Electric machinery fundamentals
5th Edition
ISBN: 9780073529547
Author: Chapman, Stephen J.
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Textbook Question
Chapter 1, Problem 1.13P
A core with three legs is shown in Figure P1-10. Its depth is 5 cm, and there are 400 turns on the center leg. The remaining dimensions are shown in the figure. The core is composed of a steel having the magnetization curve shown in Figure 1-10c. Answer the following questions about this core:
- What current is required to produce a flux density of 0.5 T in the central leg of the core?
- What current is required to produce a flux density of 1.0 T in the central leg of the core? Is it twice the current in part (a)?
- What are the reluctances of the central and right legs of the core under the conditions in part (a)?
- What are the reluctances of the central and right legs of the core under the conditions in part (b)?
- What conclusion can you make about reluctances in real magnetic cores?
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A ferromagnetic core is shown in Figure Pl-2. 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 0.005 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 800.
1-5.
10 cm-
5em
20 em
15 cm
15 cm
15 cm
Coe depth - Scm
SOLUTION There are three regions in this core. The top and bottom form one region, the left side forms a
second region, and the right side forms a third region. If we assume that the mean path length of the flux
is in the center of each leg of the core, and if we ignore spreading at the corners of the core, then the path
lengths are I, = 2(27.5 cm) = 55 cm, I, = 30 cm, and /, = 30 cm. The reluctances of these regions are:
ferromagnetic
core is shown in Figure P1-2.
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 0.005 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 800.
-10cm-
-20 cm-
500 turns
a.
670 kA t/Wb
b. 330 kA t/Wb
c.
500 kA t/Wb
d.
256 kA t/Wb
Core depth = 5 cm
15cm
+
15cm
15cm
5
E
Question 1
A ferromagnetic core is shown in Figure 1. The depth of the core is 5 cm. The other dimensions
of the core are as shown in the figure.
a) Find the value of the current that will produce a flux of 0.005 Wb.
b) With this current, what is the flux density at the top of the core?
c) What is the flux density at the right side of the core? Assume that the relative
permeability of the core is 1000.
cm
-10 cm--
20 cm
15 cm
500 turns
15 cm
15 cm
Core depth 5 cm
Figure 1
Chapter 1 Solutions
Electric machinery fundamentals
Ch. 1 - What is torque? What role does torque play in the...Ch. 1 - What is Amperes law?Ch. 1 - What is magnetizing intensity? What is magnetic...Ch. 1 - How does the magnetic circuit concept aid in the...Ch. 1 - What is reluctance?Ch. 1 - What is a ferromagnetic material? Why is the...Ch. 1 - How does the relative permeability of a...Ch. 1 - Prob. 1.8QCh. 1 - What are eddy current losses? What can be done to...Ch. 1 - Why are all cores exposed to ac flux variations...
Ch. 1 - What is Faraday law?Ch. 1 - What conditions are necessary for a magnetic field...Ch. 1 - What conditions are necessary for a magnetic field...Ch. 1 - Prob. 1.14QCh. 1 - The linear machine in Figure 1-19 is running at...Ch. 1 - Just how does a decrease in flux produce an...Ch. 1 - Will current be leading or lagging voltage in an...Ch. 1 - What are real, reactive, and apparent power? What...Ch. 1 - What is power factor?Ch. 1 - Prob. 1.1PCh. 1 - A flywheel with a moment of inertia of 4kgm2 is...Ch. 1 - A force of 10 N is applied to a cylinder of radius...Ch. 1 - A motor is supplying 50Nm of torque to its load....Ch. 1 - A ferromagnetic core is shown in Figure P1-2. The...Ch. 1 - A ferromagnetic core with a relative permeability...Ch. 1 - A two-legged core is shown in Figure P1-4. The...Ch. 1 - A core with three legs is shown in Figure P1-5....Ch. 1 - A two-legged core is shown in Figure P1-4. The...Ch. 1 - A wire is shown in Figure P1-7 that is moving in...Ch. 1 - Repeat Problem 1-10 for the wire in Figure P1-8.Ch. 1 - Prob. 1.12PCh. 1 - A core with three legs is shown in Figure P1-10....Ch. 1 - A two-legged magnetic core with an air gap is...Ch. 1 - A transformer core with an effective mean path...Ch. 1 - The core shown in Figure P1-2 has the flux shown...Ch. 1 - Prob. 1.17PCh. 1 - Prob. 1.18PCh. 1 - Prob. 1.19PCh. 1 - Demonstrate that Equation (1-59) can be derived...Ch. 1 - Prob. 1.21PCh. 1 - Prob. 1.22PCh. 1 - For the linear machine of Problem 1-22: When this...
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- 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 800arrow_forwardA 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]arrow_forward1.Consider the magnetic core below.All dimensions are shown on the figure. The core is made up of legs with 2 different cross-sectional areas.The depth of core is 10cm.The relative permeability of the core is 2000. The current in the magnetising coil is 1 A. The number of turns of the coil is 2000.Calculate: (i)the reluctances and draw the magnetic circuit (ii)the flux in the core (iii)Flux densities B and field intensities H in legs having different cross-sectional areas. (iv)Verify Ampere's Law. Depth: 10 cm I=1A 20cm 2000 Turns 65cm 15cm 15cm 50cm 15cm ndo un ofarrow_forward
- show thatvthis is a magnetic flux density: then prove and interpret it with reasons on each steparrow_forwardQuestion 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 2arrow_forwardA core with three legs is shown in the figure below. Its depth is 5 cm, and there are 400 turns on the centre leg. The remaining dimensions are shown in the figure. The core is composed of steel having the magnetization curve is also given below. Answer the following questions about this core: 1. What current is required to produce a flux density of 0.5 T in the central leg of the core? 2. What current is required to produce a flux density of 1.0 T in the central leg of the core? Is it twice the current in part (a)? 3. What are the reluctances of the central and right legs of the core under the conditions in part (a)? 4. What are the reluctances of the central and right legs of the core under the conditions in part (b)? 5. What conclusion can you make about reluctances in real magnetic cores?arrow_forward
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