Chapter 11 – Magnetic Circuits

Lecture 6

by Moeen Ghiyas

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Review

Ampere’s Circuital Law – (Applying KVL)

The Flux Φ – (Applying KCL)

Air Gaps

Series-Parallel Magnetic Circuits

Determining Flux Φ

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The spreading of the flux lines outside the common area of

the core for the air gap in fig (a) is known as fringing.

Neglect this effect of fringing as shown in fig (b)

The flux density of air gap is given by

Where,

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For most practical applications, the permeability of air is

taken to be equal to that of free space. The magnetizing

force of the air gap is then determined by

and the mmf drop across the air gap is equal to Hglg. An

equation for Hg is as follows:

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Example – Find the value of I required to establish a

magnetic flux of φ = 0.75 x 10-4 Wb in the series magnetic

circuit of fig

Solution

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Example – Find the value of I, φ = 0.75 x 10-4 Wb

Solution

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Example – Determine the current I required to establish a

flux of φ =1.5 x 10-4 Wb in the section of the core indicated

in fig

Solution

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Example – Determine the current I required to establish a

flux of φ =1.5 x 10-4 Wb in the section of the core indicated

in fig

Solution

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Example – Determine the current I required to establish a

flux of φ =1.5 x 10-4 Wb in the section of the core indicated

in fig

Solution

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Example – Determine the current I required to establish a

flux of φ =1.5 x 10-4 Wb in the section of the core indicated

in fig

Solution

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Example – Determine the current I required to establish a

flux of φ =1.5 x 10-4 Wb in the section of the core indicated

in fig

Solution

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To demonstrate that µ is sensitive to the magnetizing force

H, the permeability of each section is determined

For section bcde,

For section be,

For section efab,

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Here NI is given and the flux φ must be found.

This is a relatively straightforward problem if only one

magnetic section is involved. Then

For magnetic circuits with more than one section, there is

no set order of steps that will lead to an exact solution for

every problem on the first attempt.

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We must find the impressed mmf for a calculated guess of

flux φ and then compare this with specified value of mmf.

For most applications, a value within ±5% of the actual Φ

or specified NI is acceptable.

We can make a reasonable guess at the value of Φ if we

realize that the maximum mmf drop appears across the

material with the smallest permeability if the length and

area of each material are the same.

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Example – Calculate the magnetic flux Φ for the magnetic

circuit of fig

Solution

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Example – Find the magnetic flux Φ for the series

magnetic circuit of fig for the specified impressed mmf.

Solution

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Example – Find the magnetic flux Φ

Solution

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Example – Find the magnetic flux Φ

Solution

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Example – Find the magnetic flux Φ

Solution

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Review

Ampere’s Circuital Law – (Applying KVL)

The Flux Φ – (Applying KCL)

Series Magnetic Circuits

Air Gaps

Series-Parallel Magnetic Circuits

Determining Flux Φ

Applications

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