Magnetic circuits and transformers

Magnetic Circuits and Transformers
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Magnetic Circuits and Transformers Sattar Hussain sattar.hussain@ryerson.ca
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1- Magnetic Field It is customary to represent the magnetic field by means of lines of forces that can be traced as a closed loops exiting at magnetic north pole and entering at magnetic south pole. These line are called flux lines . The flux lines take the least resistance path; that is, they are easier to set up in an iron medium than in the air.
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The total number of flux lines is referred to as magnetic flux ϕ measured in weber (Wb) . The density of flux lines per unit of cross-sectional area perpendicular to the direction of the flux lines is called flux density, B , measured in Wb/m 2 or Tesla (T). The flux ϕ is then defined as the integral of the flux density over some surface area, A. If the flux is uniform over the cross sectional area A, then: = A BdA φ A B . =
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The magnetic resistance that tends to oppose the establishment of magnetic flux lines is referred to as reluctance, . Reluctance of iron bar is much less than air reluctance. Hence, the iron bar is an easier path than air for flux lines. 2- Magnetic Field Produced by Currents A conductor carrying an electric current I exhibits a magnetic field in the space surrounding it.
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The magnetic field is stronger near the conductor and decreases farther a way from it. The magnetic flux, ϕ , increases when the current , I increases. The direction of flux lines is determined by Ampere’s right- hand rule (RHR) . It states: when the thumb points to the current direction, the fingers point to the direction of magnetic field lines.
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Since the cause of magnetic flux is the flow of electric current, for N- turn coil carrying a current I , the induced flux will be as a result of the product NI The quantity NI is called magnetomotive force (mmf) and its unit is ampere-turn (At) ℱ= magnetomotiveforce (mmf )= NI At Replacing the iron core with similar one having shorter mean (average) length , l , while maintaining the same mmf (At), would result in stronger magnetic field. This leads to another quantity called magnetic field intensity , or the magnetizing force H =magnetizing force=ℱ/ l = NI/l At/m
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When the current or the number of turns is increased, the mmf ( ℱ) is increased, resulting in a higher flux ϕ ℱ α ϕ or = ℛϕ Ohm’s law for magnetic circuit similar to Ohm’s law in electric circuit ( V=RI ) thus: ℛ=reluctance=ℱ/ϕ The unit of ℛ is At/ Wb In analogous to the electric resistance , Where, μ is called the permeability of the material A l µ = A l A l R σ ρ = =
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Permeability is a measure of a material’s property that relates to its ability to permits the establishment of the magnetic flux μ = μ r μ o Wb /( A.m )=H/m (H=Henry= Wb /A) Where μ r is the relative permeability μ o is the air permeability = 4 π x 10 -7 H/m The relation between magnetic flux density, B, and magnetic field intensity, H, is: B=μ H
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3- Electromagnetic Induction (Faraday’s Law)
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