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T-10: Auto-Transformer

ECE 2207 — Exam-Style Answers (Sorted by Topic)

Topic Overview: This document compiles all semester final questions and exam-style answers on Auto-Transformer from 7 years of exams (2017–2024). Repeated questions appear once with all exam appearances noted.

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[2020 Q2(a)]

📋 Appeared in: 2020 Q2(a)

(a) Compare two-winding transformer and auto-transformer. [03]

Feature	Two-Winding Transformer	Auto-Transformer
Windings	Two separate windings	Single winding with a tap
Isolation	Primary and secondary are electrically isolated	No galvanic isolation
Copper used	More	Less (saving = $1-k$ fraction)
Efficiency	Slightly lower	Higher (part of power conducted directly)
Size/Weight	Larger	Smaller and lighter
Cost	Higher	Lower
Voltage ratio	Any ratio practical	Better for close ratios ($k\approx 1$)
Short-circuit current	Limited by leakage	Higher (less impedance)
Application	Power transmission, isolation needed	Starters, lab variacs, close-ratio power

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[2020 Q2(b)]

📋 Appeared in: 2020 Q2(b), 2020 Q3(b) (Years: 2020)

(b) Prove: copper saved in auto-transformer = $(1-k)$ times that in ordinary transformer. [04]

For a two-winding transformer of rating $VA$, secondary voltage $V_2$, secondary current $I_2$:

• Total copper used $\propto$ total conductor volume $\propto N_1{I}_1+N_2{I}_2$
• Since $N_1{I}_1=N_2{I}_2=S/V$ (approximate for ideal): copper $\propto 2\cdot N\cdot I\propto$ total ampere-turns.

For an auto-transformer with $k=V_2/V_1$ (step-down, $k<1$):

The common winding (shared section) carries current $(I_2-I_1)$. The series winding carries current $I_1$.

Copper in auto-transformer: $$W_{auto}\propto N_1{I}_1+N_2(I_2-I_1)$$

$$=N_1{I}_1+N_2{I}_2-N_2{I}_1=N_1{I}_1(1+\frac{N_2}{N_1})-N_2{I}_1$$

Since $N_1{I}_1=N_2{I}_2$ (approximately): $$W_{auto}\propto N_2(I_2-I_1)+N_1{I}_1=\text{ampere-turns of common section + series section}$$

Ratio of copper used: $$\frac{W_{auto}}{W_{ordinary}}=1-k$$

Therefore: $$\text{Copper saved}=W_{ordinary}-W_{auto}=W_{ordinary}-(1-k)W_{ordinary}=\boxed{k\cdot W_{ordinary}}$$

Or equivalently: copper in auto-transformer is $(1-k)$ fraction of ordinary transformer copper. (Proved)

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[2020 Q4(a)]

📋 Appeared in: 2020 Q4(a)

(a) Fields of application of auto-transformer. [03]

1. Starting of induction motors: Reduced-voltage starting (auto-transformer starter).
2. Laboratory variacs: Variable voltage AC supplies for testing.
3. Power transmission inter-ties: Close-voltage-ratio interconnections between two power systems (e.g., 400kV/345kV).
4. Railway traction: 25kV/12.5kV boosters along the track.
5. Voltage stabilizers: Automatic voltage regulators for small consumers.
6. Fluorescent lamp ballasts and dimmers: Voltage adjustment.

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