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ELECTRIC CIRCUIT ANALYSIS - I

ELECTRIC CIRCUIT ANALYSIS - I. Chapter 11 – Magnetic Circuits Lecture 6 by Moeen Ghiyas. TODAY’S LECTURE CONTENTS. Review Ampere’s Circuital Law – (Applying KVL) The Flux Φ – (Applying KCL) Air Gaps Series-Parallel Magnetic Circuits Determining Flux Φ.

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ELECTRIC CIRCUIT ANALYSIS - I

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  1. ELECTRIC CIRCUIT ANALYSIS - I Chapter 11 – Magnetic Circuits Lecture 6 by MoeenGhiyas

  2. TODAY’S LECTURE CONTENTS • Review • Ampere’s Circuital Law – (Applying KVL) • The Flux Φ – (Applying KCL) • Air Gaps • Series-Parallel Magnetic Circuits • Determining Flux Φ

  3. Ampere’s Circuital Law – (KVL)

  4. The Flux Φ – (KCL)

  5. Air Gaps • The spreading of the flux lines outside the common area of the core for the air gap in fig (a) is known as fringing. • Neglect this effect of fringing as shown in fig (b) • The flux density of air gap is given by • Where,

  6. Air Gaps • For most practical applications, the permeability of air is taken to be equal to that of free space. The magnetizing force of the air gap is then determined by • and the mmf drop across the air gap is equal to Hglg. An equation for Hg is as follows:

  7. Air gaps • Example – Find the value of I required to establish a magnetic flux of φ = 0.75 x 10-4 Wb in the series magnetic circuit of fig • Solution

  8. Air gaps • Example – Find the value of I, φ = 0.75 x 10-4 Wb • Solution

  9. Series – Parallel Magnetic Circuits • Example – Determine the current I required to establish a flux of φ =1.5 x 10-4 Wb in the section of the core indicated in fig • Solution

  10. Series – Parallel Magnetic Circuits • Example – Determine the current I required to establish a flux of φ =1.5 x 10-4 Wb in the section of the core indicated in fig • Solution

  11. Series – Parallel Magnetic Circuits • Example – Determine the current I required to establish a flux of φ =1.5 x 10-4 Wb in the section of the core indicated in fig • Solution

  12. Series – Parallel Magnetic Circuits • Example – Determine the current I required to establish a flux of φ =1.5 x 10-4 Wb in the section of the core indicated in fig • Solution

  13. Series – Parallel Magnetic Circuits • Example – Determine the current I required to establish a flux of φ =1.5 x 10-4 Wb in the section of the core indicated in fig • Solution

  14. Series – Parallel Magnetic Circuits • To demonstrate that µ is sensitive to the magnetizing force H, the permeability of each section is determined • For section bcde, • For section be, • For section efab,

  15. Determining flux φ • Here NI is given and the flux φ must be found. • This is a relatively straightforward problem if only one magnetic section is involved. Then • For magnetic circuits with more than one section, there is no set order of steps that will lead to an exact solution for every problem on the first attempt.

  16. Determining flux φ • We must find the impressed mmf for a calculated guess of flux φ and then compare this with specified value of mmf. • For most applications, a value within ±5% of the actual Φ or specified NI is acceptable. • We can make a reasonable guess at the value of Φ if we realize that the maximum mmf drop appears across the material with the smallest permeability if the length and area of each material are the same.

  17. Determining flux φ • Example – Calculate the magnetic flux Φ for the magnetic circuit of fig • Solution

  18. Determining flux φ • Example – Find the magnetic flux Φ for the series magnetic circuit of fig for the specified impressed mmf. • Solution

  19. Determining flux φ • Example – Find the magnetic flux Φ • Solution

  20. Determining flux φ • Example – Find the magnetic flux Φ • Solution

  21. Determining flux φ • Example – Find the magnetic flux Φ • Solution

  22. Summary / Conclusion • Review • Ampere’s Circuital Law – (Applying KVL) • The Flux Φ – (Applying KCL) • Series Magnetic Circuits • Air Gaps • Series-Parallel Magnetic Circuits • Determining Flux Φ • Applications

  23. Hysteresis

  24. Hysteresis

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