---
title: "Copper saving in auto-transformer"
subject: "Electrical Machines"
chapter: 2
key: "semester_4/electrical_machines:autotransformer-copper-saving"
source: https://www.bctengineer.com/q/semester_4/electrical_machines/autotransformer-copper-saving
site: BCT Engineering
---

# Copper saving in auto-transformer

Electrical Machines · Chapter 2: Transformer

- Asked in: 2070 Bhadra, 4 marks
- Video: [Saving of copper in an autotransformer](https://www.youtube.com/watch?v=hivePSSkhbU) — Dr.Jayaudhaya ,Simple and Easy Way
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines/autotransformer-copper-saving
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-2

## Question

Derive an expression for Cu saving in an auto-transformer.

## Short answer

With ratio K = N2/N1 < 1, the autotransformer copper weight is proportional to 2N1I1(1‑K), compared to 2N1I1 for a two‑winding transformer. The saving is K times the two‑winding copper, i.e., copper saved = K·W2w.

## Answer

Consider a single-phase autotransformer with $N_1$ turns across the primary and $N_2$ turns across the secondary ($N_2 < N_1$), with
$$
K = \frac{N_2}{N_1} = \frac{V_2}{V_1} = \frac{I_1}{I_2}.
$$

```text
 I1 o-->---+        section AB: (N1-N2) turns, current I1
           |        section BC: N2 turns, current (I2 - I1)
           +---o V2, I2 to load
           |
 o---------+---o
```

Copper weight is proportional to the length of conductor times its cross-section, which is proportional to turns × current. Hence:

**Autotransformer**

$$
\begin{aligned}
W_{auto} &\propto (N_1 - N_2)I_1 + N_2(I_2 - I_1) \\
&= N_1I_1 - 2N_2I_1 + N_2I_2
\end{aligned}
$$

With $N_2I_2 = N_1I_1$ and $N_2I_1 = KN_1I_1$:

$$
W_{auto} \propto 2N_1I_1 - 2KN_1I_1 = 2N_1I_1(1 - K)
$$

**Equivalent two-winding transformer**

$$
W_{2w} \propto N_1I_1 + N_2I_2 = 2N_1I_1
$$

**Ratio and saving**

$$
\frac{W_{auto}}{W_{2w}} = 1 - K
$$

$$
\boxed{\text{Saving in copper} = W_{2w} - W_{auto} = K\,W_{2w}}
$$

The saving is a fraction $K$ of the copper of the two-winding transformer. It is large when $K$ is near 1 and small when $K$ is small.

## Check yourself

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

1. On what quantity is the copper weight of a winding section taken proportional to?
   A. Voltage multiplied by turns
   B. Turns multiplied by current
   C. Current squared
   D. Turns divided by current
   Answer: B. Conductor length goes with turns and cross-section with current. (Key point: Copper weight basis)

2. Which pair correctly gives the sections of the autotransformer winding?
   A. (N1 - N2) turns carrying I1 and N2 turns carrying I2 - I1
   B. N1 turns carrying I1 and N2 turns carrying I2
   C. N1 - N2 turns carrying I2 and N2 turns carrying I1
   D. N2 turns carrying I1 and N1 turns carrying I2 - I1
   Answer: A. Section AB has N1 - N2 turns with the input current, and the common section BC carries the difference. (Key point: Auto winding sections)

3. What is the saving in copper?
   A. (1 - K) W_2w
   B. W_2w / K
   C. K W_2w
   D. 2K W_2w
   Answer: C. W_auto/W_2w = 1 - K, so the saving is K W_2w, large when K is near 1. (Key point: Final result)

## Related in Electrical Machines

- [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_i%3Aautotransformer-copper-saving) — Electrical Machines I, chapter 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

## Related in other subjects

- [Autotransformer working and Cu saving](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Aautotransformer-principle-cu-saving) — Electrical Machine, 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×