Inductors in Parallel

5 Key excerpts on "Inductors in Parallel"

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  eBook - ePub

  Basic AC Circuits

  • Clay Rawlins(Author)
  • 2000(Publication Date)
  • Newnes

    (Publisher)

  9. Given a circuit of series-connected inductors, the applied voltage, and frequency of the applied voltage, determine the inductive reactance of each inductor, the total inductance, the total current, the voltage across each inductor, the reactive power of each inductor, and the total reactive power in the circuit.

  10. Given a circuit of parallel-connected inductors, the applied voltage, and frequency of the applied voltage, determine the inductive reactance of each inductor, the total inductive reactance, the total inductance, each inductive branch current, the total current, the reactive power of each inductor, and the total reactive power in the circuit.

  INTRODUCTION

  In the last two chapters, discussion concerned the capacitor and how to analyze circuits composed of only capacitors or capacitors and resistors. This chapter is about the remaining passive circuit element — the inductor.

  Figure 8.1 some types of inductors. Basically, any inductor is a coil of thin wire wrapped on a cylinder called the core. The core may be hollow, of laminated paper — an air core — or made of some type of iron — an iron core. Often an inductor is also called a choke or coil. The turns of wire of the inductor are electrically insulated from each other by a thin, non–conductive coating.

  Figure 8.1 Typical Inductors

  As shown in Figure 8.2 the schematic symbol used to represent the inductor resembles what it is — wire wrapped on a core. The inductor’s letter symbol is a capital L which represents linkages — flux linkages.

  Figure 8.2 Schematic Symbol for an Inductor

  An inductor has magnetic properties. Therefore, a brief review of the subject of magnetism should help you understand better the electrical properties of an inductor.

  ELECTROMAGNETIC PROPERTIES

  Faraday’s Discovery

  Recall that in 1831, Michael Faraday showed that when a conductor connected in a closed circuit is moved through a magnetic field, an electron current flows as a result of a voltage induced in the conductor. (In this chapter, like in all other chapters in this book, current flow refers to electron current flow.)

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  Handbook of Power Management Circuits

  • Haruo Kobayashi, Takashi Nabeshima, Haruo Kobayashi, Takashi Nabeshima(Authors)
  • 2016(Publication Date)
  • Jenny Stanford Publishing

    (Publisher)

  6.1 Inductors and Transformers 6.1.1 Inductors 6.1.1.1 Definition of an inductor An inductor is a circuit element that is widely used in electronic circuits. Current flow through a conductive wire produces magnetic flux around the wire, following the Maxwell corkscrew (right-handed screw) rule. The main characteristic of an inductor is the magnetic flux that it produces when a current is passed through it. Although wire conductors also possess inductance components, the value is negligibly small. Chapter 6 Passive Components Yuya Tamai a and Yoshiyuki Ishihara b a Solution R & D Department, R & D Headquarters, Nippon Chemi-Con Corporation, 6-4, Osaki 5-Chome, Shinagawa-ku, Tokyo 141-8605, Japan b Electrical Engineering Department, Faculty of Science and Engineering, Doshisha University, Kyotanabe 610-0321, Japan [email protected], [email protected] Handbook of Power Management Circuits Edited by Haruo Kobayashi and Takashi Nabeshima Copyright © 2016 Pan Stanford Publishing Pte. Ltd. ISBN 978-981-4613-15-6 (Hardcover), 978-981-4613-16-3 (eBook) www.panstanford.com 136 Passive Components Inductance L (H) is the proportionality constant between the current flow I (A) through the wire and the linkage flux Φ , and the relation is expressed as follows: Φ = LI (Wb) (6.1) Here L is the value of inductance. When an inductor is used as a circuit component, it is usually constructed by winding a wire into a coil. This case, inductance is expressed as follows: L = n / R m (H) (6.2) Here, n is the number of turns and R m is the magnetic reluctance (A/Wb). Magnetic reluctance, R m , is given by R m = l /( μS ) (A/Wb) (6.3) Here, l is the average magnetic path length (m), μ is the permeability (H/m), and S is the cross-sectional area of the magnetic path (m 2 ).

