Inductance

10 Key excerpts on "Inductance"

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  eBook - ePub

  Basic Electricity

  • U.S. Bureau of Naval Personnel(Author)
  • 2012(Publication Date)
  • Dover Publications

    (Publisher)

  CHAPTER 10 Inductance

  The study of Inductance presents a very challenging but rewarding segment of electricity. It is challenging in the sense that, at first, it will seem that new concepts are being introduced. The reader will realize as this chapter progresses that these “new concepts” are merely extensions and enlargements of fundamental principles that have been acquired previously in the study of magnetism and electron physics. The study of Inductance is rewarding in the sense that a thorough understanding of it will enable the reader to acquire a working knowledge of electrical circuits more rapidly and with more surety of purpose than would otherwise be possible.

  Inductance is the characteristic of an electrical circuit that makes itself evident by opposing the starting, stopping, or changing of current flow. The above statement is of such importance to the study of Inductance that it bears repeating in a simplified form. Inductance is the characteristic of an electrical conductor which opposes a CHANGE in current flow.

  One does not have to look far to find a physical analogy of Inductance. Anyone who has ever had to push a heavy load (wheelbarrow, car, etc.) is aware that it takes more work to start the load moving than it does to keep it moving. This is because the load possess the property of inertia. Inertia is the characteristic of mass which opposes a CHANGE in velocity. Therefore, inertia can hinder us in some ways and help us in others. Inductance exhibits the same effect on current in an electric circuit as inertia does on velocity of a mechanical object. The effects of Inductance are sometimes desirable—sometimes undesirable.

  On September 22, 1791 in Newington Butts, London, a man was born who was destined to play a great part in the laying of the foundation of the growing science of electricity. This man, Michael Faraday, started to experiment with electricity around the year 1805 while working as an apprentice bookbinder. It was in 1831 that Faraday performed experiments on magnetically coupled coils. A voltage was induced in one of the coils due to a magnetic field created by current flow in the other coil. From this experiment came the induction coil, the theory of which eventually made possible many of our modern conveniences such as the automobile, doorbell, auto radio, etc. In performing this experiment Faraday also invented the first transformer, but since alternating current had not yet been discovered the transformer had few practical applications. Two months later, based on these experiments, Faraday constructed the first direct current generator. At the same time Faraday was doing his work in England, Joseph Henry was working independently along the same lines in New York. The discovery of the property of self-induction of a coil was actually made by Henry a little in advance of Faraday and it is in honor of Joseph Henry that the unit of Inductance is called the HENRY.

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  Electrical Measurement, Signal Processing, and Displays

  • John G. Webster(Author)
  • 2003(Publication Date)
  • CRC Press

    (Publisher)

  14 -1 0-8493-1733-9/04/$0.00+$1.50 © 2004 by CRC Press LLC 14 Inductance Measurement 14.1 Definitions of Inductance ................................................ 14 -2 14.2 Equivalent Circuits and Inductive Element Models ...... 14 -3 14.3 Measurement Methods .................................................... 14 -4 Current–Voltage Methods • Bridge Methods • Differential Methods • Resonance Methods 14.4 Instrumentation ............................................................. 14 -12 Inductance is an electrical parameter that characterizes electric circuit elements (two- or four-terminal networks) that become magnetic field sources when current flows through them. They are called induc-tors, although Inductance is not a unique property of them. Electric current i (A) and magnetic flux F (Wb) are interdependent; that is, they are coupled. Inductance is a measurable parameter; therefore, it has a physical dimension, a measurement unit (the henry), as well as reference standards. Inductance is a property of all electrical conductors. It is found as self-Inductance L of a single conductor and as mutual Inductance M in the case of two or more conductors. Inductors can vary in construction, but windings in the form of coils are the most frequent. In this case, they have characteristic geometrical dimensions: surface A, length l, and N number of turns of windings. The path of magnetic flux can be specially shaped by magnetic cores. Figure 14.1 shows examples of different inductive elements of electric circuits. Figures 14.1a and b present windings with self-Inductance made as a coreless coil (a), and wound on a ferromagnetic core that is the concentrator of the magnetic field (b). A transformer loaded by impedance Z L and an electromagnet loaded by impedance of eddy currents in the metal board, shown in Figures 14.1c and d, will have not only self-Inductance of windings, but also mutual Inductance between windings (c) or between winding and eddy currents (d).

