---
title: "Back emf in DC motor and its role"
subject: "Electrical Machine"
chapter: 4
key: "semester_4/electrical_machine:back-emf-dc-motor-role"
source: https://www.bctengineer.com/q/semester_4/electrical_machine/back-emf-dc-motor-role
site: BCT Engineering
---

# Back emf in DC motor and its role

Electrical Machine · Chapter 4: DC Motor

- Asked in: 2074 Bhadra, 4 marks; 2071 Magh, 2+4 marks; 2069 Poush (asked 3 times)
- Video: [What is Back EMF & what is its significance | DC Motor | TheElectricalGuy](https://www.youtube.com/watch?v=JgnPSOUoVJI) — Gaurav J - TheElectricalGuy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machine/back-emf-dc-motor-role
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-4

## Question

What is back emf in a DC motor? Explain the significance of back emf and how it helps the motor develop the required torque according to the load on the shaft.

## Short answer

Back emf is the voltage induced in the rotating armature opposing the supply, E_b = KΦN. It limits starting current, enables power conversion (E_b I_a), and self-regulates: when load increases, speed falls, E_b drops, armature current rises, developing more torque to match the load.

## Answer

#### Back emf
When the armature of a DC motor rotates in the magnetic field, its conductors cut the flux, and by Faraday's law an emf is induced in them. By Lenz's law this emf opposes the cause producing it, which is the supply voltage. It is called **back emf (counter emf)**.

E_b = PΦZN / (60A) = KΦN

The motor equation is: V = E_b + I_aR_a, so **I_a = (V − E_b) / R_a**

#### Significance
1. **Acts as a governor**: E_b depends on speed, so it automatically regulates the armature current drawn.
2. **Limits the armature current**: R_a is small, and at start (E_b = 0) the current V/R_a is very large. As the motor speeds up, E_b rises and current falls to the required value.
3. **Power conversion**: V I_a = E_b I_a + I_a²R_a. The term E_b I_a is the gross mechanical power developed. If E_b were zero, there would be no conversion of electrical to mechanical energy.
4. Gives the motor its self-regulating nature.

#### How it matches the torque to the load
```text
 Load torque increases
   -> speed N falls
   -> E_b = KΦN falls
   -> I_a = (V - E_b)/Ra rises
   -> torque T = KΦ Ia rises
   -> torque equals load torque; speed becomes steady
```
- With a lighter load, the reverse happens: speed rises, E_b rises, I_a falls, and torque falls to match the smaller load.
- Hence a DC motor draws only the current that the load demands, because the back emf adjusts the armature current.

## Check yourself

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

1. Why is the induced emf in a motor called back emf?
   A. By Lenz's law it opposes the supply voltage that causes it
   B. It adds to the supply voltage
   C. It opposes only the load torque
   D. It is induced in the field winding only
   Answer: A. V = E_b + I_aR_a, so E_b opposes V. (Key point: Nature of back emf)

2. Why is the starting current large?
   A. Torque is zero
   B. E_b is zero at start, so I_a = V/R_a with small R_a
   C. Flux is maximum
   D. Speed is high
   Answer: B. Without back emf nothing limits the current except R_a. (Key point: Starting)

3. When the load torque rises, what sequence follows?
   A. Speed rises, E_b rises, I_a falls
   B. E_b stays the same
   C. Speed falls, E_b falls, I_a rises, torque rises to match load
   D. I_a falls and torque falls
   Answer: C. Lower E_b increases (V - E_b)/R_a so torque T = KΦI_a rises. (Key point: Load matching)

## Related in Electrical Machine

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