What is the back EMF of a dc motor?

Here's how it works:

1. **Electromagnetic Induction**: As the motor's rotor (or armature) turns within the magnetic field, it induces a voltage in the windings of the rotor according to Faraday's Law of Induction. This induced voltage is in the opposite direction to the applied voltage.

2. **Voltage Opposition**: The back EMF acts against the applied voltage (the supply voltage). This opposition means that as the motor speeds up, the back EMF increases, reducing the net voltage across the motorâ€™s windings and thus the current flowing through them.

3. **Current and Speed Relationship**: The relationship between the back EMF and the motor speed is direct; the faster the motor turns, the higher the back EMF. At steady-state operation, the back EMF is equal to the applied voltage minus the voltage drop due to the resistance of the motor windings.

Mathematically, it's often expressed as:

\[ \text{Back EMF} = V_{\text{applied}} - I \cdot R \]

where \( V_{\text{applied}} \) is the voltage supplied to the motor, \( I \) is the current through the motor, and \( R \) is the resistance of the motor windings.

Understanding back EMF is crucial for controlling motor speed and efficiency, as it directly influences how much current the motor draws and thus its performance.