---
title: "Torque and speed characteristics of DC motors"
subject: "Electrical Machine"
chapter: 4
key: "semester_4/electrical_machine:shunt-series-motor-characteristics"
source: https://www.bctengineer.com/q/semester_4/electrical_machine/shunt-series-motor-characteristics
site: BCT Engineering
---

# Torque and speed characteristics of DC motors

Electrical Machine · Chapter 4: DC Motor

- Asked in: 2070 Magh, 8 marks
- Video: [CHARACTERISTICS OF A DC MOTOR](https://www.youtube.com/watch?v=NspKmk2aD6g) — EEE STUDENT HUB
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machine/shunt-series-motor-characteristics
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-4

## Question

Explain torque-armature current and speed-torque characteristics of DC shunt and DC series motor.

## Short answer

Shunt motor: torque proportional to armature current (straight line), speed nearly constant with slight droop. Series motor: torque proportional to current squared below saturation (high starting torque), speed inversely proportional to current, dangerously high at no load and falling steeply with load.

## Answer

The torque developed is T = KΦI_a and the speed is N = (V − I_aR_a)/(KΦ). The shunt and series motors behave differently because the series field carries the armature current.

#### DC shunt motor (Φ constant)
```text
 T |           /        N |------___
   |         /            |         ---___
   |       /              |
   |     /                |
   +-------------> Ia     +-------------> T
     T-Ia                   N-T
```
- **T–I_a**: T ∝ I_a, a straight line through (near) the origin.
- **N–T**: speed falls only slightly with torque (drooping line), because the drop I_aR_a is small and Φ is constant. It is nearly a constant-speed machine.

#### DC series motor (Φ ∝ I_a before saturation)
```text
 T |           /        N |\
   |         _/           | \
   |      _-'             |  \__
   |  __-'                |     ---___
   +-------------> Ia     +-------------> T
     T-Ia                   N-T
```
- **T–I_a**: T ∝ Φ I_a ∝ I_a² at light loads (parabola). After magnetic saturation Φ is constant, so T ∝ I_a (straight line). It gives a very high starting torque.
- **N–T**: N ∝ 1/Φ ∝ 1/I_a ∝ 1/√T. Speed is very high at light load and falls rapidly as torque rises (hyperbola-like). On no load the speed becomes dangerously high, so the load must never be removed.

| Aspect | Shunt motor | Series motor |
|---|---|---|
| T–I_a | straight line, T ∝ I_a | parabola then line, T ∝ I_a² |
| Starting torque | moderate | very high |
| N–T | nearly flat | falls steeply, N ∝ 1/√T |
| No-load speed | slightly above full-load | very high (dangerous) |
| Uses | lathes, pumps, fans | cranes, hoists, traction |

## Check yourself

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

1. What is T-I_a for a series motor at light loads?
   A. T ∝ I_a
   B. T ∝ I_a² (parabola)
   C. T constant
   D. T ∝ 1/I_a
   Answer: B. Φ ∝ I_a, so T ∝ Φ I_a ∝ I_a². (Key point: Series torque)

2. What is the speed-torque relation for a series motor?
   A. N constant
   B. N ∝ T
   C. N ∝ 1/√T
   D. N ∝ T²
   Answer: C. N ∝ 1/Φ ∝ 1/I_a ∝ 1/√T. (Key point: Series speed)

3. Why must a series motor never run without load?
   A. It overheats the field
   B. It reverses
   C. Torque becomes infinite
   D. Speed becomes dangerously high
   Answer: D. Flux is very low at light load so speed rises dangerously. (Key point: No-load danger)

## Close variants set in other exams

- [DC shunt motor characteristics](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Adc-shunt-motor-characteristics) — Electrical Machine, chapter 4, asked 2×

## Related in Electrical Machine

- [Characteristics of DC shunt and series motors](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Adc-motor-characteristics-shunt-series) — Electrical Machines, chapter 4
- [Shunt motor speed with series armature resistance](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Adcm-shunt-half-full-load-torque) — Electrical Machines, chapter 4
- [Shunt motor speed at 30 A armature current](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Ashunt-motor-60a-230v-speed) — Electrical Machine, chapter 4
- [Shunt motor speed at armature current 30 A](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Adcm-shunt-60a-230v-speed-30a) — Electrical Machines, chapter 4
- [Shunt motor speed with 1 Ω armature resistance added](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ashunt-motor-240v-27a-1ohm-torque) — Electrical Machines I, chapter 4, asked 5×
- [Shunt motor speed with 1.2 Ω armature resistance added](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ashunt-motor-240v-30a-1p2ohm-torque) — Electrical Machines I, chapter 4, asked 5×

## Related in other subjects

- [DC shunt motor armature torque](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_and_electronics_engineering%3Adc-shunt-motor-torque) — Basic Electrical and Electronics Engineering, chapter 2
- [Reverse current (plugging) braking of 20 kW DC shunt motor](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Adc-shunt-reverse-current-braking-20kw) — Utilization of Electrical Energy, chapter 3
- [Shunt motor driving pump: torque proportional to speed squared](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Adcm-shunt-200v-pump-torque-square) — Electrical Machines, chapter 4, asked 2×
- [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