---
title: "Transformer location for three villages (B)"
subject: "Transmission and Distribution System Design"
chapter: 7
key: "semester_8/transmission_and_distribution_system_design:three-villages-transformer-location-b"
source: https://www.bctengineer.com/q/semester_8/transmission_and_distribution_system_design/three-villages-transformer-location-b
site: BCT Engineering
---

# Transformer location for three villages (B)

Transmission and Distribution System Design · Chapter 7: Distribution System Design

- Asked in: 2067 Chaitra (old course), 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/transmission_and_distribution_system_design/three-villages-transformer-location-b
- Whole chapter: https://www.bctengineer.com/md/semester_8/transmission_and_distribution_system_design/chapter-7

## Question

Three villages A, B and C are situated at equal distance of 0.6 km and their respective loads are 40 kW, 40 kW and 60 kW. Find their distribution transformer location relative to the location of village B.

## Short answer

Transformer location determined by load centre: taking B as origin, coordinates (0.30 km, 0.223 km), distance 0.374 km at 36.6° from BA towards C.

## Answer

The distribution transformer should be located at the **load centre** (centre of gravity) so that the sum of load × distance, and hence LT drop and loss, is minimum.

Assumption: the villages are 0.6 km from each other, i.e. at the corners of an equilateral triangle of side 0.6 km. B is taken as the origin.

```text
              C (60 kW)
             /\
        0.6 /  \ 0.6
           / T  \
          /______\
   B (40 kW) 0.6  A (40 kW)
```

#### Coordinates (B at origin, BA along x-axis)
| Village | Load (kW) | x (km) | y (km) |
|---|---|---|---|
| B | 40 | 0 | 0 |
| A | 40 | 0.6 | 0 |
| C | 60 | 0.3 | 0.5196 |

#### Load centre
$$
\begin{aligned}
\bar x &= \frac{40(0)+40(0.6)+60(0.3)}{140} = \frac{42}{140} = 0.30\ \text{km}\\
\bar y &= \frac{60(0.5196)}{140} = 0.2227\ \text{km}\\
d_B &= \sqrt{0.30^2+0.2227^2} = 0.374\ \text{km}\\
\theta &= \tan^{-1}\frac{0.2227}{0.30} = 36.6^\circ
\end{aligned}
$$

Because A and B carry equal loads, the load centre lies on the perpendicular bisector of AB (x = 0.3 km), shifted towards C, the heaviest load.

#### Result
- The transformer is about **0.374 km from B**, at **36.6° from BA towards C** (0.30 km along BA and 0.223 km perpendicular towards C).
- Practically it is placed at an accessible point near this location; total load 140 kW suggests a standard 200 kVA transformer allowing for growth.

Note: if the villages were instead in a straight line A–B–C with 0.6 km spacing, the load centre would be $(−40\times0.6 + 60\times0.6)/140 = 0.086$ km from B towards C.

**Answer: Transformer at (0.30 km, 0.223 km) from B, i.e. 0.374 km from B at 36.6° to BA towards C.**

## Check yourself

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

1. The transformer is placed at the load centre because it:
   A. Makes distances to all villages equal
   B. Minimises sum of load x distance, reducing LT drop and loss
   C. Is at the middle of the triangle always
   D. Is nearest to the heaviest load
   Answer: B. Minimum load-moment gives least LT drop and loss. (Key point: Load centre idea)

2. Why does the load centre lie on the line x = 0.3 km?
   A. B and A carry equal loads, so it lies on the perpendicular bisector of BA
   B. C is on that line
   C. The total load is 140 kW
   D. The triangle has side 0.3 km
   Answer: A. Equal loads at B and A balance about the midpoint of BA, so x is 0.3 km. (Key point: Symmetry)

3. The load centre is shifted towards:
   A. B
   B. C, the heaviest load (60 kW)
   C. A
   D. Opposite C
   Answer: B. Weighted average moves towards the largest load C. (Key point: Direction of shift)

4. The transformer distance from B is about:
   A. 0.374 km
   B. 0.60 km
   C. 0.223 km
   D. 0.30 km
   Answer: A. d = sqrt(0.30^2 + 0.2227^2) = 0.374 km at 36.6° to BA. (Key point: Result)

## Close variants set in other exams

- [Transformer location for three villages (A)](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Athree-villages-transformer-location-a) — Transmission and Distribution System Design, chapter 7, asked 2×

## Related in Transmission and Distribution System Design

- [Capacitor size, feeder with three equal loads](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Acapacitor-size-equal-loads-ohms) — Transmission and Distribution System Design, chapter 7
- [Selecting distribution transformer size and location](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Atransformer-size-and-location) — Transmission and Distribution System Design, chapter 7, asked 2×