# Facts About Magnetic Circuit

#### Facts:

- To derive magnetic flux through a magnetic circuit, a Magnetic Force (mmf) is necessary.
- Magneto motive force can be produced when current flows in a coil of one or more turns. (mmf = N.I)
- H = mmf / l, (AT/m), where: l = length of the magnetic flux path (m)
- Reluctance (ampere/weber) is the property of the magnetic material which opposes the flow of magnetic flux through it.
- Reluctance (S) = mmf / Ð¤ = l / Âµ0 x Âµr x a (For magnetic materials).
- Reluctance (S) = mmf / Ð¤ = l / Âµ0 x a (For Non-magnetic materials).
- Reluctance is inversely proportional to permeance like Resistance is inversely proportional to conductance.
- emf = I x R while mmf = Ð¤ x S
- Ampere turns per unit length of the magnetic flux path for a particular part of the magnetic material can be found out from the standard curve of the materials, plotted as flux density Vs ampere turns per unit length i.e. H (B-H curve of the material), corresponding to the working value of the flux density in that part.
- Total ampere turns = B1/Âµ1.l1 + B2/Âµ2.l2 + B3/Âµ3.l3 + . . .
- In Series parallel magnetic circuit: Total ampere turns required = ampere turns required for the common section + ampere turns required for one parallel path
- In magnetic circuits, the common section generally known as Central Core or Limb.
- Useful flux Ð¤, which flows throughout the magnetic circuit.
- Leakage flux Ð¤l, links partly magnetic circuit and complete its path through air.
- Total flux Ð¤T = Ð¤ + Ð¤l
- The ratio of the total flux produced Ð¤T to the useful flux Ð¤ is called the Leakage Factor or Leakage Coefficient.
- The value of the leakage factor is always greater than unity and varies between 1.15 to 1.25 depending upon the type of magnetic circuit.
- leakage factor = Ð¤T / Ð¤
- When the flux crosses the air gap it tends to bulge out across the edge of the air gap.
- This effect of bulging is called Fringing.
- The effect of fringing is to increase the effective gap area, which in turns reduces the flux density in the air gap.
- If a magnetic material is magnetized in a strong magnetic field, it retains the considerable portion of magnetism even after removal of the magnetic force.
- This phenomenon of lagging of magnetization or flux density B behind the magnetizing force H is known as magnetic hysteresis.
- The magnetic field intensity required to wipe out the residual magnetism Br is called Coercive Force.
- Residual magnetism or remanent flux density Br is defined as the magnetic flux density which still remains in magnetic material even when the magnetizing force is completely removed.
- Hysteresis loop for Hard Steel is quite wide and hence posses high retentivity power and large coercive force.
- This type of material is well suited for permanent magnets and not suitable for rapid reversals of magnetization as in transformers core and choke cores.
- Steel and silicon alloys have a very narrow hysteresis loop.
- Since they have very high permeability and very low hysteresis losses. These materials are more suitable for transformers core and armature cores which are subjected to rapid reversal of magnetization.
- If the magnetization is carried through a complete cycle, the energy wasted is proportional to the area of hysteresis loop.
- Hysteresis Loss is equal to the energy consumed in magnetizing and demagnetizing a magnetic material.
- Dr. Charles Steinmetz suggested an Empirical Formula: Hysteresis loss Ph = Î·Vf.(Bmax)^1.6, Where - Î· = Steinmetz's coefficient, Î· = 275 (Silicon steel), Î· = 500 (Sheet steel), V= Volume (m3), f = frequency of magnetic flux reversal
- When a magnetic material is linked with a variable or alternating flux, an emf is induced in the magnetic material itself, according to Faraday's laws of electromagnetic induction,
- This induced emf circulates a current in the body of the magnetic materials.
- These circulating currents are called Eddy Currents and the power losses due to the flow of this current are called Eddy Current Losses.
- Applications of the eddy current include Eddy Current Braking in induction energy meters and Eddy Current Damping in permanent magnet moving coil instruments.
- Eddy current loss depends upon the value of induced emf and the resistance offered by the magnetic material to the flow of eddy currents.
- The resistance can be greatly increased by Laminating the Material, thereby reducing the magnitude of the eddy current to an appreciable value.
- Eddy current losses: Pe = k (Bmax)^2.f^2.t^2.V, where: k = Eddy current coefficient & its value depends upon the type of magnetic material, t = thickness of material

#### Reference:

V N Mittle and Arvind Mittal, "Basic Electrical Engineering," TATA McGRAW Hill, Tenth Reprint, 2009.

#### Author:

Paramjeet Singh Jamwal was a M.Tech Scholar in Electrical and Instrumentation Engineering Department of Sant Longowal Institute of Engineering and Technology (SLIET), Longowal, Sangrur, Punjab, India (2013-2015).

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