Transformers and transformer calculations


Transformers are devices used to increase or decrease the voltage of an electricity supply. Transformers are widely used in power stations.

Transformers are redesigned to be as efficient as possible (up to 99.99% efficient, to decrease energy losses)

Every transformer has three parts:

  1. A primary coil from where the incoming voltage (VP) is connected to the coil.
  2. A secondary coil which provides the voltage VS to the external circuit.
  3. An iron core which is a link between the two coils.


  • There is no electrical connection between the two coils. The coils are linked together only by the iron core.
  • The voltages are both alternating voltages.
  • A transformer does not change a.c to d.c or anything of that sort; it only has the task of changing the magnitudes (sizes) of an alternating voltage.
  • To step up (increase) the input voltage by a factor of 9 (for example) there must be 9 times as many turns on the secondary coil as on the primary coil. Comparing the number of turns on the two coils tells us how the voltage will be changed (whether it would be increased or decreased).
  • This brings us to the two types of transformers which either increase the voltage from the primary coil or decrease it.

Types of transformers

There are two types of transformers:

  1. A step up transformer: increases the voltage; so there are more turns on the secondary coil than on the primary coil.
  2. A step down transformer: reduces the voltage; so there are fewer turns on the secondary coil than on the primary coil

The ratio of the numbers of turns tells us the factor by which the voltage will be changed. Hence, we can write an equation known as the transformer equation to relate the two voltages:

<image for the transformer equation here>

VP and VS to the numbers of turns on each coil, NP and NS.

How transformers work

Transformers only work with alternating current (a.c.) and it makes use of electromagnetic induction.

Electromagnetic induction plays a very important role in the functioning of a transformer as the primary and secondary coils are only connected through an iron core. Let’s see how:

  1. The primary coil has alternating current flowing through it. It is thus an electromagnet, and produces an alternating magnetic field in the core.
  2. The core transports this alternating field around the secondary coil.
  3. Now, the secondary coil is a conductor in a changing magnetic field causing a current to be induced in the coil.

This is another important example of electromagnetic induction at work as the varying magnetic field of the primary coil cuts through the magnetic field of the secondary coil.

Points to note:

  • If the secondary coil has only a few turns, the e.m.f induced across it will be smaller and hence the current in the secondary coil will increase, decreasing the efficiency of the transformer.
  • Hence transformers are designed to produce higher voltages which can reduce energy losses by increasing the number of turns on the secondary coil.
  • The reason transformers only use alternating current and not direct current is that the magnetic field produced by the primary coil will be static (unchanging) which leads to no electromagnetic induction taking place and hence no voltage is induced.
  • Another point to note is that the only connection between the primary and secondary coils is the core that transfers the magnetic field. This is the reason why a soft magnetic material (an alloy of iron and silicon) is used for the core in order to increase the efficiency of the transformer.
  • However, even in a well designed transformer, some energy is lost because:
    • Of the resistance of wires
    • The core resists the flow of the charging magnetic field.

Calculating current

To transmit a certain amount of power, we can use a small current (I) if we transmit the power at a high voltage V

This creates the equation for electrical power:

<Equation to calculate power (P=Ivt) here>

Power lines and transformers

Ever wondered how the electricity reaches to your home? Here is the journey of electricity from a power station to your homes:

  • Power stations may be hundred kilometres or more from the places where the electricity is generated.
  • High voltage electricity leaves the power station. it is usually carried in cables called power lines slung high above the ground between tall pylons.
  • When the power lines approach the area where the power is to be used, they enter a local distribution centre.
  • Here the voltage is reduced to a less hazardous level, and the power is sent through more cables to local substations.
  • In the sub stations the transformers are used to reduce the voltage to the local supply voltage. (Typically 230V).
  • From the substation the electricity is distributed around the neighbouring houses.

Why use high voltages?

There is a good reason for high voltages. It means that the current flowing through the cables is relatively low and this wastes less energy.

When a current flows through a wire or cable, some of the energy it carry’s is lost because the cable’s resistance.

The resistance in the cables causes the cables to get warm.

Hence, a small current wastes less energy than a high current.

This is because power loses in cables are proportional to the square of the current flowing in the cables.

  • Double the current gives four times the losses
  • Three times the current gives nine times the loses, and so on

Energy saving

As seen before, the energy from power stations is transported at enormous voltages. This is because the higher the voltage, the lesser the current flowing, hence the lesser the energy losses.

The current flowing through the cables is a flow of coulombs of charge. At high voltages, we have fewer coulombs flowing (ignoring the fact that each coulomb carries more energy with it)

Thinking about power

If we work up to a reasonable approximation that each transformer is 100% efficient, we can work up to another useful equation which relates the primary and secondary voltages: VP and VS, to primary and secondary currents: IP and IS:



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