Solved Examples: Calculating Back EMF and Motor Speed

📚 Quick Study Guide

• ⚡ Back EMF (Electromotive Force): The voltage generated in a motor that opposes the supply voltage. It's crucial for controlling motor speed and current.
• ⚙️ Formula for Back EMF ($E_b$): $E_b = K \cdot \phi \cdot \omega$, where $K$ is a constant, $\phi$ is the magnetic flux per pole, and $\omega$ is the angular speed.
• 🔄 Relationship between Speed and Back EMF: As motor speed increases, back EMF also increases.
• 💡 Formula for Motor Speed ($N$ in RPM): $N = \frac{V - E_b}{K \cdot \phi} \cdot \frac{60}{2\pi}$, where $V$ is the supply voltage.
• 📝 Important Units: Angular speed ($\omega$) is typically in radians per second (rad/s), and motor speed ($N$) is often in revolutions per minute (RPM).
• 🧲 Factors Affecting Back EMF: Supply voltage, magnetic field strength, and motor speed.

Practice Quiz

1. What is back EMF in a DC motor?
   1. (A) The voltage applied to the motor.
   2. (B) The voltage generated that opposes the applied voltage.
   3. (C) The current flowing through the motor.
   4. (D) The resistance of the motor windings.
2. If the back EMF of a motor is equal to the supply voltage, what will happen to the motor's speed?
   1. (A) It will increase rapidly.
   2. (B) It will decrease rapidly.
   3. (C) It will stop.
   4. (D) It will run at a constant speed.
3. Which of the following factors does NOT affect the back EMF of a DC motor?
   1. (A) Supply voltage.
   2. (B) Magnetic field strength.
   3. (C) Motor speed.
   4. (D) Ambient temperature.
4. A DC motor has a supply voltage of 240V and a back EMF of 220V. What happens if the back EMF suddenly drops to 180V?
   1. (A) The motor speed decreases.
   2. (B) The motor speed increases.
   3. (C) The motor stops immediately.
   4. (D) The motor is unaffected.
5. What is the purpose of back EMF in a DC motor?
   1. (A) To increase the motor's torque.
   2. (B) To limit the motor's speed.
   3. (C) To reduce the motor's power consumption.
   4. (D) To protect the motor from overheating.
6. If the magnetic field strength in a DC motor increases, what happens to the back EMF?
   1. (A) It increases.
   2. (B) It decreases.
   3. (C) It remains the same.
   4. (D) It becomes zero.
7. A motor's speed is primarily controlled by which of the following?
   1. (A) The armature resistance.
   2. (B) The back EMF.
   3. (C) The supply voltage alone.
   4. (D) The ambient temperature.