---
title: "Synchronous motor drawing lagging and leading current"
subject: "Electric Machines II"
chapter: 2
key: "semester_5/electric_machines_ii:motor-lagging-leading-current"
source: https://www.bctengineer.com/q/semester_5/electric_machines_ii/motor-lagging-leading-current
site: BCT Engineering
---

# Synchronous motor drawing lagging and leading current

Electric Machines II · Chapter 2: Three Phase Synchronous Motor

- Asked in: 2078 Bhadra, 7 marks; 2075 Asoj, 7 marks; 2072 Chaitra, 6 marks; 2069 Chaitra, 8 marks (asked 4 times)
- Video: [Equivalent circuit of synchronous motor |Phaser diagram of synchronous motor | #phaserdiagram](https://www.youtube.com/watch?v=XMxrURPjnG8) — Mind of Engineer 
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/electric_machines_ii/motor-lagging-leading-current
- Whole chapter: https://www.bctengineer.com/md/semester_5/electric_machines_ii/chapter-2

## Question

A synchronous motor can operate as both inductive and capacitive characteristics. Justify this statement with relevant phasor diagrams. (Explain how a three-phase synchronous motor can be operated to draw lagging as well as leading current from the source.)

## Short answer

A synchronous motor's power factor is controlled by field excitation at constant load. Under-excitation (Eb < V) gives lagging current and inductive behaviour; over-excitation (Eb > V) gives leading current, acting as a capacitor. This is demonstrated by V-curves, where lowest point is unity pf.

## Answer

A synchronous motor runs at constant speed whatever its excitation. For a constant load (constant input power $VI\cos\phi$), changing the **field current** changes the back emf $E_b$, and hence the magnitude and **power factor** of the armature current. So the same motor can behave as an inductive (lagging) or a capacitive (leading) load.

Motor equation (per phase, $R_a$ neglected):
$$
\bar V = \bar E_b + jX_s\bar I \qquad\text{or}\qquad \bar I = \frac{\bar V - \bar E_b}{jX_s}
$$
The resultant voltage $\bar E_r = \bar V - \bar E_b$ drives the current, which lags $E_r$ by 90°.

#### 1. Under-excitation ($E_b < V$): lagging pf (inductive)
```text
           V
   O-------------->
    \`-.        /
     \  `-.   / Er = jIXs
      \    `/
   I   \   Eb (short)
  (lags V)
```
- $E_b\cos\delta < V$; the motor draws a **lagging** current.
- The field is too weak, so the armature takes a lagging (magnetising) current from the supply to make up the missing flux. The motor then behaves like an induction motor or an inductor.

#### 2. Normal excitation ($E_b \approx V$): unity pf
- Field current is just enough for the required flux; current is in phase with $V$ and is **minimum** for that load.

```text
   O--------------> V
   O-------->  I (in phase)
     \       /
      Eb    / Er
```

#### 3. Over-excitation ($E_b > V$): leading pf (capacitive)
```text
     I (leads V)
      ^       V
      |  O---------->
      |    \        .
      |      \    . Er
      |   Eb (long)
```
- $E_b > V$; the resultant $E_r$ makes the current **lead** $V$.
- The motor supplies reactive power to the system and acts as a capacitor. Running at no load like this, it is called a **synchronous condenser**, used for power-factor improvement and voltage control.

#### Summary
| Excitation | $E_b$ vs $V$ (approx.) | Current | pf | Acts as |
|---|---|---|---|---|
| Under | $E_b < V$ | Large | Lagging | Inductor |
| Normal | $E_b \approx V$ | Minimum | Unity | Resistor |
| Over | $E_b > V$ | Large | Leading | Capacitor |

These variations are shown by the **V-curves** (armature current vs field current at constant load), whose lowest point is at unity pf.

## Check yourself

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

1. At constant load, a synchronous motor's pf can be made lagging or leading by changing which quantity?
   A. Supply frequency
   B. Field current, which changes Eb
   C. Rotor speed
   D. Number of poles
   Answer: B. Speed is fixed at synchronous speed. Changing the field current changes the back emf Eb, which changes the magnitude and pf of the armature current. (Key point: What changes with excitation)

2. When Eb < V (under-excited), the motor behaves as which load?
   A. Capacitive, leading current
   B. Purely resistive
   C. Inductive, lagging current
   D. No reactive behaviour at all
   Answer: C. With Eb < V the current lags V and the motor draws magnetising reactive power, acting like an inductor. (Key point: Under-excitation)

3. When Eb > V (over-excited), what does the motor do?
   A. Draws lagging current and absorbs reactive power
   B. Draws leading current and supplies reactive power like a capacitor
   C. Stops because it falls out of step
   D. Runs at speed above synchronous speed
   Answer: B. For Eb > V the current leads V, so the motor supplies reactive power to the system and acts as a capacitor. (Key point: Over-excitation)

4. An over-excited synchronous motor running at no load is called a synchronous condenser. What is it used for?
   A. Increasing the starting torque
   B. Reducing hunting
   C. Power-factor improvement and voltage control
   D. Raising the speed above Ns
   Answer: C. Its leading current offsets lagging loads, improving the system pf and helping voltage control. (Key point: Synchronous condenser)

## Related in Electric Machines II

- [Synchronous motor features and lagging/leading operation](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Amotor-features-lagging-leading) — Electric Machines II, chapter 2
- [Leading kVAR supplied by synchronous motor](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Apf-correction-leading-kvar) — Electric Machines II, chapter 2
- [Justify synchronous motor is not self starting](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Amotor-not-self-starting-justify) — Electric Machines II, chapter 2
- [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×
- [Excitation emf of motor drawing 160 A](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Amotor-excitation-emf-160a) — Electric Machines II, chapter 2
- [Split phase motor added resistance and capacitance](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Asplit-phase-resistance-capacitance) — Electric Machines II, chapter 3

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