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  Aircraft Electrical and Electronic Systems

  • David Wyatt, Mike Tooley(Authors)
  • 2018(Publication Date)
  • Routledge

    (Publisher)

  1.30. This effect is called self-Inductance (or just induct-ance ) which has the symbol L . Self-Inductance is measured in henries (H) and is calculated from: e L di dt where L is the self-Inductance, di dt / is the rate of change of current and the minus sign indicates that the polarity of the generated e.m.f. opposes the change (you might like to compare this relationship with the one shown earlier for electromagnetic induction). The unit of Inductance is the henry (H) and a coil is said to have an Inductance of 1 H if a voltage of 1V is induced across it when a current changing at the rate of 1 A/s is flowing in it. Example 1.18 A coil has a self-Inductance of 15 mH and is subject to a current that changes at a rate of 450 A/s. What e.m.f. is produced? Now e L d i d t / and hence: e 1 5 10 4 50 6 7 3 . V 7 5 Note the minus sign. This reminds us that a back e.m.f. of 6.75V is induced. Example 1.19 A current increases at a uniform rate from 2 A to 6 A in a time of 250 ms. If this current is applied to an inductor determine the value of Inductance if a back e.m.f. of 15V is produced across its terminals. Now e L di dt / and hence L e di dt / Thus L ( ) ( ) . . 250 10 15 62 5 1 0 937 5 1 0 0 9 . 4 3 3 3 H Finally, when two inductors are placed close to one another, the flux generated when a changing current flows in the first inductor will cut through the other inductor (see Fig. 1.31). This changing flux will, in turn, induce a current in the second inductor. This effect is known as mutual Inductance and it occurs whenever two inductors are inductively coupled. This is the principle of a very useful component, the trans-former , which we shall meet later. Figure 1.30 Self-Inductance 19 Electrical fundamentals 1.6.4 Inductors Inductors provide us with a means of storing electri-cal energy in the form of a magnetic field. Typical applications include chokes, filters, and frequency selective circuits.

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  BTEC National Engineering

  • Mike Tooley, Lloyd Dingle(Authors)
  • 2010(Publication Date)
  • Routledge

    (Publisher)

  which will appear across the coil as the field collapses. For large values of magnetic flux and Inductance this back e.m.f. can be extremely large! Inductance Inductance is the property of a coil which gives rise to the opposition to a change in the value of current flowing in it. As a result of Inductance, any change in the current applied to a coil/inductor will result in an induced voltage or induced e.m.f. appearing across it. The unit of Inductance is the henry (H) and a coil is said to have an Inductance of 1 H if a voltage of 1V is induced across it when a current changing at the rate of 1A/s is flowing in it. The voltage induced across the terminals of an inductor will thus be proportional to the product of the Inductance ( L) and the rate of change of applied current. Hence, e L    rate of change of current Note that the minus sign indicates the polarity of the voltage, i.e. opposition to the change. The rate of change of current is often represented by the expression d i/d t, where d i represents a very small change in current and d t represents the corresponding small change in time. Using mathematical notation to write this we arrive at: e L i t   d d Electrical and Electronic Principles 517 UNIT 6 (a) No current in the inductor (b) Current builds up (c) Current remains constant (d) Current flow interrupted i Figure 6.95 Flux and e.m.f. generated when a changing current is applied to an inductor Electrical and Electronic Principles 518 UNIT 6 Example 6.49 A current increases at a uniform rate from 2 to 6 A in a period of 250 ms. If this current is applied to an inductor of 600 mH, determine the voltage induced. Now the induced voltage will be given by: e  L  (rate of change of current) Thus, e L        change in current change in time ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ 60 10 6 3 2 250 10 3   ⎛ ⎝ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ From which e          60 10 4 0 25 60 10 16 3 3 .

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  Aircraft Engineering Principles

  • Lloyd Dingle, Michael H Tooley(Authors)
  • 2013(Publication Date)
  • Routledge

    (Publisher)

