Magnetic Circuits - Equivalent Magnetic Circuits

Summary

This 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

00:00

🔌 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.

05:02

🧲 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.

10:03

🔍 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.

Keywords

💡Equivalent Magnetic Circuit

An equivalent magnetic circuit is a conceptual model used to simplify the analysis of magnetic systems by representing them with an analogy to electrical circuits. It helps in calculating the magnetic field lines (Φ) when the magnetomotive force (MMF) and reluctance are known. In the video, the concept is central to understanding how magnetic circuits can be analyzed using principles similar to those of electrical circuits, such as Ohm's law.

💡Magnetomotive Force (MMF)

Magnetomotive force, often represented as MMF, is the force that drives the magnetic field lines through a magnetic circuit, analogous to voltage in an electrical circuit. It is the product of the number of turns (N) and the current (I) in a coil. The video explains that MMF is crucial in the equivalent magnetic circuit as it is the driving force behind the magnetic field lines.

💡Reluctance

Reluctance is a measure of how much a material resists the establishment of a magnetic field and is the magnetic counterpart to electrical resistance. It is calculated using the formula R = L/(μA), where L is the length of the magnetic path, μ is the permeability of the medium, and A is the cross-sectional area. The video emphasizes that reluctance is directly proportional to the length and inversely proportional to the permeability and cross-sectional area of the medium.

💡Magnetic Field Lines (Φ)

Magnetic field lines, denoted as Φ, represent the path of the magnetic field in a magnetic circuit. They are analogous to the electric current in an electrical circuit. The video script explains that the total magnetic field lines are the same for any series magnetic path in an equivalent magnetic circuit, similar to how current is the same through all components in series in an electrical circuit.

💡Permeability (μ)

Permeability is a measure of a material's ability to support the formation of a magnetic field. It is a property of the medium through which the magnetic field lines pass. The video mentions that permeability is an essential factor in calculating reluctance, and different materials have different permeability values, affecting how they behave in a magnetic circuit.

💡Ampere Turns (NI)

Ampere turns refer to the product of the number of turns in a coil and the current flowing through it, which is analogous to the electromotive force (EMF) in an electrical circuit. The video script uses this concept to explain how the MMF is generated in a magnetic circuit, driving the magnetic field lines against the reluctance of the medium.

💡Ohm's Law for Magnetic Circuits

Ohm's law for magnetic circuits is an adaptation of Ohm's law from electrical circuits, used to relate MMF, magnetic field lines, and reluctance in a magnetic circuit. The video script uses this law to demonstrate how the principles of electrical circuits can be applied to magnetic circuits, allowing for the calculation of magnetic field lines given the MMF and reluctance.

💡Kirchhoff's Laws

Kirchhoff's laws, including Kirchhoff's voltage law (KVL) and Kirchhoff's current law (KCL), are fundamental laws in circuit analysis that are also applicable to magnetic circuits. The video script explains how these laws can be used to calculate the total MMF and the distribution of MMF across different sections of a magnetic circuit, similar to how voltage and current are distributed in an electrical circuit.

💡Magnetic Material Core

A magnetic material core is a component in a magnetic circuit that provides a path for the magnetic field lines. The video script discusses how different magnetic materials with varying lengths and permeabilities can be part of a magnetic circuit, and their reluctances must be considered when drawing the equivalent magnetic circuit.

💡BH Curves

BH curves, or hysteresis curves, represent the relationship between the magnetic field intensity (H) and the magnetic flux density (B) in a material. The video script mentions using BH curves to find the magnetic field intensity for a given magnetic flux density in the core materials of a magnetic circuit, which is essential for determining the behavior of the magnetic materials under different MMFs.

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