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T-10: Auto-Transformer

Section: A | Priority: 🟡 MEDIUM | Exam Frequency: 3/7 years Sources: Theraja Ch-32 (Art. 32.37–32.40), VK Mehta Ch-7 (Art. 7.25–7.27), Slides L-11 S32

Why This Topic Matters

The auto-transformer appeared in 3/7 papers (2020 three times). When it appears, it carries 3-4 marks per sub-question. The three standard question types are: (1) compare with 2-winding transformer, (2) prove copper saving = $(1-K)$, (3) list applications. The 2020 paper devoted 10 marks to auto-transformers alone.

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📝 Key Definitions

Auto-transformer: "An auto-transformer is a transformer with one winding only, part of the winding being common to both primary and secondary. Obviously, in an auto-transformer, the primary and secondary are not electrically isolated from each other as is the case with a 2-winding transformer. However, its theory and operation are similar to those of a two-winding transformer." — VK Mehta, Art. 7.25

Transformation ratio ($K$): "$K=V_2/V_1=N_2/N_1$. For step-down: $K<1$. The closer $K$ is to 1, the greater the copper saving." — VK Mehta

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How an Auto-Transformer Works

In a regular 2-winding transformer, primary and secondary are electrically isolated. In an auto-transformer, there is no isolation. The secondary is part of the primary winding.

Step-down auto-transformer: The full winding ($N_1$ turns) connects to the supply. A tap at $N_2$ turns provides the output. Current in the common section is $(I_2-I_1)$, which is smaller than $I_2$.

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Comparison with Two-Winding Transformer

Feature	Two-Winding	Auto-Transformer
Windings	Two separate, isolated	Single winding with tap
Electrical isolation	Yes	No
Copper required	More	Less (saving = $1-K$)
Efficiency	Slightly lower	Higher (direct conduction)
Size and weight	Larger	Smaller, lighter
Cost	Higher	Lower
Voltage ratio	Any ratio practical	Best for close ratios ($K\approx 1$)
Short-circuit current	Limited by leakage	Higher (less impedance)

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🏆 Golden Questions (Past Exam Archive)

🎯 Q1: Compare two-winding transformer and auto-transformer.

Appeared: 2020 Q2(a) — 3 marks

Full Answer:

Feature	Two-Winding Transformer	Auto-Transformer
Construction	Two separate, electrically isolated windings wound on a common core	Single winding with a tapping point, part common to both primary and secondary
Electrical isolation	Complete galvanic isolation between primary and secondary	No isolation. Primary and secondary are electrically connected. A fault on one side affects the other.
Copper requirement	Higher. Both windings need full copper for their respective currents.	Lower. Copper saving = $(1-K)$ fraction. For close ratios ($K\approx 1$), the saving is huge.
Efficiency	Slightly lower. All power transfers magnetically.	Higher. Part of the power transfers by direct electrical conduction (not through the magnetic field), reducing losses.
Size and weight	Larger (more copper, more core)	Smaller and lighter for the same VA rating
Cost	Higher	Lower
Suitable voltage ratio	Any ratio, including very high step-up/step-down	Best for close ratios ($K>0.5$). At extreme ratios, the lack of isolation becomes a safety concern.
Short-circuit current	Limited by leakage impedance	Higher than a 2-winding transformer (less leakage). Protection must be more robust.
Applications	Power transmission (isolation needed), distribution	Motor starting (reduced voltage), variacs, inter-ties between close-voltage power systems

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🎯 Q2: Prove: copper saved in auto-transformer = $(1-K)$ times that of an ordinary transformer.

Appeared: 2020 Q2(b), 2020 Q3(b) — 4 marks

Full Answer:

For a two-winding transformer of rated $S=VI$: copper is proportional to total ampere-turns in both windings.

$$W_{\text{2-winding}}\propto N_1{I}_1+N_2{I}_2$$

Since $N_1{I}_1=N_2{I}_2$ (approximately):

$$W_{\text{2-winding}}\propto 2N_1{I}_1$$

For an auto-transformer with step-down ratio $K=N_2/N_1<1$:

• Series section ($N_1-N_2$ turns) carries current $I_1$
• Common section ($N_2$ turns) carries current $(I_2-I_1)$

Copper in auto-transformer:

$$W_{\text{auto}}\propto (N_1-N_2)I_1+N_2(I_2-I_1)$$

Since $N_1{I}_1=N_2{I}_2$: we can write $N_2{I}_2=N_1{I}_1$

$$W_{\text{auto}}\propto N_1{I}_1-N_2{I}_1+N_2{I}_2-N_2{I}_1=N_1{I}_1-2N_2{I}_1+N_1{I}_1=2I_1(N_1-N_2)$$

Ratio:

$$\frac{W_{\text{auto}}}{W_{\text{2-winding}}}=\frac{2I_1(N_1-N_2)}{2N_1{I}_1}=1-\frac{N_2}{N_1}=1-K$$

Therefore: Copper in auto-transformer = $(1-K)$ × copper in ordinary transformer.

$$\boxed{\text{Copper saving}=K\times W_{\text{ordinary}}}$$

Example: For $K=0.9$ (10% step-down): auto-transformer uses only $(1-0.9)=10\%$ of the copper. Saves 90%. For $K=0.5$ (50% step-down): saves only 50%.

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🎯 Q3: Fields of application of auto-transformer.

Appeared: 2020 Q4(a) — 3 marks

Full Answer:

1. Starting of induction motors (auto-transformer starter): Provides reduced voltage during starting to limit starting current, then switches to full voltage at running speed.
2. Laboratory variacs (variable AC supply): A continuously variable auto-transformer provides any voltage from 0 to rated (and often above rated) for testing.
3. Power transmission inter-ties: Close-voltage-ratio interconnections between two power systems (e.g., 400 kV / 345 kV). The small voltage difference means large copper savings.
4. Railway traction: Voltage boosters along the track (25 kV / 12.5 kV).
5. Voltage stabilizers: Automatic voltage regulators for consumer supply.
6. Fluorescent lamp ballasts and dimmers: Voltage adjustment for lighting circuits.

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⚡ Exam Tips & Common Mistakes

1. No electrical isolation. This is the main disadvantage.
2. Copper saving = $K$, not $(1-K)$. The auto-transformer USES $(1-K)$ fraction of copper. It SAVES $K$ fraction.
3. Best for close ratios. When $K\approx 1$, savings are enormous.

🔗 Related Topics

• T-01: Fundamentals — Basic transformer principle
• T-11: Miscellaneous — Other special transformer topics

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