CHAPTER 15: MAGNETIC CIRCUITS
1.A mild-steel ring of mean circumference 400 mm and average cross-sectional area 500 mm2, is uniformly wound using an insulated conductor of 200 turns. Calculate (a) the reluctance of the ring, and (b) the current required to produce a flux of 800 μWb within the ring. Take the relative permeability of mild steel as 380. [Answer: (a) 1.68MA/Wb]
2.A current of 3 A passes through a coil of 1000 turns wound around an iron ring of mean circumference 400 mm and cross-sectional area 400 mm2. If the ring has a relative permeability of 80, calculate the (a) magnetic field strength, (b) flux density, and (c) flux. [Answer: (a) 7.5 kA/m; (b) 754 mT; (c) 302 μWb]
3.A ferromagnetic ring, having a relative permeability of 2500, has a mean diameter of 100 mm, and an average cross-sectional area of 300 mm2. Calculate the (a) the reluctance of the ring, and (b) the reluctance of a 1-mm long air gap cut into the ring. [Answer: (a) 333 kA/Wb; (b) 2.65 MA/Wb]
4.An iron ring, of mean circumference 800 mm, is uniformly-wound with 500 turns of insulated wire. When a current of 1 A is passed through the coil, a flux density of 1.1 T is achieved. Find the relative permeability of the iron core. [Answer: 1400]
5.An iron ring, uniformly wound with 480 turns, has a mean circumference of 1200mm and a cross-sectional area of 80 mm2. When a current of 2 A is passed through the winding, the resulting flux is 1 mWb. What is the relative permeability of the ring for this particular flux density? [Answer: 12440]
6.A magnetic circuit consists of an iron ring of mean length 2500 mm and an average cross-sectional area of 500 mm2, together with an air gap of 4 mm. To allow for any fringing that might occur in the air gap, assume that the flux density within the metal ring must be 1.1 times greater than that required within the air gap.What magnetic field strength is required to produce a flux of 0.5 mWb within the air gap? The magnetic circuit is manufacted from a material whose magnetising curve may be constructed from the following table.
H / (A/m) / 500 / 600 / 800 / 1000B / T / 1.01 / 1.09 / 1.17 / 1.19
[Answer: 293 A/m]
7.A composite magnetic circuit comprises three parts in series:
a.a length of 800 mm and cross-sectional area of 60 mm2.
b.a length of 70 mm and cross-sectional area of 80 mm2.
c.an air gap of length of 0.5 mm and cross-sectional area 60 mm2.
Parts a. and b. are manufactured from a material whose magnetisation curve can be constructed from the following table:
H / (A/m) / 100 / 210 / 340 / 500 / 800 / 1500B / T / 0.2 / 0.4 / 0.6 / 0.8 / 1.0 / 1.2
Neglecting any leakage or fringing, calculate the current necessary, in a coil of 4000 turns, wound on part b. of the magnetic circuit, to produce a flux density of 0.7 T in the airgap. [Answer: 82.5 mA]
8.Use the B-H curvefor cast iron, illustrated below, to answer the questions that follow:
(a)Determine the relative permeability of a sample of cast iron, in which a flux density of 0.4 T has been established. [Answer: 212]
(b)Determine the relative permeability of a sample of cast iron, in which a flux density of 0.8 T has been established. [Answer: 91]
(c)Determine the relative permeability of a sample of cast iron, in which a magnetic field strength of 4500 A/m has been established. [Answer: 124]