Magnetic Circuits - Equivalent Magnetic Circuits
Summary
TLDRThis lecture delves into the concept of equivalent magnetic circuits, drawing parallels with electrical circuits. It explains how magnetomotive force (MMF) and reluctance in a magnetic circuit mirror electromotive force (EMF) and resistance in an electrical circuit. The lecture outlines the process of calculating magnetic field lines using the equivalent magnetic circuit, emphasizing the application of Ohm's law in both domains. It also covers the construction of an equivalent magnetic circuit for an asynchronous machine, highlighting the importance of considering magnetic materials' properties and the distribution of MMF across different reluctances. The lecture concludes with a review of key principles for solving magnetic circuits, such as series and parallel reluctances and Kirchhoff's laws.
Takeaways
- 🔌 The equivalent magnetic circuit is analogous to an electrical circuit, with magnetomotive force (MMF) and reluctance playing roles similar to EMF and resistance, respectively.
- ⚡ Ohm's Law applies to magnetic circuits as well, where MMF is analogous to voltage, and magnetic flux is analogous to electric current.
- 🧲 Reluctance (R) in a magnetic circuit is calculated as R = L / (μA), where L is the mean length of the magnetic path, μ is the permeability, and A is the cross-sectional area.
- 🔗 The magnetic field lines (Φ) are analogous to electric current in an electrical circuit and are driven by the MMF against the reluctance of the medium.
- 🔄 The total MMF in a magnetic circuit is distributed across different reluctances, similar to how voltage is distributed across resistances in series in an electrical circuit.
- 📏 The magnetic field density (B) is the same for all sections of a magnetic circuit if their cross-sectional areas are equal, indicating uniform distribution of magnetic flux density.
- 📉 To draw an equivalent magnetic circuit for an electrical rotating machine, one must identify magnetic field paths, calculate MMFs and reluctances, and then represent them in a circuit diagram.
- 🔍 The BH curves of magnetic materials are used to determine the magnetic field intensity (H) for a given magnetic field density (B) in the circuit.
- 🔄 Kirchhoff's Voltage Law is applied to calculate the total MMF and ampere-turns in a magnetic circuit, which is crucial for determining the current required in the coil.
- 📚 The principles and calculations for magnetic circuits are based on certain assumptions, such as confinement of magnetic field lines within the core and uniform distribution across the cross-sectional area.
Q & A
What is the main focus of the lecture on energy conversion?
-The lecture focuses on providing more details about the equivalent magnetic circuit and its analogy with the electrical circuit.
How does the electrical circuit in the lecture compare to a magnetic circuit?
-The electrical circuit consists of a voltage source (EMF) and a resistance, while the magnetic circuit consists of a coil, current, and a magnetic material core. The magnetomotive force (MMF) or the product of the number of turns and current (NI) in the coil drives the magnetic field lines against the magnetic reluctance of the medium.
What is the Ohm's law equivalent in the magnetic circuit?
-In the magnetic circuit, Ohm's law is represented as MMF = Φ/Reluctance, where MMF is the magnetomotive force, Φ is the magnetic flux, and Reluctance is the opposition to the magnetic flux.
How is the reluctance of a magnetic circuit calculated?
-The reluctance of a magnetic circuit is calculated using the formula Reluctance = L/(μA), where L is the mean length of the magnetic path, μ is the permeability of the medium, and A is the cross-sectional area of the medium.
What is the relationship between the ampere turns (NI) and the EMF in the electrical circuit?
-The ampere turns (NI) in the magnetic circuit are analogous to the EMF in the electrical circuit; both are sources that drive their respective circuits.
Why is it important to consider the magnetic reluctance when analyzing a magnetic circuit?
-Magnetic reluctance is important because it represents the opposition to the magnetic flux, similar to resistance in an electrical circuit. It helps in calculating the magnetic field lines and understanding how the MMF is distributed across different parts of the magnetic circuit.
How does the magnetic field density (B) relate to the magnetic field lines (Φ) in a magnetic circuit?
-The magnetic field density (B) is related to the magnetic field lines (Φ) by the formula B = Φ/A, where A is the cross-sectional area. The magnetic field density is the same for all sections of a series magnetic path if their cross-sectional areas are equal.
What is the significance of Kirchhoff's voltage law in the context of magnetic circuits?
-Kirchhoff's voltage law is used to calculate the total MMF in a magnetic circuit by summing the MMFs across each reluctance in series, which is analogous to calculating the total voltage drop across series resistances in an electrical circuit.
How can the permeability and relative permeability of a magnetic material be calculated?
-The permeability (μ) can be calculated using the formula μ = B/H, where B is the magnetic flux density and H is the magnetic field intensity. The relative permeability is the ratio of the permeability of the material to the permeability of free space (μ₀).
What are the steps to draw the equivalent magnetic circuit for an electrical rotating machine?
-The steps are: 1) Draw the magnetic field paths, 2) Find the MMFs and reluctances along the magnetic field lines, and 3) Draw the equivalent circuit considering the MMFs and reluctances.
What are the main rules used to solve equivalent magnetic circuits?
