4.5.6 The Transformer

A transformer is a device that changes the voltage of an alternating current (AC) supply. It does this by using electromagnetic induction. Transformers are essential for efficient transmission of electrical power over long distances.

Key Components

A transformer has two main parts: the primary coil and the secondary coil. These coils are wound around a common iron core.

The primary coil is the coil connected to the input AC voltage source. The secondary coil is the coil from which the transformed AC voltage is output.

Transformers can be classified into two types based on their effect on voltage:

• Step-up transformer: Increases the voltage.
• Step-down transformer: Decreases the voltage.

How a Transformer Works

When an alternating current flows through the primary coil, it creates a changing magnetic field in the iron core. This changing magnetic field then induces an electromotive force (EMF), or voltage, in the secondary coil. The ratio of the number of turns in the primary coil (N_p) to the number of turns in the secondary coil (N_s) determines whether the transformer steps up or steps down the voltage.

Step-Up Transformers

A step-up transformer has more turns in the secondary coil than in the primary coil (N_s > N_p). This results in an increase in voltage.

The relationship between the primary voltage (V_p) and the secondary voltage (V_s) in an ideal step-up transformer is given by:

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

Since N_s > N_p, the ratio $\frac{N_s}{N_p}$ is greater than 1, and therefore V_s > V_p.

Step-Down Transformers

A step-down transformer has fewer turns in the secondary coil than in the primary coil (N_s < N_p). This results in a decrease in voltage.

The relationship between the primary voltage (V_p) and the secondary voltage (V_s) in an ideal step-down transformer is given by:

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

Since N_s < N_p, the ratio $\frac{N_s}{N_p}$ is less than 1, and therefore V_s < V_p.

Transformer Efficiency

Real transformers are not perfectly efficient. Some energy is lost due to factors such as:

• Hysteresis loss: Energy lost due to the magnetization and demagnetization of the iron core.
• Eddy current loss: Induced currents within the iron core that cause heat loss.
• Copper loss: Energy lost as heat due to the resistance of the coil windings.

Transformer efficiency is the ratio of the output power to the input power, expressed as a percentage.

Transformer Specifications

Transformers are often specified with their turns ratio and power rating. For example, a transformer might be rated as 1000V to 100V, indicating a step-down transformer with a turns ratio of 10:1. The power rating indicates the maximum power the transformer can handle.

Table Summary

Transformer Type	Turns Ratio (Ns/Np)	Voltage Change	Typical Use
Step-Up	> 1	Increases Voltage	Power Transmission (long distances)
Step-Down	< 1	Decreases Voltage	Household Appliances, Local Power Distribution