  The value of mutual Inductance, M, is given by: M = k  L 1 × L 2 where k is the coupling factor and L 1 and L 2 are the values of individual Inductance. 5.12.6 Inductors Inductors provide us with a means of storing electrical energy in the form of a magnetic field. Typical applications include chokes, filters and frequency selective circuits. The electrical characteristics of an inductor are determined by a number of factors, including the material of the core (if any), the number of turns and the physical dimensions of the coil. In practice every coil comprises both Inductance and resistance and the circuit of Figure 5.111 shows these as two discrete components. In reality the Inductance, L, and resistance, R, are both distributed throughout the component but it is convenient to treat the Inductance and resistance as separate components in the analysis of the circuit. Now let us consider what happens when a current is first applied to an inductor. If the switch in Figure 5.112 is left open, no current will flow and no magnetic flux will be produced by the inductor. If the switch is now closed, current will begin to flow as energy is taken from the supply in order to establish the magnetic field. However, the change in magnetic flux resulting from the appearance of current creates 5.111 A real inductor has resistance as well as Inductance 5.112 Circuit in which a current is applied to an inductor a voltage (an induced e.m.f.) across the coil which opposes the applied e.m.f. from the battery. The induced e.m.f. results from the changing flux and it effectively prevents an instantaneous rise in current in the circuit. Instead, the current increases slowly to a maximum at a rate which depends upon the ratio of Inductance, L, to resistance, R, present in the circuit.

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  Electrical Transformers and Rotating Machines

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

    (Publisher)

  3 9 Inductance in Alternating-Current Circuits UNIT 3 Objectives After studying this unit, you should be able to: • Discuss the properties of Inductance in an alternating-current circuit. • Discuss inductive reactance. • Compute values of inductive reactance and Inductance. • Discuss the relationship of voltage and current in a pure inductive circuit. • Be able to compute values for inductors connected in series or parallel. • Discuss reactive power (VARs). • Determine the Q of a coil. This unit discusses the effects of Inductance on alternating-current circuits. The unit explains how current is limited in an inductive circuit as well as the effect Inductance has on the relationship of voltage and current. Inductance Inductance (L) is one of the primary types of loads in alternating-current circuits. Some amount of Inductance is present in all alternating-current circuits because of the continually changing magnetic field (Figure 3-1) . The amount of Inductance of a single conductor is extremely small, and in most instances it is not considered in circuit calculations. Circuits are generally considered to contain Inductance when any type of load that contains a coil is used. For circuits that contain a coil, Inductance is considered in circuit calculations. Loads such as motors, transformers, lighting ballasts, and chokes all contain coils of wire. In Unit 2, it was discussed that whenever current flows through a coil of wire a magnetic field is created around the wire (Figure 3-2) . Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. 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.

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  Basic AC Circuits

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

    (Publisher)

  self–Inductance .

  Figure 8.14 A Voltage Across a Coil is a CEMF

  Recall that earlier it was stated that a coil must be composed of turns of wire in which all turns are insulated one from the other. It should be clear now why this is true. If the turns of wire are not electrically separate, then the coil would not act as an inductor, but as a conductor.

  Units of Inductance

  The amount of Inductance in a coil of wire is measured in henrys or millihenrys (thousandths of a henry). Millihenrys is abbreviated mH.

  Physical Properties that Determine Inductance of a Coil

  The Inductance of a coil can be determined by this equation:

  (8–2)

  where This equation is valid for a single–layer coil only, but it can be used to help you understand the physical properties of any type of coil.

  In the equation, L represents the magnetic flux linkages that connect one part of a coil to the next part, causing the property of Inductance. The permeability of the core material is μ, the ability of a material to conduct magnetic lines of force, also called magnetic flux. Together, μ and μo represent a constant.

  From this equation and, as shown in Figure 8.15, you can see that if the number of turns of wire is increased, the Inductance of the coil will increase by the square of the number of turns. As shown in Figure 8.16, a coil with a large cross-sectional area will have a greater value of Inductance than one of a smaller cross–sectional area. As shown in Figure 8.17,

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  University Physics Volume 2

  • William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
  • 2016(Publication Date)
  • Openstax

    (Publisher)

  Finally, if the current through the inductor were constant, no emf would be induced in the coil. Figure 14.8 The induced emf across an inductor always acts to oppose the change in the current. This can be visualized as an imaginary battery causing current to flow to oppose the change in (a) and reinforce the change in (b). One common application of Inductance is to allow traffic signals to sense when vehicles are waiting at a street intersection. An electrical circuit with an inductor is placed in the road underneath the location where a waiting car will stop. The body of the car increases the Inductance and the circuit changes, sending a signal to the traffic lights to change colors. Similarly, metal detectors used for airport security employ the same technique. A coil or inductor in the metal detector frame acts Chapter 14 | Inductance 633 as both a transmitter and a receiver. The pulsed signal from the transmitter coil induces a signal in the receiver. The self- Inductance of the circuit is affected by any metal object in the path (Figure 14.9). Metal detectors can be adjusted for sensitivity and can also sense the presence of metal on a person. Figure 14.9 The familiar security gate at an airport not only detects metals, but can also indicate their approximate height above the floor. (credit: “Alexbuirds”/Wikimedia Commons) Large induced voltages are found in camera flashes. Camera flashes use a battery, two inductors that function as a transformer, and a switching system or oscillator to induce large voltages. Recall from Oscillations (http://cnx.org/ content/m58360/latest/) on oscillations that “oscillation” is defined as the fluctuation of a quantity, or repeated regular fluctuations of a quantity, between two extreme values around an average value. Also recall (from Electromagnetic Induction on electromagnetic induction) that we need a changing magnetic field, brought about by a changing current, to induce a voltage in another coil.