-The main rules include: 1) Reluctances in series, 2) Reluctances in parallel, 3) Kirchhoff's voltage law, and 4) Kirchhoff's current law.
Outlines
🔌 Introduction to Equivalent Magnetic Circuits
This paragraph introduces the concept of equivalent magnetic circuits and their analogy with electrical circuits. It compares a simple electrical circuit with a voltage source and resistance to a magnetic circuit with a coil, current, and magnetic material core. The magnetomotive force (MMF), represented by the product of the number of turns (N) and the current (I), is likened to the electromotive force (EMF) in an electrical circuit. The reluctance (R) of the magnetic circuit is analogous to electrical resistance, and the magnetic flux (Φ) is compared to the electric current. Ohm's law is adapted for magnetic circuits, with reluctance calculated as the mean length (l) of the magnetic path divided by the product of the permeability (μ) and the cross-sectional area (A). The purpose of the equivalent magnetic circuit is to facilitate the calculation of magnetic flux given the MMF and reluctance.
🧲 Detailed Analysis of Magnetic Circuit Components
The second paragraph delves into the specifics of drawing an equivalent magnetic circuit, using a magnetic circuit with three different magnetic materials of varying lengths as an example. It explains that each section of the magnetic circuit has its own reluctance due to differences in material and dimensions. The magnetic flux (Φ) is constant across all sections of a series magnetic path, but the magnetic field density (B) is only equal if the cross-sectional areas are the same. The total MMF is distributed across the reluctances, with higher reluctance requiring more MMF. The paragraph also discusses how to calculate the magnetic field intensity (H) using the BH curves of the materials and Kirchhoff's voltage law to find the total MMF and current. It concludes with a method for calculating permeability and relative permeability of the magnetic materials and outlines the steps for drawing the equivalent magnetic circuit of an electrical rotating machine, such as an asynchronous machine.
🔍 Assumptions and Calculations in Magnetic Circuits
The final paragraph addresses the assumptions and approximations underlying the analysis and calculations of magnetic circuits. It states that all magnetic field lines are assumed to be confined within the magnetic core and uniformly distributed across the cross-sectional area. It also assumes a linear relationship between electric current and magnetic field linkage. The paragraph reviews the main rules for solving equivalent magnetic circuits, including the treatment of reluctances in series and parallel, and the application of Kirchhoff's voltage and current laws. It concludes the lecture with a summary of these rules and expresses gratitude to the audience for their attention.
Mindmap
Keywords
💡Equivalent Magnetic Circuit
💡Magnetomotive Force (MMF)
💡Reluctance
💡Magnetic Field Lines (Φ)
💡Permeability (μ)
💡Ampere Turns (NI)
💡Ohm's Law for Magnetic Circuits
💡Kirchhoff's Laws
💡Magnetic Material Core
💡BH Curves
Highlights
Introduction to the concept of equivalent magnetic circuits and their analogy with electrical circuits.
Comparison between a simple electrical circuit and a simple magnetic circuit, highlighting the similarities.
Explanation of how Ohm's law applies to magnetic circuits, drawing parallels with electrical resistance.
Definition of magnetomotive force (MMF) and its role in driving magnetic field lines against magnetic reluctance.
The analogy between ampere turns (A-turns) in a magnetic circuit and electromotive force (EMF) in an electrical circuit.
Description of how reluctance in a magnetic circuit is calculated, similar to resistance in an electrical circuit.
The importance of developing equivalent magnetic circuits for calculating magnetic field lines.
Application of Ohm's law and other electrical laws to equivalent magnetic circuits.
Formula for magnetic circuit reluctance and its dependence on the mean length, permeability, and cross-sectional area.
Explanation of how magnetic field lines (Φ) are analogous to electric current in an electrical circuit.
Procedure for converting coils and currents to MMF and mediums to magnetic reluctance in an equivalent magnetic circuit.
Illustration of how to draw an equivalent magnetic circuit for a magnetic circuit with different materials and lengths.
Discussion on the distribution of total MMF across different reluctances in a magnetic circuit.
Explanation of how magnetic field density (B) varies across different sections of a magnetic circuit.
Use of BH curves to find magnetic field intensity (H) for given magnetic field density (B) in core materials.
Calculation of total ampere turns and current in the coil using Kirchhoff's voltage law.
Method to calculate permeability and relative permeability of magnetic circuit sections.
Guidelines for drawing the equivalent magnetic circuit of an electrical rotating machine, such as an asynchronous machine.
Assumptions and approximations made in the development and calculation of magnetic circuits.
Review of main rules for solving equivalent magnetic circuits, including series and parallel reluctances, and Kirchhoff's laws.
Conclusion of the lecture and anticipation for the continuation in the next lecture.
