7.5.8

# Operation of a Transformer

Test yourself

## 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.