Question E6D04:
Why are cores of inductors and transformers sometimes constructed of thin layers?  

Choices:  
A: To simplify assembly during manufacturing  
B: To reduce power loss from eddy currents in the core  
C: To increase the cutoff frequency by reducing capacitance  
D: To save cost by reducing the amount of magnetic material    

Correct Answer is  B: To reduce power loss from eddy currents in the core  

Correct answer: B — To reduce power loss from eddy currents in the core

1) Why B is correct
- A changing magnetic field in a conductive core induces circulating “eddy” currents. These cause heat loss ($I^2R$ loss) and lower efficiency.
- Making the core from thin, insulated laminations breaks up current loops, increases their resistance, and reduces loop area. This greatly reduces eddy currents and their losses.

Key relation for eddy-current loss per unit volume:
$$P_e \propto B_{\max}^2 f^2 t^2$$
where:
- $B_{\max}$ = peak flux density
- $f$ = frequency
- $t$ = lamination thickness

Smaller $t$ means much smaller $P_e$.

Skin depth perspective:
$$\delta = \sqrt{\frac{2\rho}{\omega \mu}}$$
Choosing lamination thickness $t \lesssim \delta$ helps restrict eddy currents.

2) Why the other choices are incorrect
- A: To simplify assembly during manufacturing  
  Incorrect. Laminating cores complicates manufacturing; it is done to cut eddy-current loss, not to simplify assembly.

- C: To increase the cutoff frequency by reducing capacitance  
  Incorrect. Core laminations don’t meaningfully reduce interwinding capacitance (which drives self-resonance). Laminations address conductive losses in the core, not capacitive effects in the windings.

- D: To save cost by reducing the amount of magnetic material  
  Incorrect. Laminated cores generally cost more to make. The purpose is loss reduction, not material savings.

3) Useful formulas and rules of thumb
- Total core loss is often modeled as:
  $$P_{\text{core}} \approx P_h + P_e$$
  $$P_h \propto f B_{\max}^n \quad (n \approx 1.6\text{–}2)$$
  $$P_e \propto B_{\max}^2 f^2 t^2$$
- Reduce eddy currents by using:
  - Thin laminations (power frequencies: silicon steel, e.g., 0.35 mm for 50/60 Hz; thinner for higher frequencies like 400 Hz)
  - High-resistivity cores (powdered iron, ferrite) for kHz–MHz operation
- Faraday’s law reminder:
  $$E = -N \frac{d\Phi}{dt}$$
  The induced EMF drives eddy currents in conductive cores; breaking the conductive path (laminations or high resistivity) reduces these currents.