---
title: "Armature reaction at different load power factors"
subject: "Electric Machines II"
chapter: 1
key: "semester_5/electric_machines_ii:armature-reaction-power-factor-effect"
source: https://www.bctengineer.com/q/semester_5/electric_machines_ii/armature-reaction-power-factor-effect
site: BCT Engineering
---

# Armature reaction at different load power factors

Electric Machines II · Chapter 1: Three Phase Synchronous Generator

- Asked in: 2082 Bhadra (new course), 3 marks; 2081 Bhadra, 8 marks; 2079 Bhadra, 2+6 marks; 2078 Kartik, 7 marks; 2072 Chaitra, 6 marks; 2072 Kartik, 8 marks; 2071 Chaitra, 8 marks (asked 7 times)
- Video: [Armature Reaction of Alternators [Year - 3]](https://www.youtube.com/watch?v=8HFa_YjZIFc) — Mtutor & Mschool
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/electric_machines_ii/armature-reaction-power-factor-effect
- Whole chapter: https://www.bctengineer.com/md/semester_5/electric_machines_ii/chapter-1

## Question

What is meant by armature reaction in a synchronous generator? Explain the effect of armature reaction on the terminal voltage (emf) of an alternator at (i) unity power factor (resistive) load, (ii) lagging power factor (inductive) load and (iii) leading power factor (capacitive) load. Draw relevant phasor diagrams.

## Short answer

Armature reaction is the effect of stator current on the rotor field flux. At unity pf it is cross-magnetizing (slight voltage drop), at lagging pf demagnetizing (large drop, V<E), and at leading pf magnetizing (voltage rise, V>E). It is represented by reactance Xa in the equivalent circuit.

## Answer

**Armature reaction** is the effect of the magnetic field set up by the armature (stator) current on the main field flux produced by the rotor poles. When the alternator is loaded, the three-phase armature currents produce a rotating mmf that rotates at synchronous speed along with the rotor. This mmf distorts, weakens or strengthens the main flux depending on the **power factor of the load**, and so changes the terminal voltage.

In the equivalent circuit, armature reaction is represented by a fictitious reactance $X_a$; together with the leakage reactance $X_l$ it forms the synchronous reactance $X_s = X_a + X_l$, and
$$
\bar E = \bar V + \bar I (R_a + jX_s)
$$

#### (i) Unity power factor (resistive) load
- The armature current is in phase with the emf, so each conductor carries its maximum current at the instant it is under the centre of a pole (where its emf is maximum). The armature mmf is then at **90° (in quadrature)** to the main flux.
- The effect is **cross-magnetising**: flux is distorted (crowded at one pole tip, weakened at the other) but its average value changes little.
- The terminal voltage drops only slightly (mainly due to $IR_a$ and the small quadrature drop). $E$ is only a little greater than $V$.

```text
 (a) Unity pf load
                    E
                  / |
                /   |  j I Xs
              /     |
            O-------+  V
            O------->  I  (in phase with V)
```

#### (ii) Lagging power factor (inductive) load
- For zero pf lagging, the current lags the emf by 90°; armature flux acts **directly opposite** to the main flux along the pole axis.
- The effect is **demagnetising**; the resultant air-gap flux and generated voltage fall.
- For a practical lagging pf (e.g. 0.8) the effect is partly cross-magnetising and partly demagnetising.
- The terminal voltage falls considerably with load; $V < E$, and regulation is large and positive. More field current is needed to keep $V$ constant.

```text
 (b) Lagging pf load
                      E
                     /|
                   /  |  j I Xs
                 /    |
               O------+ V
                `-.
                   `-. I  (lags V by phi)
```

#### (iii) Leading power factor (capacitive) load
- For zero pf leading, the current leads the emf by 90°; the armature flux acts **along** the main flux.
- The effect is **magnetising** (strengthening); the air-gap flux increases.
- The terminal voltage rises with load; $V$ can be greater than $E$, so regulation can be negative. Less field current is needed.

```text
 (c) Leading pf load
             I      E
              \    /'.
               \  /   '.  j I Xs
                \/      '.
                O----------+ V
      I leads V by phi;  E < V
```

#### Summary
| Load pf | Nature of armature reaction | Effect on terminal voltage |
|---|---|---|
| Unity | Cross-magnetising (distorting) | Small drop |
| Zero lagging | Purely demagnetising | Large drop ($V < E$) |
| Zero leading | Purely magnetising | Rise ($V > E$) |
| Practical lag/lead | Cross + de-/magnetising | Drop / rise |

## Check yourself

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

1. What is armature reaction in an alternator?
   A. The effect of the armature-current mmf on the main field flux
   B. The loss of field current due to brush drop
   C. The reaction of the prime mover to a sudden load
   D. The heating of the armature winding by load current
   Answer: A. Armature reaction is the effect of the stator current's magnetic field on the main flux from the rotor poles. (Key point: Armature reaction)

2. At unity power factor, how is the armature flux related to the main flux and what is the effect?
   A. Directly opposing it; demagnetising
   B. At 90° to it; cross-magnetising, flux distorted with little change in average
   C. Directly aiding it; magnetising
   D. In phase with it; no effect at all
   Answer: B. With current in phase with emf, armature mmf is in quadrature to the field, so the effect is cross-magnetising. (Key point: Unity pf)

3. Why does the terminal voltage fall considerably for a zero-pf lagging load?
   A. Armature flux aids the main flux, raising losses
   B. Armature flux is at 90° and increases the field current
   C. Armature flux directly opposes the main flux (demagnetising), so V < E
   D. The lagging current increases the speed of the rotor
   Answer: C. Lagging current produces a demagnetising mmf along the pole axis, reducing air-gap flux and V. (Key point: Lagging pf)

4. For a leading power factor load, armature reaction is and V compared with E is
   A. demagnetising; V is less than E
   B. cross-magnetising; V equals E
   C. magnetising; V is always much less than E
   D. magnetising; V can be greater than E
   Answer: D. Leading current produces an mmf aiding the field, so flux and voltage rise and regulation can be negative. (Key point: Leading pf)

## Related in Electric Machines II

- [Terminal voltage above emf and armature reaction](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Aterminal-voltage-greater-ar-effect) — Electric Machines II, chapter 1
- [Why terminal voltage exceeds emf on capacitive load](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Aterminal-voltage-greater-capacitive) — Electric Machines II, chapter 1, asked 3×
- [Synchronous motor drawing lagging and leading current](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Amotor-lagging-leading-current) — Electric Machines II, chapter 2, asked 4×
- [Load characteristics and capacitive load voltage rise](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Aload-characteristics-capacitive-load) — Electric Machines II, chapter 1, asked 3×
- [Change in emf to raise power factor to unity](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Apercentage-change-emf-unity-pf) — Electric Machines II, chapter 1
- [Internal emf and armature reaction reactance](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Ainternal-emf-armature-reactance) — Electric Machines II, chapter 1

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- [Synchronous generator load characteristics, capacitive load](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Async-gen-load-characteristics-capacitive) — Electrical Machines, chapter 6
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