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  Electronics and Electronic Systems

  • George H. Olsen(Author)
  • 2013(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  ., _ Induced voltage (e) in the secondary coil Rate of change of current in the primary When inductors are connected in series the total inductance is calculated in the same manner as that used for resistors in series. Since each inductor contributes to the opposition to change of current the total inductance, L, is equal to the sum of the individual inductors. L = L x + L 2 + L 3 . . . If, however, mutual inductance exists between the individual coils, then the total inductance will depend upon the relative connections of the coils. If the magnetic fields are mutually assisting then the total inductance is given by L = L x + L 2 + 2Af ; whereas if the fields are opposing L = L x + L 2 - 2M. Inductors in Parallel can be represented by a total inductance, L, given by L L L2 L$ provided no magnetic coupling exists between coils. Chapter 3 Basic circuit theory In the past, those studying electronics have found circuit theory to be one of the less attractive aspects of the subject. This has been largely because many tedious algebraic manipulations and arithmetic calculations were involved. Nowadays all colleges and universities are well-equipped with computers, and many students possess their own microcomputers. Much of the tedium of calculation can therefore be avoided by using readily available software packages. Many of the solutions to problems posed later in this chapter, and elsewhere in the book, have been obtained with the aid of a BBC Model B computer. In the field of scientific computers the BBC instrument is very modest; nevertheless it is sufficiently powerful to tackle many of the problems commonly encountered by students embarking on their studies of electronic circuits. Those wishing to write their own programs cannot, of course, do so unless they understand the basic principles of the circuit network analyses.

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  Electrical Transformers and Rotating Machines

  • Stephen Herman(Author)
  • 2016(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. UNIT 3 INDUCTANCE IN ALTERNATING-CURRENT CIRCUITS 5 7 8. When inductors are connected in series the total inductance is equal to the sum of all the inductors. 9. When inductors are connected in parallel the reciprocal of the total inductance is equal to the sum of the reciprocals of all the inductors. 10. The current lags the applied voltage by 90° in a pure inductive circuit. 11. All inductors contain some amount of resistance. 12. The Q of an inductor is the ratio of the inductive reactance to the resistance. 13. Inductors with a Q of 10 are generally considered to be “pure” inductors. 14. Pure inductive circuits consume no true power or watts. 15. Reactive power is measured in VARs. 16. VARs is an abbreviation for volt-amps-reactive. Review Questions 1. How many degrees are the current and voltage out of phase with each other in a pure resistive circuit? 2. How many degrees are the current and voltage out of phase with each other in a pure inductive circuit? 3. To what is inductive reactance proportional? 4. Four inductors, each having an inductance of 0.6 H, are connected in series. What is the total inductance of the circuit? 5. Three inductors are connected in parallel. Inductor 1 has an induc-tance of 0.06 H; inductor 2 has an inductance of 0.05 H; and induc-tor 3 has an inductance of 0.1 H. What is the total inductance of this circuit? 6. If the three inductors in question 5 were connected in series, what would be the inductive reactance of the circuit? Assume the induc-tors are connected to a 60-Hz line. 7. An inductor is connected to a 240-V, 1000-Hz line.

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  Electrical and Electronic Principles

  Volume 3

  • S.A. Knight(Author)
  • 2014(Publication Date)
  • Newnes

    (Publisher)

  Figure 4.1 shows the general circuit details. There is one other basic difference between series and parallel circuit considerations and that lies in the choice of a reference phasor. In series circuits where, as we have seen, the current is common to all parts of the circuit, we have taken the current as our reference phasor. In parallel circuits the applied voltage V is common to all branches of the circuit ; as a consequence we now choose Fas our reference phasor and relate the various branch currents I x , I 2 etc to it in their respective magnitudes and phases. Further, the total circuit current / is the phasor sum of the individual branch currents, so that / = Λ + / 2 + These branch currents are, or course, given by the ratio of the applied voltage V (common to all branches) and the branch impedances Z x , Z 2 etc. Hence V V V / = - = - + - + Z Z, Z 2 68 I v Figure 4.1 Alternating current: parallel circuits 69 from which, by elimination of the common factor V, we arrive at the impedance formula given earlier above. To sum up: when drawing phasor diagrams for parallel circuits, we draw the applied voltage phasor as reference and set off from it the phasors for the various branch currents, scaled (if necessary) to their proper magnitudes and positioned to their proper phase angles relative to K, lagging or leading as the case may be. In an inductive circuit a lagging current will then appear in the fourth quadrant, i.e. φ will be negative. For a capacitive circuit a leading current will appear in the first quadrant so that φ will be positive. The most simple parallel combinations are those of resistance in parallel with either a pure inductance or capacitance, and we shall begin our study with these elementary examples. RESISTANCE AND Figure 4.2(a) shows the circuit diagram with the branch impedances INDUCTANCE and currents indicated. The inductance branch is, of course, purely reactive in this instance.

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