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**Analysis of magnetic circuits**

Tutorial Problems On Analysis of magnetic circuits

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Problem 1 A coils of 200 turns is wound uniformly over a wooden ring having a mean circumference of 600 mm and a uniform cross sectional area of 500 mm2. If the current through the coil is 4 A, calculate: (a) the magnetic field strength, (b) the flux density, and (c) the total flux Problem 2 A mild steel ring having a cross sectional area of 500 m2 and a mean circumference of 400 mm has a coil of 200 turns wound uniformly around it. Calculate: (a) the reluctance of the ring (b) the current required to produce a flux of 800 µWb in the ring. (Given that µr is about 380).

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Problem 3 Figure below shows an iron circuit with a small air gap cut in it. A 6000 turn coil carries a current I=20 mA which sets up a flux within the iron and across the air gap. If the iron cross section is , the mean length of flux path in iron is 0.15 m, =800 in iron and air gap length is 0.75 mm, calculate the air gap flux density. It may be assumed that the flux lines flow straight across the air gap, i.e. air gap cross section is also Answer: 0.16 T

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Problem 4 Find the value of I required to establish a magnetic flux of in the series magnetic circuit as shown in figure below. The relative permeability for the steel is = 1424. Answer I = 4.12 A

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Problem 5 Determine the value of I required to establish a magnetic flux of Wb in the section of the core indicated in figure below. The relative permeability for the steel at region bcde, be, and efab are = 4972, = 4821, and = 2426, respectively. Answer I = 1.76 A

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**Problem 6 The physical parameters of the synchronous motor are:**

Air gap length g = 2 cm, I = 15 A, N = 1200 turns, Rotor pole face area Assume that the rotor and the stator of the synchronous motor have negligible reluctance and neglect fringing. (a.) Draw the magnetic circuit. (b.) Determine the magneto-motive force. (c.) Determine the reluctance of each air gap. (d.) Determine the total magnetic flux in each air gap. (e.) Determine the magnetic flux density in each air gap.

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