---
title: "Autotransformer working and Cu saving"
subject: "Electrical Machine"
chapter: 2
key: "semester_4/electrical_machine:autotransformer-principle-cu-saving"
source: https://www.bctengineer.com/q/semester_4/electrical_machine/autotransformer-principle-cu-saving
site: BCT Engineering
---

# Autotransformer working and Cu saving

Electrical Machine · Chapter 2: Transformer

- Asked in: 2073 Magh, 8 marks
- Video: [15 Copper Saving in Aurotransformer Compare with Two Winding Transformer - Derivation and Equation](https://www.youtube.com/watch?v=ZlHx1DKC5ME) — SP Engg. ACADEMY
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machine/autotransformer-principle-cu-saving
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-2

## Question

Explain working principle of an auto-transformer. Derive an expression for Cu saving in an auto-transformer.

## Short answer

A single winding with a common section carries only the difference current I₂−I₁. Copper weight: Wₐ ∝ (N₁−N₂)I₁ + N₂(I₂−I₁) = 2N₁I₁(1−K). Two-winding transformer requires 2N₁I₁. Saving = K·Wₜ, a fraction K of the copper is saved.

## Answer

An **autotransformer** has only one winding. A part of it is common to both the input and the output circuits. Power passes from input to output partly by conduction (direct electrical connection) and partly by transformer action.

#### Working principle
```text
 I1 -->  A o---------+---------o  (input)
                     |
             N1-N2   |
             turns   | I1
                 B o-+-----+---o  (output tap)
             N2      |     | I2
             turns   |     v
                 C o-+---------o  (common)
          V1 across AC, V2 across BC
```
- The supply V1 is applied across the full winding AC (N1 turns). The alternating flux in the core induces the same emf per turn all along the winding.
- The output is taken between a tap B and the common terminal C (N2 turns), so V2/V1 = N2/N1 = K.
- By ampere-turn balance, I1/I2 = N2/N1 = K.
- For a step-down unit, the section AB carries I1; the common section BC carries only (I2 − I1), the difference, which is why it can use thinner copper.

#### Copper saving
Weight of copper ∝ turns × current.
```text
Auto:      Wa ∝ (N1 − N2) I1 + N2 (I2 − I1)
                = N1 I1 + N2 I2 − 2 N2 I1
Two-wdg:   Wt ∝ N1 I1 + N2 I2
Using N1 I1 = N2 I2:
           Wa ∝ 2 N1 I1 (1 − K),   Wt ∝ 2 N1 I1
           Wa / Wt = 1 − K
```
**Saving of copper = Wt − Wa = K · Wt**, i.e. a fraction K of the copper of an equivalent two-winding transformer. For K = 0.5 the saving is 50 %; for K = 0.9 it is 90 %.

**Advantages:** less copper, smaller size, lower losses, better efficiency and regulation. **Disadvantage:** no electrical isolation, so a fault on the high-voltage side can reach the low-voltage side. It is used for starting induction motors, voltage regulators (variacs), and joining systems of nearly equal voltage.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How does an autotransformer pass power?
   A. Entirely by conduction
   B. Entirely by transformer action
   C. Partly by conduction and partly by transformer action
   D. By capacitive coupling
   Answer: C. Part of the winding is common, so some power is conducted directly. (Key point: Power transfer)

2. With input across N1 turns and output across N2 turns, V2/V1 = ?
   A. 1 - K
   B. N1 N2
   C. N1/N2
   D. N2/N1 = K
   Answer: D. Emf per turn is equal along the winding. (Key point: Ratio)

3. What fraction of a two-winding transformer's copper is saved?
   A. K^2
   B. K
   C. 1/K
   D. 1 - K
   Answer: B. Wa/Wt = 1 - K, so saving = K Wt. (Key point: Copper saving)

4. What is the main disadvantage?
   A. Higher copper weight
   B. Larger size
   C. Poor regulation
   D. No electrical isolation between input and output
   Answer: D. A fault on the high-voltage side can reach the low-voltage side. (Key point: Disadvantage)

## Related in Electrical Machine

- [Auto transformer merits and Cu saving](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aautotransformer-merits-copper-saving) — Electrical Machines, chapter 2
- [Copper saving in auto-transformer](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aautotransformer-copper-saving) — Electrical Machines, chapter 2
- [Copper saving in auto transformer](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aautotransformer-copper-saving) — Electrical Machines I, chapter 2
- [Copper saving in an autotransformer](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Aautotransformer-copper-saving) — Electrical Machine, chapter 2, asked 2×
- [CT secondary open; auto transformer economy](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Act-open-autotransformer-economical) — Electrical Machines, chapter 2