Transformers

A transformer is an electrical equipment that is used for increasing or decreasing the voltage of an alternating current. Changing the voltage of an electrical current is important for transporting electricity because a higher voltage requires less current and hence less power loss. This will be further explored later on.

A transformer operates due to the following:

• There are 2 coils at a distance from one another; a primary coil and a secondary coil

• Alternating current flowing through the primary coil is continuously changing direction (as an alternating current does) and this results in a continuously changing magnetic flux which is fed through a soft iron core and into the secondary coil

• The secondary coil opposes this change in magnetic flux (according to Lenz’s law) by inducing an emf (Faraday’s law)

• Induced emf in the secondary coil produces an alternating current if the secondary coil is connected to an external closed circuit

There are 2 types of transformers; step-up and step-down. A step-up transformer increases the secondary emf compared to the primary and there are more turns of wire in the secondary than the primary. A step-down transformer decreases the secondary emf compared with primary and there are less turns of wire in the secondary than the primary.

Calculations

Power can be calculated by the relationship:

In an ideal transformer, the input power (power in primary coil) is equal to the output power (power in secondary coil); meaning the transformer has 100% efficiency. In some questions, the transformer won’t be an ideal and so you will be given its efficiency, which you can multiply by the input power, to calculate the output power.

Another relationship relevant to transformers is:

This states that the ratio of voltage in the primary coil to voltage in the secondary coil is equal to the ratio of number of turns in the primary coil to number of turns in the secondary coil. The equation can be rearranged to calculate any value, assuming the other three are provided.

The third relationship which is frequently used is:

This equation is used to find the power lost when transporting electricity through a transmission line. Here, I is the current in the secondary coil and R is the resistance of the transmission line.