Fundamentals of Energy Systems HW 4 Q4 4. Consider the toroid type inductance shown below. It is made from a materialwith a relative permeability of 4,-2500. The average magnetic flux density inthe core is B-1.25 Tesla measured at the mean diameter of the toroid.1. Find the current i applied to the coil to establish this magnetic flux density.2. Find the magnetic flux in the core.3. If a small air gap with the length of 1 mm is cut in the toroid, determinethe required current to produce the same magnetic flux density. (Ignorethe fringing effect at the air gap.)2N=250r1-8 cmr2-12 cm

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Answered: 4. Consider the toroid type inductance…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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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 is shown below. The depth of the core is 5 cm. The other dimensions of the core are as shown in the figure. Find the value of the current that will produce a flux of 0.003 Wb. With this current, what is the flux density at the top of the core? What is the flux density at the right side of the core? Assume that the relative permeability of the core is 1000. 1. - 10 cm--- - 20 cm - 15 cm 500 tums 15 cm 15 cm [1.21 A, 0.4 T, 1.2 T]
The saturation curve of a particular core material shows that at a magnetic field intensity of 1250 At/m and the flux density is 0.80 Tesla. Determine the relative permeability of the core material.
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Consider a ferromagnetic ring (nucleus) that has a mean circumference of 40 cm, 300coiled copper turns and a sectional area of 5 cm2. A current of 2 is appliedA to winding, producing a flux of 1.5 mWb.Determine the permeability of the core material.Determine the relative permeability of the core material.If the ferromagnetic ring has an air gap of 2 mm. Find the required MMFso that the flux density in the gap is 0.5 T.
A magnetic circuit with a cross-sectional area of 20 cm? is to be operated at 50 Hz from a 120 V rms supply. The number of turns required to achieve a peak magnetic flux density of 1.8 T in the core is
A toroidal core with a mean circumference of 100 cm and a cross-sectional area of 10 cm2 is wound with 500 turns of wire. What current would be required to generate a flux of 1 mWb in the core. Assume the core has a relative permeability of 800
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. The amount of current driving the solenoid is 0.1 A. Determine the magnetic flux intensity H in the core. Provide your answer in A/m. Round off to your answer to one decimal.
4. A two-legged magnetic core with an air gap is shown in figure below. The depth of the core is 5 cm, the length of the air gap in the core is 0.07 cm, and the number of turns on the coil is 500. The magnetization curve of the core material is shown next to it. Assume a 5 percent increase in effective air-gap area to account for fringing. How much current is required to produce an air-gap flux density of 0.5 T? What are the flux densities of the four sides of the core at that current? What is the total flux present in the air gap? 10 cm 1.25 1.00 0.75 N- 500 tums 0.07 cm : 30 cm 0.50 0.25 10 cm 0.0 100 1000 30 cm Magnetizing intensity, A turns/m Depth = 5 cm [0.00131 Wb, 0.524 T, 0.262 T, 1.46 A] Flux density, T
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.
Consider the magnetic circuit in Figure. Assuming that the core µ= 1000µo has a uniform cross section of 4 cm2,N= 600 , the flux density in the air gap. 0.2 A L=42 cm 4 = 0.1 cm
2.3

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