Transcripts
welcome back to the energy conversion
lectures
in previous lectures
i have provided some hints about the
equivalent magnetic circuits
in this lecture
i will provide more details
about the equivalent magnetic circuit
and its analogy with the electrical
circuit
let's start with some comparison between
a simple electrical circuit and a simple
magnetic circuit
the electrical circuit consists of a
voltage source e or
electromotive force emf
and a resistance r
the emf
produces or drives an electrical current
i
against the electrical resistance r
the electric current of this electrical
circuit
can be determined by applying ohm's law
as follows
r is equal to l over rho a
as you can see the resistance r
can be calculated
based on the
length of the resistance l
material conductivity row
and the cross section area of the
resistance a
now let's look at the magnetic circuit
this magnetic circuit
consists of a coil
current and magnetic material core
we learned from previous lectures that
the magnetomotive force mmf
or the impaired turns ni
produces and drives a magnetic field
lines phi
against the magnetic reluctance r of the
medium
it is very clear that the ampere turns
an i
is like the emf of the electrical
circuit
and the reluctance r
of the magnetic circuit is like the
resistance of the electrical circuit
also
the magnetic field lines phi
is like the electric current
of the electrical circuit
based on this analogy between the
electric and magnetic circuits
the magnetic circuit can be represented
by an equivalent circuit called
equivalent magnetic circuit
the purpose
of developing the equivalent magnetic
circuit any practice is to calculate the
magnetic field lines phi if the impaired
turns ni
and the reluctance
are known
it should be noted here that ohm's law
and other important electrical laws such
as care curves voltage and current laws
that apply to electrical circuit can
also be applied to the equivalent
magnetic circuit
based on the analogy with the electrical
circuit
ohm's law of the magnetic circuit can be
represented as
follows also
the reluctance of the magnetic circuit
will be equal to l over mu a
where l is the mean length
of the magnetic path
mu is the permeability of the medium
and a
is the cross section area of the medium
basically
these
new formulas of the magnetic circuit
have been driven using the analogy
between the electric and magnetic
circuit
these formulas
can also be confirmed by using the
following relationships
as you can see
the relationship between n i
phi
and reluctance r
matches and confirms
what i explained earlier
it is very clear from the formula of the
reluctance
that the reluctance r
is directly proportional to the mean
length of the magnetic field path l
and is inversely proportional to the
cross section area a
and the permeability of the medium mu
in general for any equivalent magnetic
circuit
the coils and currents
are converted to mmf
and any medium
must be considered and converted into a
magnetic reluctance r
the medium could be a magnetic material
or non-magnetic material such as air
now assume we have the following
magnetic circuit
this magnetic circuit consists of three
different magnetic materials with
different lengths
the equivalent magnetic circuit can be
drawn as shown
basically
the magnetomotive force f or the ampere
turns ni
represents
the source of the equivalent circuit
that drives or produces the magnetic
field lines phi
each section
of the magnetic circuit
has its own reluctance because they are
from different magnetic materials
and have different lengths
basically
if the length or the permeability
or the cross-section area of the medium
sections
of the magnetic circuit are different
means we have different reactances
another important note
is that the magnetic field lines phi
is same for any series magnetic path
and the equivalent magnetic circuit
however the magnetic field densities b
of the series magnetic path
are same
only
if the cross section area of the
magnetic path
are equals
in other words
if the cross section areas of the
reluctances are different
the magnetic field densities are
different as well
another important note is that the total
magnetomotive force
or the total and paired turns and i
will be distributed across the
reluctances
the higher the reluctance
medium
will require higher and paired turns
across it
comparing with the low
reluctance medium
these distributed ampere turns
are like the voltage drop
across the series resistances of the
electric circuit
now based on what i have explained
the total ampere turns
will be equal to the following
since the magnetic field phi
and the cross section area a are same
for all magnetic circuit sections
the magnetic field density b
for this equivalent magnetic circuit is
same
through the three magnetic materials
and is equal to the following
let's assume we have the bh curves
of the three magnetic materials of the
magnetic circuit as shown
we can find
the magnetic field intensity h for each
of the core materials
for the calculated magnetic field
density b
by applying kirchhoff's voltage law
we can calculate the total and paired
turns
and i as follows
the current
required in the coil can be calculated
as shown
based on the information we have
we can also calculate the permeability
and relative permeability of any
sections
of the magnetic circuit
for instance
the permeability and relative
permeability
of the nickel iron alloy
can be calculated as follows
let's see how to draw the equivalent
magnetic circuit for some electrical
rotating machine
this magnetic circuit in this example
represents a basic structure of
asynchronous machine
the steps to draw the equivalent
magnetic circuit are as follows
first draw the magnetic field paths
second find the mmfs
and the reluctances along the magnetic
field lines
then draw the equivalent circuit
it should be noted here that the
relationships
and calculations
of the magnetic circles in this and
previous lectures
are developed and performed under some
assumptions and approximations
these assumptions are first assume all
magnetic field lines are confined within
the magnetic core
second the magnetic field lines are
uniformly distributed on the cross
section area
and third the relationship between the
electric current and the magnetic field
linkage
is linear
before ending this lecture
let's review the main rules
used to solve the equivalent magnetic
circuits as follows
reluctances in series
reluctances in parallel
care calls voltage law
and kirchhoff's current law
now let's conclude this lecture at this
point and will continue in the next
lecture
thanks for listening
i am essen and nabi and it was a
pleasure sharing this lecture with you
thank you
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