---
title: "Shunt generator voltage build-up, critical resistance and speed"
subject: "Electrical Machines I"
chapter: 3
key: "semester_4/electrical_machines_i:shunt-buildup-critical-define"
source: https://www.bctengineer.com/q/semester_4/electrical_machines_i/shunt-buildup-critical-define
site: BCT Engineering
---

# Shunt generator voltage build-up, critical resistance and speed

Electrical Machines I · Chapter 3: DC Generator

- Asked in: 2078 Baisakh, 8 marks; 2077 Chaitra, 8 marks; 2076 Bhadra, 6+2 marks; 2076 Baisakh, 8 marks; 2074 Bhadra, 8 marks; 2073 Bhadra, 4+2+2 marks; 2072 Asoj, 4+2+2 marks; 2071 Bhadra, 8 marks; 2070 Magh, 4 marks (asked 9 times)
- Video: [Lecture 21: Critical Resistance and Critical Speed in Voltage Build Up Process @DC Shunt Generator](https://www.youtube.com/watch?v=OciRkbrP2no) — Anuprita Mishra's Electrical Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines_i/shunt-buildup-critical-define
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/chapter-3

## Question

Explain the voltage build-up process of dc shunt generator and define the meaning of critical resistance and critical speed.

## Short answer

Residual magnetism induces a small EMF, driving field current. If field MMF aids residual flux, flux cumulatively increases, raising EMF until OCC intersects field resistance line. Critical field resistance is the maximum Rf that allows build-up (tangent to OCC). Critical speed Nc = N * Rf / Rc is the minimum speed for build-up with given Rf.

## Answer

A **self-excited DC shunt generator** builds up its own field current from the small voltage due to residual magnetism, with no external DC source.

#### Voltage build-up process
```text
     +---------+-----------o +
     |         |
   ( G )     [Rsh]  field         V
     |         |  winding
     +---------+-----------o -
```
1. The poles keep a little **residual magnetism**. When the armature is driven at rated speed, a small EMF $E_r$ (a few volts) is induced.
2. This EMF drives a small current through the shunt field winding (connected across the armature).
3. If the field is connected so that its MMF **aids** the residual flux, the flux increases, so the induced EMF increases.
4. The higher EMF drives more field current, which increases flux further, and so on (cumulative process).
5. Build-up stops where the **OCC** (magnetisation curve, $E$ vs $I_f$) meets the **field resistance line** ($V = I_fR_f$), because at that point the generated EMF just equals the drop across the field circuit. Saturation of the iron makes the OCC bend over, so the two curves intersect at a definite point.

```text
  E ^           field resistance line
    |         /     (slope = Rf)
    |        /   ___....--- OCC
    |       / .-'
    |      /.'   <- operating point
    |     .'      (OCC meets Rf line)
    |   .'/
    |  / /  steps of build-up
    | / /
    |//
 Er +------------------------> If
```

#### Critical field resistance
The **critical field resistance** $R_c$ is the maximum shunt-field circuit resistance at which the generator will just build up voltage at a given speed. It equals the slope of the **tangent** to the linear part of the OCC drawn from the origin. If $R_f > R_c$, the field line lies above the OCC, they meet only near the residual voltage, and the machine fails to build up.

#### Critical speed
The **critical speed** $N_c$ is the minimum speed at which a shunt generator with a given field resistance $R_f$ will just build up. At that speed the slope of the OCC's initial tangent equals $R_f$. Since EMF ∝ speed:
$$
\frac{N_c}{N} = \frac{R_f}{R_c} \quad\Rightarrow\quad N_c = N\,\frac{R_f}{R_c}
$$
where $R_c$ is the critical resistance at speed $N$.

**Example:** if $R_c = 200\ \Omega$ at 1000 rpm and the field resistance is $150\ \Omega$, then $N_c = 1000 \times \frac{150}{200} = 750$ rpm.

#### Conditions for build-up
- Residual magnetism must be present.
- Field MMF must aid the residual flux (correct field connection / direction of rotation).
- Field circuit resistance must be less than critical resistance.
- Speed must be above critical speed.
- At start, load resistance should be high (no load), so the armature voltage is not pulled down.

## Check yourself

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

1. What starts the voltage build-up in a self-excited shunt generator?
   A. Residual magnetism inducing a small EMF
   B. An external DC source
   C. Armature reaction
   D. Series field
   Answer: A. Residual flux gives a small EMF that drives a small field current, which then builds up cumulatively. (Key point: Start of build-up)

2. Build-up stops at the point where:
   A. The OCC meets the field resistance line
   B. The OCC crosses zero
   C. Speed reaches critical
   D. Armature current is maximum
   Answer: A. At the intersection, generated EMF equals the drop Rf If, so no further rise occurs; saturation makes this a definite point. (Key point: Where build-up stops)

3. Critical field resistance Rc is:
   A. The minimum field resistance
   B. The maximum field circuit resistance at which the generator just builds up at a given speed
   C. The armature resistance
   D. The load resistance at rated voltage
   Answer: B. It is the slope of the tangent to the linear part of OCC; Rf > Rc means no build-up. (Key point: Critical resistance)

4. If Rc = 200 ohm at 1000 rpm and Rf = 150 ohm, critical speed is:
   A. 1333 rpm
   B. 750 rpm
   C. 1000 rpm
   D. 200 rpm
   Answer: B. Nc = N Rf/Rc = 1000 x 150/200 = 750 rpm. (Key point: Critical speed)

## Related in Electrical Machines I

- [Shunt generator build-up conditions, critical speed and resistance](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ashunt-buildup-conditions-critical) — Electrical Machines I, chapter 3
- [Starting shunt generator on no load and voltage build-up](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ashunt-generator-no-load-buildup) — Electrical Machines I, chapter 3
- [Critical resistance, critical speed and shunt generator characteristics](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Acritical-resistance-speed-shunt-characteristics) — Electrical Machines I, chapter 3
- [Voltage build-up in isolated induction generator](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ainduction-generator-isolated-buildup) — Electrical Machines I, chapter 5

## Related in other subjects

- [Voltage build-up, critical resistance and speed](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Avoltage-buildup-critical-resistance-speed) — Electrical Machines, chapter 3, asked 3×
- [Voltage build-up; series generator at no load](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Avoltage-buildup-series-generator-no-load) — Electrical Machines, chapter 3
- [DC shunt motor speed at reduced voltage and starting resistance](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Adc-shunt-reduced-voltage-starting-resistance) — Utilization of Electrical Energy, chapter 3
- [Voltage build-up in induction generator](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Ainduction-generator-voltage-buildup) — Electrical Machines, chapter 5