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

4.5.6 The Transformer

Objective

Explain the principle of operation of a simple iron‑cored transformer and describe its construction, performance relationships, real‑world uses and safety considerations (Cambridge IGCSE Physics 0625).

1. What is a Transformer?

• A static electrical device that transfers electrical energy between two or more circuits by electromagnetic induction.
• It changes the voltage level (step‑up or step‑down) while the frequency of the supplied AC remains unchanged.

2. Basic Construction

• Iron core – provides a low‑reluctance path for the magnetic flux.
  It is built from thin, insulated laminations; the insulation breaks up circulating eddy currents, thereby reducing core (iron) losses and keeping the transformer cooler.
• Primary winding – insulated copper wire that is connected to the input (source) voltage.
• Secondary winding – insulated copper wire in which the transformed voltage is induced.

3. Principle of Operation

When an alternating current flows in the primary winding it creates a **time‑varying magnetic flux Φ** in the core. By Faraday’s law a changing flux that links a coil induces an electromotive force (emf) in that coil.

For a coil of N turns:

Because the same core flux links both windings, the induced emfs are

Dividing the two equations gives the **turns‑ratio relationship**:

From this we can define the two practical cases:

• If \(N_s > N_p\) the transformer is a step‑up (output voltage higher than input).
• If \(N_s < N_p\) the transformer is a step‑down (output voltage lower than input).

4. Ideal‑Transformer Equations

• Voltage ratio \(\displaystyle \frac{V_s}{V_p}= \frac{N_s}{N_p}\)
• Current ratio \(\displaystyle \frac{I_s}{I_p}= \frac{N_p}{N_s}\)
• Power conservation (ideal) \(V_p I_p = V_s I_s\) (assumes no losses)

5. Example Calculation – Step‑down Transformer

Given:

• Primary turns \(N_p = 500\)
• Secondary turns \(N_s = 200\)
• Applied primary rms voltage \(V_p = 240\ \text{V}\)

1. Secondary voltage \[ V_s = V_p\frac{N_s}{N_p}=240\ \text{V}\times\frac{200}{500}=96\ \text{V (rms)} \]
2. If the secondary supplies a load drawing \(I_s = 2\ \text{A}\), the primary current is \[ I_p = I_s\frac{N_s}{N_p}=2\ \text{A}\times\frac{200}{500}=0.8\ \text{A} \]
3. Apparent power (ideal) \[ P_{\text{in}} = V_p I_p = 240\ \text{V}\times0.8\ \text{A}=192\ \text{W} \] \[ P_{\text{out}} = V_s I_s = 96\ \text{V}\times2\ \text{A}=192\ \text{W} \] (Both are equal because the transformer is assumed ideal.)

6. Real‑World Losses

Quantitative illustration: A 100 W transformer with a total loss of 3 % delivers

7. Voltage Regulation (Effect of Load)

When a load is connected, the secondary voltage falls slightly because of winding resistance and leakage flux. Regulation is defined as

Worked example: A transformer has \(V_{\text{no‑load}} = 240\ \text{V}\) and \(V_{\text{full‑load}} = 230\ \text{V}\). \[ \text{Regulation} = \frac{240-230}{230}\times100\% \approx 4.3\% \] Thus the voltage drops by about 4 % under full load.

8. Typical Applications (Why the Transformer is Used)

9. Safety Notes

10. Simple Demonstration Experiment – “Induction in Action”

1. Equipment: function generator (or low‑voltage AC source), two insulated copper coils (~50 turns each), digital voltmeter or galvanometer, wooden base, connecting leads.
2. Setup:
   • Connect the first coil (primary) to the function generator.
   • Place the second coil (secondary) close to, but not electrically connected with, the primary.
   • Connect the voltmeter across the secondary coil.
3. Procedure:
   • Set the generator to a sinusoidal output of 50 Hz (or 60 Hz) and a low voltage (e.g., 5 V rms).
   • Record the secondary voltage – a small AC voltage will be induced.
   • Increase the number of turns on the secondary or move the coils closer together; note the increase in induced voltage, confirming the turns‑ratio relationship.
   • Reverse the secondary leads; the polarity of the induced voltage reverses, demonstrating Lenz’s law.
4. Data‑table template (students can copy into their notebook):

   Run	Primary voltage (V rms)	Primary turns (\(N_p\))	Secondary turns (\(N_s\))	Coil separation (cm)	Secondary voltage (V rms)
   1
   2
   3

5. Conclusion: The experiment shows that a changing magnetic flux produced by the primary induces an emf in the secondary, and that the magnitude of the induced emf is proportional to the number of turns – the fundamental principle of a transformer.

11. Summary Table – Ideal vs. Real Transformer

12. Key Points to Remember

• The alternating primary current creates a changing magnetic flux in the iron core.
• Both windings experience the same flux; the induced emf is proportional to the number of turns.
• Voltage transformation follows the turns‑ratio; current transformation follows the inverse of the turns‑ratio.
• In an ideal transformer, apparent power is conserved; real transformers lose a small fraction as heat (core + copper losses).
• The output frequency is the same as the input frequency.
• Safety: treat the primary as a live mains circuit, never touch the secondary while the primary is energized, and always disconnect before inspection.