ELECTRIC CIRCUIT ANALYSIS - I
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Transcript of ELECTRIC CIRCUIT ANALYSIS - I
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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