📘 Magnetic Circuits – Advanced Worked Numerical Problems
This section contains GATE-level numerical problems on magnetic circuits. Careful unit handling and formula clarity are essential.
🔹 Problem 1 – Reluctance & Flux
Given: Length = 0.4 m Area = 4 × 10⁻⁴ m² μᵣ = 1500 Turns = 300 Current = 1.5 A Find flux.Step 1: Calculate μ
μ = μ₀ μᵣ = (4Ï€×10⁻⁷)(1500)Step 2: Reluctance
ℜ = l / (μA)Step 3: MMF
MMF = NI = 300 × 1.5Step 4: Flux
Φ = MMF / â„œ Final answer in Weber.🔹 Problem 2 – With Air Gap
Core length = 0.3 m Air gap length = 1 mm Area = 5 × 10⁻⁴ m² μᵣ = 1000 N = 500 I = 2 A Find flux.Important Concept:
Air gap reluctance dominates because: μ_air ≈ μ₀Total Reluctance:
â„œ_total = â„œ_core + â„œ_air Where: â„œ = l / (μA) Compute separately and add. Then: Φ = NI / â„œ_total Observation: Even small air gap drastically reduces flux.🔹 Problem 3 – Flux Density
If flux = 0.002 Wb Area = 4 × 10⁻⁴ m² Find B. Solution: B = Φ / A = 0.002 / (4×10⁻⁴) = 5 Tesla Check if saturation occurs.🔹 Problem 4 – Core Loss Calculation
Frequency = 50 Hz B_max = 1.2 T If: P_h ∝ f B_max^1.6 P_e ∝ f² B_max² If frequency doubled to 100 Hz: Hysteresis loss doubles Eddy loss becomes four times Very common GATE concept.🔹 Problem 5 – Required Turns
Flux required = 0.001 Wb Total reluctance = 2 × 10⁵ A/Wb Current = 2 A Find N. MMF = Φ × â„œ = 0.001 × (2×10⁵) MMF = 200 A-turns N = MMF / I = 200 / 2 = 100 turns🎯 GATE Important Observations
- Air gap controls flux in machines
- Reluctance adds like resistances
- Check units carefully
- Core loss frequency dependency very important
Air Gap = Major Control Element in Electrical Machines
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