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Magnetic Circuits

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What is the analogy between magnetic and electric circuits?

Magnetic Electric
MMF (N·I) EMF (V)
Flux (Φ) Current (I)
Reluctance (ℛ) Resistance (R)
Φ = MMF / ℛ I = V / R

Series reluctances add; parallel reluctances combine as reciprocal sums.

How does an air gap affect a magnetic circuit?

Air gaps have very low permeability (μ₀), so even a short gap adds significant reluctance and reduces total flux. Air gaps are intentionally used in inductors to prevent saturation and store magnetic energy, and in rotating machines to allow mechanical clearance.

How do you calculate flux in a toroidal core?

For a toroid with mean path length l = 2πr and cross-section A:
1. Apply Ampere's Law: H = NI / l
2. Calculate flux density: B = μH
3. Calculate flux: Φ = B • A If an air gap is present: Φ = NI / (ℛ_core + ℛ_gap)
 

What is the coupling coefficient (k)?

The coupling coefficient measures how much flux from one coil links another: k = M / √(L₁ • L₂), where 0 ≤ k ≤ 1. k = 1 means perfect coupling (ideal transformer); k < 1 means leakage flux exists.
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