Cambridge Syllabus Notes

4.5.6 The Transformer

🔌 Transformers are the unsung heroes of modern electricity, letting us safely step voltage up or down for everything from phone chargers to power plants.

What is a Transformer?

A simple iron‑cored transformer has two main parts:

Primary coil – the coil that receives the input AC voltage.
Secondary coil – the coil that delivers the transformed voltage.
Iron core – a piece of soft iron that concentrates the magnetic field produced by the primary coil.

Think of the iron core as a magnetic bridge that carries the “magnetic traffic” from the primary to the secondary, much like a road that lets cars move from one side of a city to the other.

Principle of Operation

The transformer works on two key ideas:

Electromagnetic induction – a changing current in the primary coil creates a changing magnetic flux in the core, which induces a voltage in the secondary coil.
Turns ratio – the number of turns in each coil determines how the voltage changes.

Mathematically, the relationship is:

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

Where:

$V_p$ = primary voltage
$V_s$ = secondary voltage
$N_p$ = number of turns in primary coil
$N_s$ = number of turns in secondary coil

Because power is (approximately) conserved in an ideal transformer, we also have:

$$P_p \approx P_s \;\;\;\;\text{or}\;\;\;\; V_p I_p \approx V_s I_s$$

From this we can deduce the current relationship:

$$\dfrac{I_p}{I_s} = \dfrac{N_s}{N_p}$$

Why the Iron Core Matters

The iron core keeps the magnetic field lines together, reducing the amount of magnetic flux that leaks into the surroundings. This makes the transformer more efficient and safer.

Exam Tip Box

📝 Remember:

Use the turns ratio formula to find unknown voltages or currents.
When the secondary has more turns than the primary, the voltage increases (step‑up transformer).
When the secondary has fewer turns, the voltage decreases (step‑down transformer).
Power conservation helps check your answers: $V_p I_p$ should equal $V_s I_s$ (ignoring losses).
Draw a quick sketch: label primary, secondary, core, and arrows for magnetic flux.

Quick Practice Problem

⚡ A transformer has 200 turns on the primary and 800 turns on the secondary. If the primary voltage is 120 V, what is the secondary voltage?

Solution: $$\dfrac{V_p}{V_s} = \dfrac{N_p}{N_s} \;\;\Rightarrow\;\; V_s = V_p \dfrac{N_s}{N_p} = 120 \times \dfrac{800}{200} = 480\text{ V}$$

Real‑World Example

📚 The mains supply in most homes is 230 V. To power a 12 V laptop charger, a step‑down transformer reduces the voltage from 230 V to 12 V, making it safe and efficient.

Summary Table

Parameter	Formula	Key Point
Voltage Ratio	$$\dfrac{V_p}{V_s} = \dfrac{N_p}{N_s}$$	More turns → higher voltage.
Current Ratio	$$\dfrac{I_p}{I_s} = \dfrac{N_s}{N_p}$$	More turns → lower current.
Power Conservation	$$V_p I_p \approx V_s I_s$$	Ideal transformer has no power loss.

Explain the principle of operation of a simple iron-cored transformer