---
title: "Methods of three-phase connection"
subject: "Fundamental of Electrical and Electronics Engineering"
chapter: 3
key: "semester_1/fundamental_of_electrical_and_electronics_engineering:three-phase-connection-methods"
source: https://www.bctengineer.com/q/semester_1/fundamental_of_electrical_and_electronics_engineering/three-phase-connection-methods
site: BCT Engineering
---

# Methods of three-phase connection

Fundamental of Electrical and Electronics Engineering · Chapter 3: AC Circuit Analysis

- Asked in: 2081 Chaitra (new course), 4 marks
- Video: [Star and Delta Connection - Explained | TheElectricalGuy](https://www.youtube.com/watch?v=-PuVmOLr5K8) — Gaurav J - TheElectricalGuy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/fundamental_of_electrical_and_electronics_engineering/three-phase-connection-methods
- Whole chapter: https://www.bctengineer.com/md/semester_1/fundamental_of_electrical_and_electronics_engineering/chapter-3

## Question

Explain different methods of connection of three phase system with necessary diagrams.

## Short answer

Star connection: similar winding ends joined to neutral, V_L = √3 V_ph, I_L = I_ph, used for distribution. Delta connection: windings connected end-to-end forming closed loop, V_L = V_ph, I_L = √3 I_ph, used for motors and transmission.

## Answer

A three-phase system has three windings (phases R, Y, B) whose voltages are equal in magnitude and 120° apart. The six ends of the windings can be connected in two ways.

#### 1. Star (Y) connection

The similar ends (say the finishing ends) of the three windings are joined to a common point called the **star or neutral point (N)**. The other three ends are connected to the three lines. A fourth wire may be taken from N (3-phase 4-wire system).

```text
            R
            o  I_L
            |
           (Ph R)
            |
            N o------ neutral
          /   \
     (Ph B)   (Ph Y)
        /       \
       o         o
       B         Y
```

- Line voltage V_RY = V_R − V_Y (phasor difference).
- **V_L = √3 V_ph**, line voltage leads the phase voltage by 30°.
- **I_L = I_ph** (each line is in series with one phase).
- Gives two voltages: 400 V line-to-line and 230 V line-to-neutral (Nepal's LV supply), so it is used for distribution.

#### 2. Delta (Δ) or mesh connection

The finishing end of one winding is joined to the starting end of the next, forming a closed triangle. Lines are taken from the three junctions. There is no neutral.

```text
            R
            o
           / \
     Ph RB/   \Ph RY
         /     \
        o-------o
        B Ph YB  Y
```

- **V_L = V_ph** (each phase is directly between two lines).
- Line current I_R = I_RY − I_BR (phasor difference).
- **I_L = √3 I_ph**, line current lags the phase current by 30°.
- Used for motors and transmission where no neutral is needed.

#### Comparison

| Point | Star | Delta |
|---|---|---|
| Neutral | Available | Not available |
| Voltage | V_L = √3 V_ph | V_L = V_ph |
| Current | I_L = I_ph | I_L = √3 I_ph |
| Insulation per phase | Less (V_L/√3) | More (full V_L) |
| Use | Distribution, 3φ 4-wire | Motors, high current loads |

Power in both: P = √3 V_L I_L cos φ = 3 V_ph I_ph cos φ.

## Check yourself

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

1. In a star connection, what is joined to form the neutral?
   A. Similar ends of the three windings
   B. The start of one winding to the end of the next
   C. All three lines to ground
   D. Only two of the windings
   Answer: A. Star joins similar ends at point N; the other ends go to the lines. (Key point: Neutral point in star)

2. In a delta connection, the line current is:
   A. equal to the phase current
   B. sqrt3 times phase current, lagging by 30 degrees
   C. 1/sqrt3 times phase current
   D. sqrt3 times phase current, leading by 30 degrees
   Answer: B. I_R = I_RY - I_BR, giving I_L = sqrt3 I_ph lagging by 30 degrees. (Key point: Delta line current)

3. Why is star preferred for distribution?
   A. It has no neutral
   B. Phase current is sqrt3 times line current
   C. It provides a neutral, giving line-to-line and line-to-neutral voltages
   D. It uses more insulation per phase
   Answer: C. The neutral provides 400 V line-to-line and 230 V line-to-neutral. (Key point: Why star for distribution)

4. What is the total power in both star and delta connections?
   A. 3 V_L I_L cos phi
   B. sqrt3 V_ph I_ph cos phi
   C. V_L I_L cos phi
   D. sqrt3 V_L I_L cos phi
   Answer: D. P = sqrt3 V_L I_L cos phi = 3 V_ph I_ph cos phi in either connection. (Key point: Power in three-phase)

## Related in Fundamental of Electrical and Electronics Engineering

- [Three-phase connections and series RC phasor](https://www.bctengineer.com/question.md?key=semester_1%2Ffundamental_of_electrical_and_electronics_engineering%3Athree-phase-connections-series-rc) — Fundamental of Electrical and Electronics Engineering, chapter 3

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