1. A magnetic circuit containing a ferromagnetic core with an air-gap is shown in Fig. 1.1. The ferromagnetic core has a square cross-section (wxw) and is made from a material with a relative permeability 12000. The core is excited by two coils: Coil 1 (N₁ = 1000 turns, current 1 A) and Coil 2 (N2 = 780 turns, current 12). The required magnetic flux density in the air-gap is B, = 2.2 T. I₁=1 A H-12000 N₁ = 1000 turns Air-gap width 5=2 mm (drawing not to scale) N₂ = 780 turns h=0.125 m w=0.012 m d=0.25 m Figure 1.1. (a) In magnetic circuit analysis, what is meant by the term 'fringing', and how are the effects of fringing usually accounted for in the calculation process? (b) Calculate the mean flux path length l of the magnetic core. (c) Calculate the reluctance Rc (H-1) of the magnetic core. (d) Calculate the reluctance R, (H-1) of the air-gap. (Do not ignore fringing.) (e) Why is it frequently possible to ignore the reluctance of the core in magnetic circuits that contain an air-gap? (f) Calculate the magnetic flux + (Wb). (g) Calculate the magnetic field intensity Hc (A/m) in the core.

1. A magnetic circuit containing a ferromagnetic core with an air-gap is shown in Fig. 1.1. The ferromagnetic core has a square cross-section (wxw) and is made from a material with a relative permeability 12000. The core is excited by two coils: Coil 1 (N₁ = 1000 turns, current 1 A) and Coil 2 (N2 = 780 turns, current 12). The required magnetic flux density in the air-gap is B, = 2.2 T. I₁=1 A H-12000 N₁ = 1000 turns Air-gap width 5=2 mm (drawing not to scale) N₂ = 780 turns h=0.125 m w=0.012 m d=0.25 m Figure 1.1. (a) In magnetic circuit analysis, what is meant by the term 'fringing', and how are the effects of fringing usually accounted for in the calculation process? (b) Calculate the mean flux path length l of the magnetic core. (c) Calculate the reluctance Rc (H-1) of the magnetic core. (d) Calculate the reluctance R, (H-1) of the air-gap. (Do not ignore fringing.) (e) Why is it frequently possible to ignore the reluctance of the core in magnetic circuits that contain an air-gap? (f) Calculate the magnetic flux + (Wb). (g) Calculate the magnetic field intensity Hc (A/m) in the core.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Similar questions

A ferromagnetic core in the shape of a doughnut has a cross-sectional area of 0.11 m2 and an average length of 1.4 m. The permeabil ity of the core is 1.206 × 10-3 Wb/A-t. m. Determine the reluctance of the magnetic circuit
Problem 4 The magnetic circuit shown in the figure has two windings and two air gaps. The core can be be of infinite 8: |- Core, u o0 Arca A2 assumed to permeability. dimensions are indicated in the The core Area A N turns figure. inductances of windings 1 and 2 Find the self- 81 Na turas and the mutual inductance between the windings.
An iron core 0.4 m long and 5 cm2is wound with 300 turns. When a current of 0.5A flows in the coil, how much is the inductance of the coil. Assume the core has a permeability of 2500.
A flux of 0.0016 Wb flows in a silicon sheet steel coil/core. The arrangement appears as shown below with the following dimensions: Ac = 0.0025 m? Core/gap area: Flux path length: le = 0.350 m lg = 0.0015 m N = 500 Air gap length: Number of turns: %3D A. What is the current, I, through the winding? B. What is the energy stored in the inductance? C. Assume that the current is given by i =9.75 sin (3147) A. What is the RMS voltage that would appear across the winding? D. Assume that the gap is removed from the arrangement with the flux path remaining at 0.350 m. For a flux of 0.0016 Wb, what is the inductance of the arrangement? E. What is the energy stored in the inductance with the gap removed?
Please answer all parts of the question with step by step working and explanantions so i understand the questions and solution better thank you.
Question 1 A ferromagnetic core with a relative permeability of 1500 is shown in Figure 2. The dimensions are as shown in the diagram, and the depth of the core is 7 cm. The air gaps on the left and right sides of the core are 0.070 and 0.020 cm, respectively. Because of fringing effects, the effective area of the air gaps is 5 percent larger than their physical size. If there are 400 turns in the coil wrapped around the center leg of the core and if the current in the coil is 1.0 A, what is a) the flux in each of the left, center, and right legs of the core? b) the flux density in each air gap? 7 cm ст ст 30 cm 30 cm 7 cm 400 turns 0.05 cm 30 cm 0.07 cm 7 cm Core depth = 7 cm Figure 2
A ten-turn solenoid has a ferromagnetic core with a relative permeability of 10,000. The length of the solenoid is l=10 cm and its cross section area is A=1 cm2. Determine the inductance L in mH. Round off to your answer to one decimal.
A.With the aid of a diagram, describe fringing, and explain the impact that it has on the relevant magnetic circuit parameter. B. A coil of 1500 turns give rise to a magnetic flux of 2.5 mWb when carrying a certain current. If this current is reversed in 0.2 s, what is the average value of the e.m.f. induced in the coil? C.Define Mutual Inductance.Two coils are connected in series and their total inductance is measured as 0.12 H, and when the connection to one coil is reversed, the total inductance is measured as 0.04 H. If the coefficient of coupling is 0.8, determine:The self-inductance of each coil, and the mutual inductance between the coils.
A ferromagnetic core with a relative permeability of 1500 is shown in the following figure. The depth of the core is 5 cm. Because of fringing effects, the effective area of the air gaps is 5 percent larger than their physical size. If there are 300 turns in the coil wrapped around the center leg of the core, and if the current in the coil is 1.25 A, find the magnetic flux and the field density in all three legs of the core, as well as the magnetic flux and flux density in the two air gaps.
A ferromagnetic core with a relative permeability of 1500 is shown in the Figure. The dimensions are shown in the diagram, and the depth of the core is 5cm. The air gaps on the left and right sides of the core are 0.050 and 0.070 cm, respectively. Because of the fringing effects, the effective area of the air gaps is 5 percent larger than their physical size. If there are 300 turns in the coil wrapped around the center leg of the core and if the current in the coil is 1.0 A, what are the flux values for the left, center, and right legs of the core? What is the magnetic field in each air gap? |7 cm 7 cm 7 cm to 30 cm 30 cm 7 cm 30 cm 0.07 cm 300 turns 0.05 cm 7 cm Core depth = 5 cm
10 Given a common magnetic core whose length is 100 cm, its cross-sectional area is 25 cm square. The relative permeability of the core material is 5000. Two coils are tightly wound on the core. N1 =1000 turns and N2 = 500 turns. The self-inductance of coil N1 will be: [ 7.85 m H 15.7 m H 3.927 m H 5.17 mH
Two identical coils are wound on a ring-shaped iron core that has a relative permeability of 500. Each coil has 100 turns, and the core dimensions are: cross- sectional area A=3 cm2 and magnetic path length l=20cm. Assume k=0.5. Calculate: a. Mutual inductance b. Total inductance in series if their fields reinforce.