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  Grounds for Grounding

  A Handbook from Circuits to Systems

  • Elya B. Joffe, Kai-Sang Lock(Authors)
  • 2022(Publication Date)
  • Wiley-IEEE Press

    (Publisher)

  Sub- sequently, magnetic flux occurs only outside the conductors; hence, Inductance, as defined above, is termed external induc- tance. The concept of loop Inductance derived above implicitly is considered external Inductance only. Real-world conductors, however, exhibit high but finite conductivity, and some nonzero current distribution can be observed within such conductors. Consequently, some magnetic flux exists within a conductor, associated with the portion of current flowing internal to it, resulting in Inductance internal to the conductor, called internal Inductance. The frequency dependence of the internal Inductance is observed to start at some DC value and begins to decrease as fre- quency increases, approaching zero at a rate proportional to 1/f 1/2 . This decrease of internal Inductance is due to the dimin- ishing field penetration into the conductors (a.k.a. “skin effect” discussed in the next section). At very low frequencies, the fields are uniformly distributed throughout the cross-section conductor, and the total Inductance approaches its value at DC (the combined external Inductance and DC internal Inductance, as shown above). At very high frequencies, only a small fraction of the field penetrates the conductor and the Inductance approaches its HF limit (external Inductance only). In the intermediate frequency range, the Inductance has contributions due to both the external and internal Inductances. In the high frequencies, where skin effect is small compared to the thickness of the metal, the internal Inductance diminishes as frequency increases as 1/f 1/2 . This behavior is illustrated in Figure 2.31, where a decrease in Inductance (and subsequent increase in resistance) as frequency increases is observed for the intermediate frequencies. At the high frequencies, Inductance approaches a constant (i.e. the external Inductance). E 1 I 2 I 1 L p11 L p12 L p22 + − E 2 − + Figure 2.30 Total partial Inductance of two parallel conductors in free space.

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  Fundamentals of Physics, Extended

  • David Halliday, Robert Resnick, Jearl Walker(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  From Eq. 30.3.4 we can write Faraday’s law in its most general form, ∮ E → ⋅ d s → = − d Φ B ____ dt (Faraday’s law). (30.3.5) A changing magnetic field induces an electric field E → . Inductors An inductor is a device that can be used to pro- duce a known magnetic field in a specified region. If a current i is established through each of the N windings of an inductor, Review & Summary a magnetic flux Φ B links those windings. The Inductance L of the inductor is L = N Φ B _____ i (Inductance defined). (30.4.1) The SI unit of Inductance is the henry (H), where 1 henry = 1 H = 1 T· m 2 /A. The Inductance per unit length near the middle of a long solenoid of cross-sectional area A and n turns per unit length is L __ l = μ 0 n 2 A (solenoid). (30.4.4) Self-Induction If a current i in a coil changes with time, an emf is induced in the coil. This self-induced emf is ℰ L = −L di __ dt . (30.5.3) The direction of ℰ L is found from Lenz’s law: The self-induced emf acts to oppose the change that produces it. Series RL Circuits If a constant emf ℰ is introduced into a single-loop circuit containing a resistance R and an Inductance L, the current rises to an equilibrium value of ℰ/R: i = ℰ __ R (1 − e −t/ τ L ) (rise of current). (30.6.6) Here τ L (= L/R) is the inductive time constant. When the source of constant emf is removed, the current decays from a value i 0 according to i = i 0 e −t/ τ L (decay of current). (30.6.10) Magnetic Energy If an inductor L carries a current i, the inductor’s magnetic field stores an energy given by U B = 1 _ 2 Li 2 (magnetic energy). (30.7.4) If B is the magnitude of a magnetic field at any point (in an inductor or anywhere else), the density of stored magnetic energy at that point is u B = B 2 ___ 2 μ 0 (magnetic energy density). (30.8.3) Mutual Induction If coils 1 and 2 are near each other, a changing current in either coil can induce an emf in the other.

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