Explanation Concept used: Write the expression for the average length of the steel. l avg = l e f + l a f + l a b + l b e − l d c ............(1) Here, l avg is the average length of the steel, l e f is the length of the path e f , l a f is the length of the path a f , l a b is the length of the path a b , l b e is the length of the path b e and l d c is the length of the path d c . Write the expression for the magnetic field intensity. H = B μ o μ r ............(2) Here, H is the magnetic field intensity, B is the magnetic flux density, μ o is the relative permeability in the air and μ r is the relative permeability in the medium. Write the relation for the ampere turn. N I = H l ............(3) Here, N is the number of turns of the coil, I is the current flowing in the coil and l is the length. Write the expression for the flux. ϕ = B A ............(4) Here, A is the area. Write the expression for the % error. E % = F m − F t F m × 100 % ............(5) Here, E % is the % error, F m is the measured value and F t is the true value. Calculation: The diagram of the caste steel is drawn as shown in the Figure 1. Substitute 0.2 m for l e f , 0.2 m for l a f , 0.2 m for l a b , 0.2 m for l b e and 8 × 10 − 4 m for l d c in equation (1). l avg = 0.2 m + 0.2 m + 0.2 m + 0.2 m − 8 × 10 − 4 m = 0.7992 m Substitute 150 for N , 2 A for I and 8 × 10 − 4 m for l in equation (3). ( 150 ) ( 2 A ) = H ( 8 × 10 − 4 m ) H = 300 8 × 10 − 4 At/m = 375 × 10 3 At/m Substitute 375 × 10 3 At/m for H , 4 π × 10 − 7 for μ o and 1 for μ r in equation (2). 375 × 10 3 = B ( 4 π × 10 − 7 ) ( 1 ) B = ( 375 × 10 3 ) ( 4 π × 10 − 7 ) = 0.471 T Therefore, the magnetic flux density in air is 0.471 T . The graph of B-H curve is shown in Figure 2. Form the cast steel B-H curve the magnetic field intensity for 0.471 T magnetic flux density in air is 275 At/m . The flux in the air is equal to the flux in the core of the steel. Substitute 0.471 T for B and 2 × 10 − 4 m 2 for A in equation (4). ϕ = ( 0.471 T ) ( 2 × 10 − 4 m 2 ) = 0.942 × 10 − 4 Wb Apply Ampere's circuital law. The equation (3) is written as N I = H steel l steel + H air l air Here, H steel is the magnetic field intensity in the steel, l steel is the length of the average length of the steel, H air is the magnetic field intensity in the air and l air is average length of the gap. Substitute 150 for N , 2 A for I , 275 At/m for H steel , 0.7992 m for l steel , 375 × 10 3 At/m for H air and 8 × 10 − 4 m for l air in the above equation. ( 150 ) ( 2 ) = ( 275 At/m ) ( 0.7992 m ) + ( 375 × 10 3 At/m ) ( 8 × 10 − 4 m ) 300 = 219

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN: 9780133923605

Author: Robert L. Boylestad

Publisher: PEARSON

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Stator and Rotor Magnetic Field

The stator and rotor magnetic field is the resulting magnetic field generated by a system of coils that are symmetrically aligned. They are supplied with polyphase currents. The magnetic field is generated by poly-phase (two or more phases) current or si…

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Chapter 12, Problem 20P

To determine

The magnetic flux ϕ.

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Chapter 12, Problem 19P

Chapter 12, Problem 21P

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Chapter 12 Solutions

Introductory Circuit Analysis (13th Edition)

Ch. 12 - Using Appendix E, fill in the blanks in the...Ch. 12 - Repeat Problem 1 for the following table if...Ch. 12 - For the electromagnet in Fig. 12.34 a. Find the...Ch. 12 - Which section of Fig. 12.35-(a), (b), or (c)-has...Ch. 12 - Find the reluctance of a magnetic circuit if a...Ch. 12 - Prob. 6P Ch. 12 - Find the magnetizing force H for Problem 5 in SI...Ch. 12 - If a magnetizing force H of 600 At/m is applied to...Ch. 12 - For the series magnetic circuit in Fig. 12.36,...Ch. 12 - Find the current necessary to establish a flux of...

Ch. 12 - a. Find the number of turns N1 required to...Ch. 12 - a. Find the mmf (NI) required to establish a flux...Ch. 12 - For the series magnetic circuit in Fig.12.40 with...Ch. 12 - a. Find the current I required to establish a flux...Ch. 12 - Prob. 15P Ch. 12 - Determine the current I1 required to establsh a...Ch. 12 - a. A flux of 0.210-4Wb will establish sufficient...Ch. 12 - For the series-parallel magnetic circuit in Fig....Ch. 12 - Find the magnetic flux established in the series...Ch. 12 - Prob. 20P Ch. 12 - Note how closely the B-H curve of cast steel in...

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