Electric machinery fundamentals
5th Edition
ISBN: 9780073529547
Author: Chapman, Stephen J.
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 1, Problem 1.5P
A 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.
FIGURE P1-2
The core of Problems 1-5 and 1-16.
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A 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?
An iron-cored choke is designed to have an inductance of 12.5 H when operating at a flux density 3 T, the corresponding relative permeability of iron core is 1500. Determine the number of turns in the winding, given that the magnetic flux path has a mean length of 20 cm in the iron core and 2 mm in air-gap that its cross-section is 15 cm2.
* ROUNDING OFF is ALLOWED only in the final answers expressed up to FIVE (5) DECIMALPLACES.
In figure, a magnetic flux of F is generated with a constant current of i. The core material used has a relative permeability of 4000. Assuming that the mean cross sectional area that the magnetic flux passing through in core is A=4 [cm2] and there is no fringing in air gap, N= 1000 turns and i=10 [A], lair=2 [mm].
what is the reluctance in air gap?
what is the total reluctance?
what are the flux and flux density in air gap?
Remember: µ0 = 4πx10-7
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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- In figure, a magnetic flux of F is generated with a constant current of i. The core material used has a relative permeability of 4000. Assuming that the mean cross sectional area that the magnetic flux passing through in core is A=4 [cm2] and there is no fringing in air gap, N= 1000 turns and i=10 [A], lair=2 [mm]. what is the reluctance in air gap? what is the total reluctance? what are the flux and flux density in air gap? Remember: µ0 = 4πx10-7 Answers:Rair = ___________ [At/Wb]Rtotal = _________ [At/Wb]φ = ___________ [Wb]B = ________[T]arrow_forwardBelow you can find a ferromagnetic core and its magnetization curve. If i1=0.4 A and i2= 0.9A, find magnetic flux in the core and the relative permeability under these conditions.arrow_forwardAn autotransformer is shown in Figure P14.68. Assume that all of the flux links all of the turns and that negligible mmf is needed to establish the flux. Determine the values of I1, I2, I3 and V2.arrow_forward
- Q1. A core with three legs is shown in Figure. Its depth is 5 cm, and there are 100 turns on the leftmost leg. The relative permeability of the core can be assumed to be 2000 and constant. What flux exists in each of the three legs of the core? What is the flux density in each of the legs? Assume a 5% increase in the effective area of the air gap due to fringing effects.arrow_forwardFor the magnetic circuit shown in the figure, the iron core with N = 500 turns -Magnetic permeability is 200. its average length is 40 cm -The diameter of the cross-sectional area is 1 cm. Find the current that must pass through the winding to produce 0.5 mWb of flux in a 1mm air-gap magnetic circuit?arrow_forwardA 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.arrow_forward
- A solenoid similar to the figure below, has a core made of cast steel (refer to the figure on the next slide). It has a cross-sectional area of 4cm2 and a mean length of 20cm. The coil has 100turns, and the coil current is 3.2A. Find the following: d)Permeability, μ e) the relative permeability, μr f) the core reluctance, R and g) the flux, Øarrow_forwardAn iron-cored choke is designed to have an inductance of 12.5 H when operating at a fluxdensity 3 T, the corresponding relative permeability of iron core is 1500. Determine thenumber of turns in the winding, given that the magnetic flux path has a mean length of 20cm in the iron core and 2 mm in air-gap that its cross-section is 15 cm2arrow_forwardi. Calculate the current that required to produce a flux density of 0.5 T in the central leg of the core. ii. Calculate the current that required to produce a flux density of 1.0 T in the central leg of the core? Is it twice the current in Q1(b) (i). iii. Calculate the reluctances of the central and right legs of the core under the conditions in Q1(b) (i). iv. Calculate the reluctances of the central and right legs of the core under the conditions in Q1(b) (ii). v. Explain the conclusion that you can make about reluctances in real magnetic cores.arrow_forward
- A solenoid similar to the figure below, has a core made of caststeel (refer to the figure on the next slide). It has a cross-sectional area of 4cm2 and a mean length of 20cm. The coil has 100turns, and the coil current is 3.2A. Find the following:a)magnetomotive force, mmfb)magnetic field intensity, Hc)flux density, B (with graph)arrow_forward1) A ferromagnetic core is shown in Figure 1. The relative permeability of the core isassumed to be 2500 and constant. There is a 5% increase in the effective area ofthe air gap due to fringing effects. The depth of the core is given as 5 cm.a) Calculate the total reluctance, total, of the corearrow_forwardAnswer the following a. How does the relative permeability of a ferromagnetic material vary with magnetomotive force? b. How does a decrease in flux produce an increase in speed in a linear machine? c. Will current be leading or lagging voltage in an inductive load? Will the reactive power of the load be positive or negative? Explain in detail.arrow_forward
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