MAGNETIC CIRCUITS

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Chapter 3 : MAGNETIC CIRCUITSLesson Outcome:At the end of the lesson, students should be able to:

Define the basic concept of magnetic flux, magneto-motive force, reluctance, permeability, flux density in magnetic circuit.Describe and apply the concepts of Amperes Circuital Law in magnetic circuit.Solve/determine the magnetic circuit parameter for a series and series parallel magnetic circuit.

Flux DensityWhen magnetomotif force (mmf) applied to magnetic material, flux will be inducedMagnetic flux () measured in Webers (Wb)Number of flux lines per unit area is called flux density (B) and measured in Tesla (T)Where, = flux in Wb A = area in m2*nsmh...

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PermeabilityThe strength of magnetic will vary in accordance with the core usedThis variation in strength is due to the number of flux lines passing through the core

Where, o = permeabilty of free space (4 x 10-7)r = relative permeabilty of the core*nsmh...

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Amperes Circuital LawSimilarity between electric circuit and magnetic circuit Electric Circuit Magnetic Circuit

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EmfElectromotif Force, EMmfMagnetomotif Force, F = NIRResistance, R RReluctance, R =

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DC

E

R

I

Kirchoffs Voltage Law in Magnetic CircuitIn electric circuit

In magnetic circuit

Practical equation for mmf drop

Where; H = magnetizing force l = length of section*nsmh...

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ironsteelcobaltNI

All terms are known except magnetizing force (H) for each materialH can be obtained from B-H Curve (if flux or flux density B is known)*nsmh...

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Kirchoffs Current Law in Magnetic CircuitFluxes entering a junction is equal to the sum of fluxes leaving the junctionNIabcaAt junction a:a = b + c*nsmh...

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Example 1The magnetic core below consists of three types of materials which are sheet steel, cast steel and cast iron. The cross sectional areas for the materials are 2 x 10-3 m2. If the flux that pass through the air gap is 4 x 10-4 Wb, find the value of current I that flows in the windings. Given that the number of turns is 1000 turns. Neglect fringing and magnetic effect. (use o = 4 x 10-7)

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150 mm

150 mm

200 mm

100 mm

400 mm

1 mm

I

N = 1000

Sheet steel

Cast steel

Cast iron

Example1Given,A = 2 x 10-3 m2, gap = 4 x 10-4 Wb,N = 1000lss = 450 mm, lcs = 300 mm, lci = 649 mm, lg = 1mm

= gap = 4 x 10-4 Wb

For air gap:

Form B-H curve:Cast Steel: At B = 0.2 T, Hcs = 170 At/mCast Iron: At B = 0.2 T, Hci = 400 At/mSheet Steel: At B = 0.2 T, Hss = 40 At/mBy performing KVL at magnetic circuit loop:

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DC

1000 I

(Hl)ss

(Hl)cs

(Hl)ci

(Hl)gap

Example 2The magnetic circuit shown in Figure Q4b is made of cast steel. The cross-sectional area of all limbs is 5 x 10-4 m2. If the number of turns is 500, determine the current i that will produce a magnetic flux of 1 x 10-4 Wb in the air gap 1. (Neglect magnetic leakage and fringing effect)

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200 mm

170 mm

200 mm

100 mm

100 mm

i

N = 500 turns

1 mm

1 mm

Air gap 1

Air gap 2

Example 2Given, g1 = 1 x 10-4 Wb A = 5 x 10-4 m2l1 =199 mm, lg1 = 1 mm, l2 = 540 mmlg2 = 1 mm, lT =599 mm

1 = g1 = 1 x 10-4 Wb

For air gap 1:

From B-H curve:At B1 = 0.2 T, H1 = 170 At/mH2l2 = H1l1 + Hg1lg1H2 (540 m) = (170)(199 m) + (159.15 k) (1 m)

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DC

500 i

H2l2

H1l1

Hg1lg1

HTlT

Hg2lg2

Example 2From B-H curve:At H2 = 377.37 At/m, B2 = 0.62 TFrom B-H curve:At BT = 0.82 T, HT = 525 At/mKVL at right oop:*nsmh...

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