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LESSON and

INDUCTORS AND INDUCTANCE

he term inductance refers to the property of an electric circuit that opposes any change in the existing current. It follows that inductance is Tpresent in a circuit only when the current is changing. The symbol for inductance is the letter L.The basic unit of measurement for inductance is the , named for an American physicist,SAMPLE , and abbreviated “H.” You do not have to look far to find a physical analogy of inductance. If you have ever had to push a heavy load—a wheelbarrow, for example—you know that it takes a lot more work to start the wheelbarrow moving than it does to keep it moving. Likewise, once a load is moving, it is easier to keep the load moving than to stop it again. Inductance has the same effect on current in an electric circuit. It requires more to start or stop current than it does to keep it flowing.

An is a component used to introduce inductance into an electric circuit—that is, it opposes any change in current flow (magnitude or direction). Even a very simple straight piece of wire will have some measure of inductance in it. Usually, though, the length of wire is wound into a coil to increase its

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inductance. The central core around which the wire is wound may be or some other magnetic material, or it may be a non-magnetic tubular form, in which case it is called an air core. Figure 3-1 shows both an iron-core inductor and an air-core inductor. Iron-core inductors are sometimes called coils.

SELF-INDUCTANCE

Electromotive force (EMF) is a difference of potential, or , that exists between two points in an electric Iron-core inductor circuit. In inductors, an EMF is developed by the forces between a and the electrons in a conductor. You know that a magnetic field is created any a current is passed through a conductor. Figure 3-2 shows a battery connected to an inductor. When the is closed, a magnetic field is produced. When the switch is opened, the magnetic field collapses. Notice that the field is circular in configuration, and is expanding outward, away from the wire. As the current through the wire is Air-core inductor increased, the magnetic field will expand proportionately. FIGURE 3-1. Inductors

Because the magnetic field changes when the current changes, a voltage (or EMF) is induced in the conductor. This phenomenon is called self-inductance, since the EMF is induced in the conductor carrying the current. As the number of turns of wire in a coil increases, so does the magnetic field. If a soft iron core is added to the coil of wire, not only does the inductance increase, but so does the magnetic field. Intense magneticSAMPLE flux fields are exhibited at the ends of the core, as shown in Figure 3-3. + + + +++ + The EMF produced by a moving magnetic field is known as counter (CEMF), or back EMF. The term refers to the fact that the polarity of the CEMF is in the opposite direction to the voltage applied to the conductor. This effect is +– summarized by Lenz’s Law, named for Heinrich Lenz, a German scientist. Lenz’s Law states that the induced FIGURE 3-2. Magnetic field of an inductor

34 LESSON 3

EMF in any circuit is always in a direction opposite the effect that produced it. Figure 3-4 illustrates CEMF, which always opposes any change in the current.

MUTUAL INDUCTION

Figure 3-5 on the next page shows how a changing magnetic field can induce a current in a nearby wire (one that is not electrically connected to the circuit producing the field). This phenomenon is called mutual induction. Its discovery led to the development of , which you will learn more about in the next Lesson.

Figure 3-5A shows the condition of the current and the magnetic field produced by the current Without immediately following the closing of the switch. Note that the moves outward from Coil A. Note also that the current induced in coil B is in the opposite direction from the current in Coil A. Once the magnetic field is fully established, it will not change or move unless there is a change in the current. When this steady-state condition is reached, the current in Coil B drops to zero and remains at zero until there is another change in the magnetic field. This is true even though there is a continuous With magnetic core current in Coil A. SAMPLEFIGURE 3-3. Self-inductance In Figure 3-5B, the switch has just been opened, and there is no longer a current in Coil A. Without a current to establish a magnetic field, the field collapses (implodes). The flux lines now move through the coils in the opposite direction, which also causes the direction of the current induced in Coil B to be reversed (from what it was in Figure 3-5A). The induced current exists only for the time during which the field is collapsing. Meter The current becomes zero as soon as the field has collapsed, and remains at zero until the magnetic field changes again.

There are two factors that determine the amount of mutual induction FIGURE 3-4. Counter electromotive (as measured by the current produced). These are: force (CEMF)

35 ELECTRICITY

ª Proximity. In general, the closer the coils are to each other, the stronger the induced current will be. The current will vary as Expanding flux the inverse of the square of the distance Coil B between the centers of the coils. Coil A

ª Orientation. The induced current will be greatest if the (axes of the) coils are

, and will be zero if the (axes of SSN N the) coils are perpendicular. The mutual induction is directly dependent on the cosine of the angle between the axis of the two coils.

Meter FACTORS AFFECTING COIL INDUCTANCE

A. Switch closed There are several factors that affect the inductance of a coil. They include:

Collapsing flux ª the number of turns in the coil Coil A Coil B ª the diameter of the coil

ª the length of the coil

SNN S ª the type of material used in the core

ª the number of layers of winding in the coils.

SAMPLE Meter The number of turns in the coil. Increasing the number of turns increases the inductance. If you B. Switch open increase the number of turns from one turn to two turns, for example, the inductance will increase FIGURE 3-5. Mutual induction by four . Adding a third turn to the coil increases the inductance by nine times. Therefore, it can be said that the inductance varies as the square of the number of turns.

The diameter of the coil. It requires more wire to construct a large-diameter coil than a small-diameter coil with an equal number of turns. Therefore, more lines of force exist to induce a CEMF in the coil with the larger diameter. The inductance increases directly as the cross-sectional area of the coil increases.

36 LESSON 3

Recall that the formula for the area of a circle is πr2. Doubling the radius of a coil, then, increases the inductance by a factor of 4.

The length of the coil. If one coil has three widely spaced turns, making a relatively long coil, and another coil has three closely spaced turns, making a relatively short coil, the shorter coil will have a higher inductance. In other words, when the length of the coil is increased while keeping the number of turns the same, the inductance is decreased. Mathematically, doubling the length of a coil while keeping the same number of turns halves the inductance.

The type of core material. A material with a high permeability has less reluctance to the magnetic flux, resulting in more magnetic lines of force. Therefore, the inductance of a coil increases directly as the permeability of the core material increases.

Winding the coil in layers. The more layers used to form a coil, the greater effect the magnetic field has on the conductor. The inductance of the coil increases with each layer added.

INDUCTIVE REACTANCE

Inductors produce the same effect as in dc circuits. You know from an earlier Lesson that resistance can be measured with an ohmmeter, and is determined by the diameter of the wire, the length of the wire, and the composition of the wire. By definition, the current in a dc circuit is steady (unchanging), and therefore inductance—which, remember, is defined as opposition to any change in the current—occurs only when voltage is applied and when voltage is removed. In an ac circuit, however, the currentSAMPLE is continually changing. The opposing force that an inductor presents to the flow of is called inductive reactance, because it is the “reaction” of the inductor to the changing value of the alternating current. The symbol for inductive reactance is XL. Like resistance, inductive reactance is measured in , but it cannot be measured with an ohmmeter.

In order to calculate inductive reactance, you first must determine the inductance of the coil in question. Then you must find the of the current. The equation used for inductive reactance is as follows:

π XL = 2 fL where:

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