📘 Composite Magnetic Circuits – Series & Parallel Paths
In practical machines, magnetic circuits contain multiple materials and air gaps. These behave like series or parallel magnetic circuits.
🔹 1. Series Magnetic Circuit
If flux flows through different sections sequentially: Reluctances add:â„œ_total = â„œ₁ + â„œ₂ + â„œ₃
Flux remains same through all sections. Analogous to series resistors.🔹 2. Example – Series Magnetic Circuit
Given: Section 1: l₁ = 0.2 m A₁ = 4×10⁻⁴ m² μᵣ₁ = 1000 Section 2: l₂ = 0.1 m A₂ = 4×10⁻⁴ m² μᵣ₂ = 500 Find total reluctance.Step 1: Calculate μ for each
μ₁ = μ₀ μᵣ₁ μ₂ = μ₀ μᵣ₂Step 2: Compute â„œ₁ and â„œ₂
ℜ = l / (μA)Step 3: Add
â„œ_total = â„œ₁ + â„œ₂🔹 3. Parallel Magnetic Circuit
If flux splits into multiple paths: MMF same Flux divides Reluctance rule:1/â„œ_total = 1/â„œ₁ + 1/â„œ₂
Analogous to parallel resistors.🔹 4. Example – Parallel Magnetic Circuit
Given: Two parallel limbs with same length but different areas. Find flux in each branch.Step 1: Compute â„œ₁ and â„œ₂
Step 2: Find total reluctance
Step 3: Total flux
Φ_total = NI / ℜ_totalStep 4: Flux division
Flux divides inversely proportional to reluctance.Φ₁ / Φ₂ = â„œ₂ / â„œ₁
🔹 5. Air Gap in Composite Circuit
Air gap reluctance:â„œ_air = l_air / (μ₀ A)
Usually much larger than core reluctance. Therefore: Air gap controls total flux.🔹 6. Important GATE Observations
- Flux same in series path
- MMF same in parallel path
- Air gap dominates total reluctance
- Cross-sectional area affects flux density
🎯 Quick Comparison
| Electric Circuit | Magnetic Circuit |
|---|---|
| Voltage | MMF |
| Current | Flux |
| Resistance | Reluctance |
Composite Circuits = Real Machine Behavior
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