---
title: "Synchronous generator principle and EMF equation"
subject: "Electric Machines II"
chapter: 1
key: "semester_5/electric_machines_ii:generator-principle-emf-equation"
source: https://www.bctengineer.com/q/semester_5/electric_machines_ii/generator-principle-emf-equation
site: BCT Engineering
---

# Synchronous generator principle and EMF equation

Electric Machines II · Chapter 1: Three Phase Synchronous Generator

- Asked in: 2070 Asar, 8 marks
- Video: [Construction and EMF Equation of Synchronous machine](https://www.youtube.com/watch?v=hPjP_7GCgF0) —  Electrical Engineering Courses(B.tech.& M.tech)
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/electric_machines_ii/generator-principle-emf-equation
- Whole chapter: https://www.bctengineer.com/md/semester_5/electric_machines_ii/chapter-1

## Question

Explain the working principle of synchronous generator and also derive the E.M.F equation.

## Short answer

A synchronous generator converts mechanical energy to AC by rotating a DC-excited rotor field, inducing emf in stationary armature conductors via Faraday's law. Frequency f = PNs/120. RMS phase emf E = 4.44 f Φ T kp kd, where T is turns per phase, kp and kd are pitch and distribution factors.

## Answer

A **synchronous generator (alternator)** converts mechanical energy into AC electrical energy by electromagnetic induction, at a frequency fixed by its speed.

#### Working principle
1. The rotor carries the field winding, excited by DC through slip rings (or a brushless exciter); it produces alternate N and S poles.
2. The prime mover (water/steam turbine, engine) drives the rotor at synchronous speed $N_s$.
3. The rotating flux cuts the stationary three-phase armature conductors on the stator. By **Faraday's law**, an emf $e = Blv$ is induced; its direction is given by **Fleming's right-hand rule**.
4. Under a N pole the emf is in one direction, under a S pole in the other, so an **alternating** emf results. One cycle is produced per pair of poles: $f = \dfrac{PN_s}{120}$.
5. The three phase windings are displaced by 120° electrical, giving three balanced emfs 120° apart.
6. When load is connected, current flows and power is delivered; the field current is adjusted to keep voltage constant.

```text
   N  ->  rotor turns  ->  S
   |  flux cuts stator     |
   v  conductors           v
  e = B l v  (sinusoidal, f = P Ns / 120)
```

#### EMF equation
Let $P$ = poles, $\Phi$ = flux per pole (Wb), $N_s$ = rpm, $Z$ = conductors per phase in series, $T = Z/2$ turns per phase.

$$
\begin{aligned}
\text{Flux cut per revolution} &= P\Phi \\
\text{Time for one revolution} &= \frac{60}{N_s}\ \text{s} \\
\text{Average emf per conductor} &= \frac{P\Phi N_s}{60} \\
\text{With } f = \frac{PN_s}{120}:\quad &= 2f\Phi\ \text{V} \\
\text{Average emf per phase} &= 2f\Phi\times Z = 4f\Phi T\ \text{V} \\
\text{RMS emf per phase} &= 1.11\times4f\Phi T = 4.44\,f\Phi T\ \text{V}
\end{aligned}
$$
using form factor 1.11 for a sine wave. For practical windings, which are short-pitched and distributed:
$$
E_{ph} = 4.44\,k_p\,k_d\,f\,\Phi\,T
$$
where
- pitch factor $k_p = \cos(\alpha/2)$, $\alpha$ = angle by which the coil is short of 180° electrical;
- distribution factor $k_d = \dfrac{\sin(m\beta/2)}{m\sin(\beta/2)}$, $m$ = slots per pole per phase, $\beta$ = slot angle.

Line voltage: $E_L = \sqrt3 E_{ph}$ for star, $E_L = E_{ph}$ for delta.

## Check yourself

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

1. On what principle does an alternator generate emf, and which rule gives its direction?
   A. Faraday's law; Fleming's right-hand rule
   B. Lenz's law only; Fleming's left-hand rule
   C. Ampere's law; right-hand screw rule
   D. Ohm's law; left-hand rule
   Answer: A. The rotating flux cuts stator conductors; emf e = Blv follows Faraday's law, with direction by Fleming's right-hand rule. (Key point: Law of induction)

2. How is frequency related to speed in an alternator?
   A. f = N/P
   B. f = 120 N / P
   C. f = P Ns / 120
   D. f = P / (120 Ns)
   Answer: C. One cycle per pair of poles gives f = P Ns / 120. (Key point: Frequency)

3. In the derivation, the average emf per conductor equals:
   A. f Phi
   B. 2 f Phi
   C. 4.44 f Phi
   D. Phi N / 120
   Answer: B. Flux cut per revolution P Phi in 60/Ns seconds gives P Phi Ns/60 = 2 f Phi. (Key point: Average emf per conductor)

4. Why does the RMS emf per phase equal 4.44 f Phi T?
   A. Form factor 1.11 multiplies the average 4 f Phi T
   B. Peak factor 1.41 multiplies 3.14 f Phi T
   C. Because of three phases
   D. Because of star connection
   Answer: A. Average emf per phase is 4 f Phi T, and the sine-wave form factor 1.11 gives 4.44 f Phi T. (Key point: Form factor and 4.44)

## Related in Electric Machines II

- [Excitation emf of salient pole generator](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Asalient-generator-excitation-500v) — Electric Machines II, chapter 1
- [Construction and operation of synchronous generator](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Asynchronous-generator-construction-principle) — Electric Machines II, chapter 1
- [Pitch factor, distribution factor and EMF equation](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Apitch-distribution-factor-emf) — Electric Machines II, chapter 1, asked 3×
- [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×
- [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
- [Emf, regulation and loading with given load impedance](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Aemf-regulation-load-impedance) — Electric Machines II, chapter 1

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