Lecture Notes: AC Machinery Fundamentals - Induced EMF in a Loop

Introduction

• First lecture session on AC machinery fundamentals.
• Focus on simple concepts of a loop in a uniform magnetic field.
• Contrast with DC machines, where field is constant and stationary.

Simple Loop in a Uniform Magnetic Field

• Basic Concept: A loop of wire through a uniform magnetic field generates an alternating voltage.
• In AC machines, neither the field value is constant nor stationary.

AC Machines vs. DC Machines

• DC Machines: Constant and stationary magnetic field.
• AC Machines: Interaction with rotating magnetic fields.
• The equations for induced voltage and torque are applicable with some constructional adjustments.

Coil Construction

• Coil Components: Conductors A-B and C-D.
• Coil Specifications: Length (L) and Distance from center (R).

Induced EMF Calculation

• Equation for Induced EMF: E = V cross B dot L.
• Vectors and Angles:
  • Velocity vector (V) and magnetic field vector (B).
  • Angles defined as θ_AB and θ_CD.

Segment Analysis

1. **Segment AB: **

   • V cross B is into the paper.
   • Resulting EMF: E_AB = BLV sin θ_AB.

2. Segment BC (First Half):

   • Counter clockwise direction.
   • Resulting EMF: Zero (angle is 90 degrees).

3. Segment BC (Second Half):

   • V cross B is out of the paper.
   • Resulting EMF: Zero (angle is 90 degrees).

4. Segment CD:

   • V cross B is out of the paper.
   • Resulting EMF: E_CD = BLV sin θ_CD.

Total Induced EMF

• Total EMF: E_total = E_AB + E_BC + E_CD.
• Both E_AB and E_CD are equal due to sin θ_AB = sin(180° - θ_CD).
• Final Result: E_total = 2BLV sin θ.
• Graphically represented as a sine wave.

Alternative Derivation

• Using angular speed (Ω) and linear velocity (V = RΩ).
• E_induced = 2BLRΩ sin Ωt.
• Area of Coil: A = 2RL.
• Final Expression: E_induced = Φ_max Ω sin Ωt.

Key Takeaways

• Dependence on:
  1. Flux (Φ_max): Inside the machine.
  2. Speed of Rotation (Ω).
  3. Constructional Features: Loops, turns, conductors.
• Basic expression sufficient for concept understanding before detailed armature flux distribution.

Conclusion

• Basic understanding of induced EMF in a simple loop for AC machines.
• Importance of flux, speed, and construction in determining EMF.
• Future sessions will cover more complex aspects.

• Reminder: If you enjoyed the session, like, share, and subscribe.
• Next Steps: Further explorations in AC machinery concepts.