Electrical Engineering ⇒ Topic : Analysis of Magnetic Circuit

David
 
ANALYSIS OF MAGNETIC CIRCUITS The presence of charges in space or in a medium creates an electric field, similarly the flow of current in a conductor sets up a magnetic field. Electric field is represented by electric flux lines, magnetic flux lines are used to describe the magnetic field.The path of the magnetic flux lines is called the magnetic circuit. Just as a flow of current in the electric circuit requires the presence of an electromotive force, so the production of magnetic flux requires the presence of magnetomotive force (m.m.f).We now discuss some properties related to magnetic flux. (1) Flux density (B) The magnetic flux lines start and end in such a way that they form closed loops. Weber (Wb) is the unit of magnetic flux (Φ). Flux density (B) is the flux per unit area. Tesla (T) or Wb/m^{2}_{ }is the unit of flux density.
where B is a quantity called magnetic flux density in teslas, Φ is the total flux in webers and A is the area perpendicular to the lines in m^{2}. (2) Magnetomotive force MMF A measure of the ability of a coil to produce a flux is called the magnetomotive force. It may be considered as a magnetic pressure, just as emf is considered as an electric pressure. A coil with N turns which is carrying a current of/amperes constitutes a magnetic circuit and produces an mmf of NI ampere turns. The source of flux (Φ) in the magnetic circuit is the mmf. The flux produced in the circuit depends on mmf and the length of the circuit. (3) Magnetic field strength (H) The magnetic field strength of a circuit is given by the mmf per unit length.
The magnetic flux density (B) and its intensity (field strength) in a medium can be related by the following equation B = μ H where μ = μ_{o}μ_{r }is the permeability of the medium in Henrys/metre (H/m), μ_{0} = absolute permeability of free space and is equal to 4π X 10^{7} H/m and μ_{r} = relative permeability of the medium. Relative permeability is a nondimensional numeric which indicates the degree to which the medium is a better conductor of magnetic flux as compared to free space. The value μ_{r} = 1 for air and nonmagnetic materials. It varies from 1,000 to 10,000 for some types of ferromagnetic materials. (4) Reluctance (ℜ) It is the property of the medium which opposes the passage of magnetic flux. The magnetic reluctance is analogous to resistance in the electric circuit. Its unit is AT/Wb. Air has a much higher reluctance than does iron or steel. For this reason, magnetic circuits used in electrical machines are designed with very small air gaps Thus reluctance is a measure of the opposition offered by a magnetic circuit to the setting up of the flux. The reluctance of the magnetic circuit is given by
where l is the length, a is the crosssectional area of the magnetic circuit and μ is the permeability of the medium. From the above equations  
 
Peter
 
Analysis of Magnetic Circuit Consider the magnetic circuit shown in Fig. (a). Suppose the mean length of the magnetic circuit (i.e. length ABCDA) is 1 metres, crosssectional area of the **core is 'a' m^{2} and relative permeability of core material is μ_{r}. When current I is passed through the coil, it will set up flux (Φ) in the material.
According to work law, the work done in moving a unit magnetic pole once around the magnetic circuit (i.e. path ABCDA in this case) is equal to the ampereturns enclosed by the magnetic circuit
The quantity NI which produces the magnetic flux is called the magnetomotive force (m.m.f.) and is measured in ampereturns. The quantity l/aμ_{r}μ_{0}, is called the reluctance of the magnetic circuit. Reluctance is the opposition that the magnetic circuit offers to magnetic flux.
Note that the relationship expressed in eq. (i) has a strong resemblance to Ohm's law of electric circuit (I = E/R). The m.m.f. is analogous to e.m.f. in the electric circuit, reluctance is analogous to resistance and flux is analogous to current. Because of this similarity, eq. (i) is sometimes refened to as Ohm's law of magnetic circuit  
 
!! OOPS Login [Click here] is required for more results / answer