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:
\[
\mathcal{E} = -N\frac{d\Phi}{dt}
\]
Because the same core flux links both windings, the induced emfs are
\[
\mathcal{E}p = -Np\frac{d\Phi}{dt}, \qquad
\mathcal{E}s = -Ns\frac{d\Phi}{dt}
\]
Dividing the two equations gives the turns‑ratio relationship:
\[
\frac{Vs}{Vp}= \frac{Ns}{Np}
\]
From this we can define the two practical cases:
- If \(Ns > Np\) the transformer is a step‑up (output voltage higher than input).
- If \(Ns < Np\) the transformer is a step‑down (output voltage lower than input).
4. Ideal‑Transformer Equations
- Voltage ratio \(\displaystyle \frac{Vs}{Vp}= \frac{Ns}{Np}\)
- Current ratio \(\displaystyle \frac{Is}{Ip}= \frac{Np}{Ns}\)
- Power conservation (ideal) \(Vp Ip = Vs Is\) (assumes no losses)
5. Example Calculation – Step‑down Transformer
Given:
- Primary turns \(N_p = 500\)
- Secondary turns \(N_s = 200\)
- Applied primary rms voltage \(V_p = 240\ \text{V}\)
- Secondary voltage
\[
Vs = Vp\frac{Ns}{Np}=240\ \text{V}\times\frac{200}{500}=96\ \text{V (rms)}
\]
- If the secondary supplies a load drawing \(I_s = 2\ \text{A}\), the primary current is
\[
Ip = Is\frac{Ns}{Np}=2\ \text{A}\times\frac{200}{500}=0.8\ \text{A}
\]
- Apparent power (ideal)
\[
P{\text{in}} = Vp I_p = 240\ \text{V}\times0.8\ \text{A}=192\ \text{W}
\]
\[
P{\text{out}} = Vs I_s = 96\ \text{V}\times2\ \text{A}=192\ \text{W}
\]
(Both are equal because the transformer is assumed ideal.)
6. Real‑World Losses
| Loss Type | Cause | Typical Effect on Performance |
|---|---|---|
| Core (iron) losses | Hysteresis + eddy currents (suppressed by laminated core) | Consumes a few % of input power; produces heat in the core. |
| Copper (I²R) losses | Resistance of the windings | Proportional to the square of the current; appears as heat in the windings. |
| Leakage flux | Flux that links only one winding | Reduces voltage regulation; limits the maximum transferable power. |
Quantitative illustration: A 100 W transformer with a total loss of 3 % delivers
\[
P_{\text{out}} = 100\ \text{W}\times(1-0.03)=97\ \text{W}
\]
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
\[
\text{Regulation (\%)} = \frac{V{\text{no‑load}}-V{\text{full‑load}}}{V_{\text{full‑load}}}\times 100\%
\]
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)
| Application | Purpose (why a transformer is needed) |
|---|---|
| Step‑up transformers in high‑voltage power transmission | Increase voltage to reduce I²R losses in long cables, allowing efficient bulk power transport. |
| Step‑down transformers in domestic lighting and appliances (e.g., 240 V → 12 V) | Provide safe low‑voltage supply for low‑power devices and LED lamps. |
| Power supplies for electronic devices (phone chargers, TV sets) | Convert mains voltage to a lower, regulated voltage suitable for sensitive electronics. |
| Isolation transformers in medical equipment | Separate the user‑accessible circuit from the mains for safety, preventing electric shock. |
9. Safety Notes
- Never touch the primary winding while the transformer is energized. The primary is usually connected to mains voltage, which is lethal.
- Never assume the secondary is safe. If the primary is still connected to a live source, a voltage is induced in the secondary and can cause shock.
- Insulated windings prevent accidental contact.
- Laminated cores keep eddy‑current heating low, reducing the risk of overheating.
- Always disconnect the supply and discharge any stored energy before inspecting or modifying a transformer.
10. Simple Demonstration Experiment – “Induction in Action”
- Equipment: function generator (or low‑voltage AC source), two insulated copper coils (~50 turns each), digital voltmeter or galvanometer, wooden base, connecting leads.
- 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.
- 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.
- 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 - 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
| Parameter | Ideal Transformer | Real Transformer |
|---|---|---|
| Voltage ratio | \(\displaystyle \frac{Vs}{Vp}= \frac{Ns}{Np}\) | Same, but small deviation due to regulation and losses. |
| Current ratio | \(\displaystyle \frac{Is}{Ip}= \frac{Np}{Ns}\) | Same, plus extra current to supply copper losses. |
| Power | \(Vp Ip = Vs Is\) (100 % efficient) | Input power > output power; difference appears as heat (core + copper losses). |
| Efficiency | 100 % | Typically 95 %–99 % (depends on size, frequency, core material). |
| Frequency | Unchanged (same as supply) | Unchanged – the transformer does not alter frequency. |
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.