Question

Explain the principle and working of an AC Generator or a Transformer (including energy losses).

Hint:

- AC Generator: Converts mechanical energy → electrical energy (Faraday’s law). - Transformer: Transfers electrical energy using mutual induction. - Laminated cores reduce eddy current losses.

Answer 1

Concept: Both AC generators and transformers work on the principle of electromagnetic induction discovered by Faraday. A changing magnetic flux induces an emf in a circuit.
Option 1: AC Generator
Principle: Based on Faraday’s law of electromagnetic induction: \[ e = -\frac{d\Phi}{dt} \] An emf is induced when a coil rotates in a magnetic field, causing change in magnetic flux.
Construction:

• Rectangular coil of wire (armature)
• Strong magnetic field (permanent magnet or electromagnet)
• Slip rings
• Carbon brushes
• Axle for rotation

Working:

• Coil rotates in magnetic field.
• Magnetic flux linked with coil changes continuously.
• Induced emf alternates in direction every half rotation.
• Slip rings collect alternating current.

If the coil rotates with angular velocity \( \omega \): \[ \Phi = BA \cos \omega t \] Induced emf: \[ e = -\frac{d\Phi}{dt} = BA\omega \sin \omega t \] \[ \boxed{e = e_0 \sin \omega t} \] Thus, output is alternating current.
Applications:

• Power generation in power plants
• Bicycle dynamos

Option 2: Transformer
Principle: Based on mutual induction — a changing current in one coil induces emf in another nearby coil. \[ \frac{V_s}{V_p} = \frac{N_s}{N_p} \] where:

• \( V_p, V_s \) = primary and secondary voltages
• \( N_p, N_s \) = number of turns

Construction:

• Two insulated coils (primary and secondary)
• Soft iron laminated core
• Core provides low reluctance path for magnetic flux

Working:

• AC applied to primary coil.
• Alternating current produces changing magnetic flux in core.
• This changing flux links secondary coil.
• Induced emf appears in secondary coil.

If \( N_s>N_p \) → Step-up transformer If \( N_s<N_p \) → Step-down transformer
Energy Losses in Transformer:

• 
  Copper Loss (I\(^2\)R Loss): Due to resistance of windings.
• 
  Iron Losses:
  • Hysteresis loss (magnetization cycles)
  • Eddy current loss (circulating currents in core)
• 
  Flux Leakage: Not all magnetic flux links both coils.
• 
  Mechanical Losses: Vibrations and heating.

Minimizing Losses:

• Laminated iron core (reduces eddy currents)
• Soft iron (reduces hysteresis loss)
• Thick copper windings (reduces resistance)

Efficiency of Transformer: \[ \eta = \frac{\text{Output Power}}{\text{Input Power}} \times 100% \] Practical transformers have efficiency up to 95–99%.