to 'primary'.
• The secondary coil - this is connected to the second AC circuit and it provides the voltage to the second circuit. This voltage is called \(V_s\) , with the subscript referring to 'secondary'.
• The iron core - this links the two coils, which are wrapped around opposite sides. There is no electrical connection between the two coils, they are only joined by the iron core.

How does a transformer work?

The circuit must have alternating current flowing through it. The reason for this can be understood by considering how a transformer functions in steps:

1. The primary coil has the alternating current from the original circuit running through it. The coil is a metal so it becomes an electromagnet and produces an alternating magnetic field. An alternating magnetic field constantly changes direction.
2. The changing magnetic field is carried around the iron core to the secondary coil, as can be seen in the figure above.
3. When the alternating magnetic field reaches the secondary coil, a current is induced in it as the coil acts as a conductor.

The above points show why direct current cannot be used in the first circuit. It will produce a magnetic field that is not alternating. As the magnetic field is not changing, no current and hence no voltage is induced in the secondary coil.

The dotted green lines in the diagram above represent the magnetic field lines running through the iron core.

The energy from the primary coil is transferred to the secondary coil by the magnetic field - there are no electrical connections. This means that the magnetic field must be able to be transferred very efficiently through the core.

For this to be the case, a magnetically "soft" material should be used, such as an alloy of iron with silicon. However, some of the initial energy is always lost in real-life situations due to the resistance in the wires and the iron core resisting the changing of the magnetic field.

Transformer formula

The voltage leaving the secondary coil to the external circuit is related to the ratio of the number of turns on the coils of the transformer. Using the symbols for the incoming and outgoing voltage as stated in the earlier diagram, a simple formula relates the number of turns on the two coils to the output voltage:

$\frac{V_p}{V_s}=\frac{N_p}{N_S}$$$\frac{N_p}{N_s}=\frac{V_p}{V_s}$$

\(N_p\) represents the number of turns on the primary coil and \(N_s\) the same for the secondary coil. The equation is very simple and is just saying that the ratio of the number of turns on the secondary coil to the number on the primary coil is equal to the ratio of the output voltage to the incoming voltage.

Types of transformer

There are two types of transformers; step-up and step-down transformers. The names give you a clue about what they do - step-up transformers increase the voltage from one alternating circuit to the next whereas step-down transformers decrease the voltage.

Fig. 2: A step-up transformer found inside a microwave, Wikimedia CC SA 4.0.

For a transformer to increase (step-up) the voltage from the first circuit to the next, the number of turns on the secondary coil must be greater than that on the primary coil. Conversely, to decrease (step-down) the voltage from one circuit to the next, the turns on the secondary coil must be less than on the primary coil.

Examples of transformers

Transformers have many useful applications. Both step-up and step-down transformers are used in different situations.

The national grid

Electrical Power is supplied across the UK from power stations that send the electricity along high-voltage power cables.

The reason that high voltages are used to transmit electrical power is that it results in transmitting the same amount of power with a lower current flow through cables, which means that the energy lost as heat will be less. Energy is lost because the resistance in the wires is fighting against the current, and they become warm resulting in a loss of thermal energy to the surroundings.

A diagram showing the step-up and step-down transformers used in the power transmission system in North America. The UK system is very similar, operating at slightly different voltages.

High voltages are very dangerous and this is why the cables that transport the electrical power are high above the ground on pylons, as shown in the diagram above.

Power stations usually generate electricity at \(25\, \mathrm{kV}\) . This is increased by step-up transformers to a voltage of up to \(400\, \mathrm{kV}\) be transmitted along the pylons, and this voltage is then decreased to around \(240\, \mathrm{V}\) once the high-voltage cables reach our local sub-station.

Household appliances

Radios and other electronic devices will often run off the mains voltage supply. However, their operating voltage is normally quite a lot lower than \(240\, \mathrm{V}\)! There are step-down transformers built into devices to reduce the voltage to a suitable level. On the other hand, the operating voltage of microwave ovens is higher than the mains voltage for a household so they also have a step-up transformer inside to increase the voltage.