Formula & Calculator
Back EMF of a DC Motor
The voltage generated by a spinning DC motor's armature, opposing the applied terminal voltage.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| E_b | Back EMF | V |
| V | Supply voltage | V |
| I_a | Armature current | A |
| R_a | Armature resistance | Ω |
What it means
In a DC motor, the back EMF (electromotive force) E_b is the voltage induced in the armature winding due to its rotation in the magnetic field. It opposes the applied voltage V and is proportional to the motor speed. The relationship is E_b = V − I_a·R_a, where I_a is the armature current and R_a is the armature resistance. The back EMF limits the current; at start, the motor has no back EMF, so the current is high (V/R_a). As the motor speeds up, E_b increases, reducing the current. This is why motors draw high starting current. The back EMF is essential for torque‑speed regulation. Example: A motor with V=240V, I_a=10A, R_a=0.5Ω gives E_b = 240 − (10*0.5) = 235V. If the speed increases, E_b increases, reducing I_a.
Worked example
DC Motor Back EMF – Practical Example
Real‑World| Parameter | Value |
|---|---|
| V | 12 V |
| Ia | 2 A |
| Ra | 1 Ω |
| Formula | Eb = V − Ia·Ra |
Common mistakes
Watch unit consistency and the assumptions behind the formula; misapplying it outside its valid conditions is the most frequent error.Applications
Back EMF of a DC motor E_b = V − I_a·R_a is the voltage generated in the armature that opposes the applied voltage. It limits the armature current and is proportional to motor speed. Engineers use it to analyse motor performance, to design speed controllers, and to protect against overcurrent. By monitoring the back EMF, they can estimate speed and detect faults. This formula is essential for DC motor control and protection.
- DC motor speed control and analysis
- Current limiting and protection circuits
- Motor parameter estimation (speed from back EMF)
- Diagnostics and fault detection in motor drives
- Educational understanding of motor operation