In this topic, you study Magnetic Circuit.
The magnetic circuit consists of the magnetic path followed by the magnetic flux.
An electric circuit is the path provided for electric current. On similar lines, the magnetic circuit can be defined as the closed path traversed by the magnetic flux. In the electrical circuit, various electrical quantities like current, e.m.f. and resistance can be easily calculated with the help of the simple Ohm’s law. In magnetic circuit also, it is possible to determine the values of different magnetic quantities associated with the circuit with the help Of simple quantitative relations existing between them. Now, let us study these quantities and quantitative relations existing between them. For that, consider the simple magnetic circuit shown in Fig. 4.9.Fig. 4.9: Simple magnetic circuit. The circuit consists of an iron ring of cross-sectional area ‘a’ square metres and mean circumference (length of the mean magnetic path) ‘l’ metres. A coil of ‘N’ turns is wound on it. Let
Current flowing through the coil (in amperes)
Absolute and relative permeabilities of the magnetic material of the ring.
Then, magnetic field strength inside the solenoid will be,
— amperes / metre
Now, using the Equation (4.10), the flux density in the ring will be given by
B = uH tesla
Substituting the value of H in the above expression, we get
Total flux in the ring,
In the above expression, the term ‘NI’ is known as magnetomotive force (M.M.F.) and
the term is called the reluctance of the magnetic circuit.
The above expression is quite similar to the fol owing expression for electric circuit.
Obviously, the quantities m.m.f. and reluctance in the magnetic circuit are analogous to the quantities e.m.f. and resistance in an electric circuit. The significance of these and other quantities associated with the magnetic circuit will now be discussed in the following section.
Define the following:
(a) Magnetomotive force, (b) Ampere turns, (c) Reluctance, (d) Permeability, (e) Magnetic leakage, (f) Residual magnetism, (g) Permeance, (h) Intensity of agnetisation, (i) Susceptibility.
(a) Magetomotive force (m.m.f.). The magnetomotive force is defined as the force which compels the magnetic lines of force to complete their path. It is denoted by F, in m.k.s. system of unit, its unit is AT (ampere turns). It is similar to that of e.m.f. in electrical circuit.
(b) Ampere turns. It is the product of current flowing through the coil and the number of turns in that coil. It’s symbol is IN or AT.
Ampere turns Current x No. Of turns in the coil.
For example, if a coil has 100 turns and carrying 0.5 amp Current. then the ampere turns are
= 0.5 x 100 = 50 AT
(c) Reluctance. It is the opposition offered by the magnetic path to establish the magnetic flux in the magnetic circuit. It is represented as Rel. It is similar to that of the resistance in the electrical circuits.
Reluctance = Magnetomotive force / Magnetic flux
Its unit is AT/Wb. The reluctance of the magnetic path is directly proportional to the length of the magnetic path and inversely proportional to the area Of cross-section.
(d) Permeability (p). It is the ratio of the magnetic flux produced in a magnetic substance to the magnetic flux produced in the air or vacuum, by the same coil. Its symbol is g. The permeability of the non-magnetic substances is less than one and of the magnetic substances more than one.
So the permeability = The magnetic flux produce in the medium / (The flux produced in the vacuum or air by the same coil)
In terms of magnetic flux density and magnetising force it is given as
B Magnetic flux density / H Magnetising force
(e) Magnetic leakage. Whenever the magnetic lines of force takes some other path then the desired one, it is called the magnetic leakage. The sum of all the lines of force which cannot be utilized for doing useful work, because their path takes them away from the desired one, are called leakage flux.
Leakage factor. As shown in Fig. 11.20 the flux passing through the air gap between two poles is the useful flux and this flux is used in electric machine, so flux which does not take the required path and can not be utilized is known as leakage flux. The total flux is the sum of the leakage flux and the useful flux.
Fig. 11.20. Magnetic flux.
The leakage factor is defined as the ratio of total flux to the useful flux.
Leakage factor = Total flux produced / Useful flux
The leakage factor is always more than one. It is generally 1.1 or 1.15.
(f) Residual magnetism. It is the magnetism left in a magnetic substance after removing the magnetomotive force or the lagging of the magnetism behind the magnetising force is called the residual magnetism. It is used in the generator for producing the initial voltages etc.
(g) Permeance. It is the property of the magnetic circuit which helps in establishing the magnetic flux. It is the reciprocal of the magnetic reluctance and similar to that of the conductance in electric circuits.
It is denoted by letter p.
The unit is Wb/AT.
(h) Intensity of magnetisation. It is defined as the pole strength developed per unit area of the magnet. Let a magnet has the pole strengthas m, pole face area as A. Then the intensity of magnetisation is Wb/m2
The unit is Wb/m2.
(ii) Susceptibility. It is defined as the ratio of the intensity of magnetisation to the magnetising force. It is denoted by letter K.
k = I Intensity of magnetisation / Magnetising force
Retentivity. The property of retaining the magnetism by a magnetic substance is called the retentivity. The retentivity of steel is higher than the retentivity of iron.
Magnetising force. It is defined as the magnetomotive force per unit length. It is represented by H and
Magnetomotive force per unit length = IN / l
The unit is AT/m.
Derive an expression for the ampere-turms required for a
single and composite circuit?
Let in any magnetic circuit,
I = Current to energise the coil in amp.
N = Number Of turns in the coil.
The flux established in Wb. I-Arnperøs
I The length of the path.
Permeability in free space or vacuum.
g r Relative permeability.
Flux = m.m.f /Reluctance
The m.m.f. = IN
Similarly for a composite circuit, let Al, .A2 and .A3 be the area of cross section and Il, I2 and I3 the lengths respectively, the total ampere turns can be determined,
Total
and
or
Obviously
so
Total reluctance