Earth Is the Lords
5th Edition
ISBN: 9781121660069
Author: Caldwell, Taylor
Publisher: MCG/CREATE
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Chapter 1, Problem 1.8P
A core with three legs is shown in Figure P1-5. 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 percent increase in the effective area of the air gap due to fringing effects.
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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
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]
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?
Chapter 1 Solutions
Earth Is the Lords
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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- Which of the following statements is false? A. Magnetic flux density is a vector, and the direction of current will be an important determinant of the direction of magnetic flux density. B. When we apply a magnetic field to the material and we want to understand how much magnetized it is, we basically investigate permeability. C. When the current on a wire reaches 3A, the free space permeability and relative permeability will not have an impact on the magnetic flux density as they cancel out each other. D. Biot-Savart Law is necessary when we need to understand the impacts of the characteristics of electric current (e.g., direction, magnitude, etc.) on magnetic field. E. If we alter the length of a current-carrying straight wire, the magnetic field is also altered.arrow_forwardAn iron ring of mean length 100 cm with an air gap of 2 mm has a winding of 500 turns. The relative permeability of iron is 600. When a current of 3 A flows in the winding, determine the flux density. Neglect fringing.arrow_forwarda. If the material is the ideal material, N1I1 = 200, NIA = 100 and NIB = 150 If I am ampersand, what is the flux density in the middle of the air gap? okay? Calculate by drawing the magnetic circuit. b. If the material is not the ideal material (µr), the core material of each winding Find the inductance in terms of parameters c. What is mutual inductance between windings? D. Check the magnetic equivalent circuit of this system that there are no leakage fluxes. draw assuming. New magnetic with leakage fluxes in mind How about a circuit, draw?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_forwardA 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_forward. A mild steel ring of 30 cm mean circumference has a cross-sectional area of 6 cm2and has a winding of 500 turns on it. The ring is cut through at a point so as to provide an air-gap of 1 mm in the magnetic circuit. It is found that a current of 4 A in the winding, produces a flux density of 1 T in the air-gap. Find the relative permeability of the mild steelarrow_forward
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