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## Chapter 1 MAGNETIC CIRCUIT

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**Chapter 1**MAGNETIC CIRCUIT**MAGNETIC CIRCUIT**It is the path which is followed by magnetic flux. It is basically ferromagnetic with coil wound around them**Why MAGNETIC CIRCUIT?**It is an important component in the design of electrical machines.**Examples of**Magnetic Circuits**The object of today lecture**It is required to understand the concepts of magnetic circuits By making Analogy between Electric circuit and magnetic circuit**Definitions Related to Electromagnetic Field**• (Unit is Weber (Wb)) = Magnetic Flux • is the number of flux lines • crossing a surface area. B (Unit is Tesla (T)) = Magnetic Flux Density Is the number of flux lines per unit area= /A H (Unit is Amp/m) = Magnetic Field Intensity =**Permeability**It is the degree of magnetization of a material to allow magnetic flux to pass through it. It is analogous to conductivity in an electricalcircuit • relative permeability. • µ permeability of a material • For ferromagnetic materials • For non-ferromagnetic materials o = Permeability of air = 4*10-7 H/m**Magnetic Reluctance**•It is the property of a material which opposes the creation of magnetic flux in it •It is analogous to •resistance in an electricalcircuit •The reluctance of a material is given by**Magneto Motive Force (mmf)F**• It is the external force required to set up the magnetic flux lines within the magnetic material. • The magneto motive force F is equal to the product of the number of turns around the core and the current through the turns of wire.**Magnetic Field Intensity (H)**• It is The magneto motive force per unit length • magnetic field intensity (H) produce a magnetic flux density B (Tesla). • a magnetic flux density is given by:**Magnetic Circuit Calculations**•In magnetic circuit calculations, • it is required to determine • the excitation mmf (F) needed • to establish • a desired flux or • flux density at a given point.**Magnetic Circuit Calculations**The magnetic circuit for the toroidal coil can be analyzed to obtain an expression for flux.Magneto motive force F isWhere the reluctance is`and the magnetic flux is**Magnetic Circuit Calculations**obtain an expression for flux for the shown magnetic circuit**Effect of air gap on a magnetic circuit**obtain an expression for flux for the shown magnetic circuit**Summary of Effect of air gap on a magnetic circuit**• Increase the reluctance. • Greater values of ampere-turn • are required to obtain the same • value of B for circuit without air gap • linearize magnetic circuits • i.e. no saturation**Effect of air gap on Magnetization Curves**Air gap is practically an unavoidable part of any magnetic circuit The B-H loop of a magnetic circuit is affected by the presence of air gap. so greater values of H are required to obtain the same value of B as compared with magnetically materials.**Effects of air gaps on Magnetization Curves**As a result the B-H loop gets slanted,**Example 1**Find magneto motive force (mmf) F in a coil, if the number of turns is 100, and I=2 A. Find the reluctance if the flux produced is 100mWb. Find the permeability if l=50cm and A=0.5 m2 Find the flux density B Find the magnetic force H**Example 2:**Given : i=1 A, N=100, lc=40 cm, A= 100 cm2 r =5000 Calculate : F, H, B, and**Magnetic Circuits (Example 3)**In the shown Magnetic circuit relative permeability of the core material is 6000, its rectangular cross section is 2 cm by 3 cm. The coil has 500 turns. Find the current needed to establish a flux density in the gap of Bgap=0.25 T.**Magnetic Circuits (Solution Example 3)**The current needed to establish a flux density in the gap of Bgap can be calculated as follow: where**Magnetic Circuits (Solution Example 3)**Medium length of the magnetic path in the core is lcore=4*6-0.5=23.5cm, and the cross section area isAcore= 2cm*3cm = 6*10-4 m2the core permeability is**Continue Solution Example 3**The core reluctance isthe gap area is computed by adding the gap length to each dimension of cross-section:thus the gap reluctance is:**Continue Solution Example 3.**Total reluctance isbased on the given flux density B in the gap, the flux isthus magneto motive force isthus the coil current must be**Magnetic Circuits with AC Excitation**• AC Excitation will increase core losses • It is important for the engineer to understand • Why the core losses increase ? • Core losses are important in • determining heating, • temperature rise, • rating and efficiency.**CORE LOSSES (iron losses) are**1-Hysteresis Losses: hysteresis loss is proportional to the loop area (shaded). • To minimize hysteresis loss use materials with thin hysteresis • (Silicon steel)**CORE LOSSES (iron losses) are**2-Eddy Current Losses: Eddy currents are created when a conductor experiences changes in the magnetic field.**CORE LOSSES (iron losses) are**These induced currents cause Eddy Current Losses. These losses can be reduced by using thin sheets of laminations of the magnetic material.**Thus, Iron Losses in Magnetic Circuit are:**• Hysteresis losses • Eddy Current Losses The iron loss is the sum of these two losses