Operation of a Transformer

Physics: AQA A Level, topic 7.5.8

Transformers

Transformers can be used to convert an alternating current from one voltage to another.

Transforming voltage

The output voltage of a transformer can be less than, greater than, or equal to the input voltage.
This depends on the ratio of the number of loops in their coil.

Types of transformers

There are two classes of transformers:
Step-up transformers increase voltage.
Step-down transformers decrease voltage.

Transformer equation

Assuming that resistance is negligible, the electrical power output of a transformer equals its input.
$P={I_p}{V_p}={I_s}{V_s}$
We can combine this with the transformer equation ( ${N_p}{N_s}={V_p}{V_s}$ ) to get:
$\frac{{N_s}}{{N_p}}=\frac{{V_s}}{{V_p}}$

Efficiency of a Transformer

Modern transformers are very efficient. They waste little energy as heat because of improvements in design over time.

Eddy currents

The core is made of iron, which is a magnetic metal.
As the magnetic flux in the core changes, the free electrons in the iron experience a force which causes them to move.
The moving electrons mean that a current has been induced in the core.
These currents are known as “eddy currents” and cause the core to heat up.

Reducing eddy currents

Eddy currents can be reduced by forming the core out of layers of iron glued together with an insulator.
The magnetic properties are not severely reduced but the resistance (and so current in) the core is dramatically reduced.
This process is known as “laminating the core”.

Examples of other losses

Energy can still be lost by the changing magnetic field, causing the layers of iron to vibrate.
The wire forming the coils has resistance, so will heat up when a current flows.
Not all of the flux may pass from the primary to the secondary coil.

Transmission of Electrical Power

Transformers are used to either step-up an a.c. potential difference or to step it down. An important application is in mains transmission via the National Grid.

National Grid

The National Grid produces a.c. in power stations.
Typically this is around 15 kV.
The step-up transformer steps the p.d. up to an RMS (root mean square - a type of average) amplitude of 330 kV.
The p.d. is then stepped back down so that consumers can apply it more safely (and at a higher current).

Transformer power equation

Since the input power = output power for a 100% efficient transformer:
$V_{in}I_{in} = V_{out}I_{out}$
$I_{out}=\frac{V_{in}}{V_{out}}I_{in}$
If the output transformer has more turns on it than the input transformer, causing $V_{out} > V_{in}$ , then the output current is less than the input current.

Reducing transmission losses

A lower current through the transmission cables means less energy is wasted heating the surroundings.
This is because the heating loss per metre of cable = I²R, where R is the resistance of 1 metre of cable.

Test yourself on Operation of a Transformer

What is the equation for the power of a transformer?
Formation of Eddy Current in Transformers
Which of these is NOT a reason for energy losses in transformers?
Explain how Eddy currents can be reduced in the core of a transformer.
Transformers in the National Grid

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