: ea he Learning Outcomes This chapter will help you to: ‘Ht Name the electric quantity that opposes ‘changes in current. 14-2 Name and define the base nit of inductance. 14-3 List four factors that ere the major ‘determiners of the inductance of an inductor, 11-4 Explain why: (a) some inductors resemble resistor, (b) some inductors are shielded, Som inductors use laminated iron cores, and some inductors ae called chokes. 1-5 List and explain five ratings, in addition to inductance, that are given for some inductors. 11-6 Explain how an inductor contcols the tate at which current can increase in do circuit. AN-7_ Practice using the X, formula to determine the opposition ofan ideil inductor. And, Show that V leeds / by 90° with an ideal inductor. © {14-8 Define “quality” for sn inductor and show how itis caeulated 11-9 Discuss how connecting inductors in parallel affects total inductance and total reactance, 31-10 Discuss bow connecting inductors in < series affects total inductance and total Bs reactance. A114 Calculate the time constant for either series or parallel RL de circuits, M-12 Reduce muwal inductance between two 2 inductors. 1413. Explain bow non-induetive wire-wound resistors are made, Inductance any electric and electronic devices Joperate on the principle of induc- tance. Therefore, it is important that you develop a sound understanding of induc- tance and inductors. 11-1 Characteristics of Inductance Inductance is the electrical property that op- Poses any change in the magnitude of current in a circuit. The letter “L” is the symbol used to represent inductance. Devices that are used to provide the induc- tance in a circuit are called inductors, Inductors are also known a8 chokes, reactors, and coils, ‘These three names are descriptive of the way inductance behaves in a circuit. Inductance, and thus an inductor, “chokes off” and restricts sudden changes in current. Inductance reacts against (resists) changes, either increases or decreases, in curen.iietors are usually coils of wire. Inductance is the result of a voltage being induced in a conductor. The magnetic field that induces the voltage in the conductor is pro- duced by the conductor itself. that previously we discussed how a mag- netic field is formed around a current-carrying conductor, ‘When current begins to flow in a conductor, ‘magnetic flux rings start to expand out from the conductor, as in Fig. 11-1). This expanding fiax induces a small voltage in the conductor. ‘The induced voltage has a polarity that opposes the increasing source voltage which is creating Inductance (L)‘Mutual inductance Counter electromotive force tcemfl the increasing current, Thus, the inductance of the conductor opposes the rising cuzrent and tries to keep it constant. Of course, the induc- tance cannot completely stop the increase in current because the induced voltage is caused by the increasing fiux. And the increasing flax depends on the increasing current, The indue- tance of the conductor, therefore, restricts only the rate at which the current can increase. When the current in a conductor starts to decrease, as in Fig. 11-1), the flux starts to collapse, The collapsing flux reverses the po- larity of the induced voltage from what it was ‘wen the flux was increasing. Thus, the voltage induced by a decreasing flux aids the source voltage and tends to keep the current from de- creasing. Again, the inductance restricts the rate at which the current can change. The amount of voltage induced in a single conductor like that in Fig, 11-1 is very small. So small, in fact, that it has no practical significance {in most low-frequency electric and electronic de- vices. However, at high frequencies, like those used in television systems, the inductance of a single conductor can be very significant. Increasing magneto fold Potery ofinduced voltage (2) Increasing curent and tux Cotapsing ‘maghetic Held Direction of curont + Polaiy of Indvoed vettage — (b) Dacraasing curent and th Fig. 14-1 Induced valtage in e conductor The polarity of the induced valtage is dependent on whether the current is increasing or decreasing. 284 Ghapter 11 Inductance: fig. 11-2. Multiturn col. Some of the flux ereated by ‘one turn links to all the other turns. ‘The inductance of a conductor can be greatly increased by forming the conductor into a coil as in Fig. 11-2. Now the flux produced by one tum of the coil induces voltage not only in itself but in adjacent tums as well. The long, closed flux loops in Fig. 11-2 are the result of the magnetic fields of all three tums of the coil. They are stronger than the flux created by any one of the tums. Yet, they induce a voltage into each of the three tums. The inductance of the coil is much greater than the inductance of the straight length of conductor from which it was made, Self-Inductance The inductance of an inductor is called self- inductance. It is given this name because the inductor induces voltage in itself. That is, its ‘own changing magnetic field induces voltage in its own turns of wire. In the case of a single straight conductor, its own field induces a voltage init Mutual Inductance ‘When the magnetic flux from one conductor induces a voltage in another, electrically iso- lated conductor, itis called mutwal inductance. With mutual inductance, circuits that are elec- trically separated can be magnetically coupled together. A transformer uses the principle of mutual inductance. Transformers are fully dis- cussed in Chap. 12. Lenz's Law and CEMF ‘The voltage induced in a conductor or coil by its ‘own magnetic field is called a counter electro motive force (cem!).A. aed from an earlier chapter that electro- motive force (emf) is another name for voltage. Since the induced emf (voltage) is always opposing, or countering, the action of the source voltage, it is known as a cemf. Counter electromotive force is sometimes referred to as back electromotive force (bem). The term back implies that the induced voltage is backward, or working against the effort of the source voltage. The concept contained in Lenz's law is used to explain how inductance behaves Lenz’s law states that a cemf always has a polarity that opposes the force that created it, ‘This idea is illustrated in Fig. 11-3(a), which shows, in schematic form, an inductor and an ac voltage source, When the voltage is in- creasing, as shown in the graph, the cemf op- poses the source voltage. When the voltage is decreasing (Fig. 11-3(6)], the cemf aids the source voltage and tries to keep the current ‘constant. Energy Storage and Conversion Another way to look at inductance is in terms of energy conversion and storage. When cur- rent flows through an inductor, the induc- tor builds up a magnetic field. In the process ‘of building its magnetic field, the inductor 8 Polarity of a OY) thecont Tine (@)reeasngvotago 3 Potty of i WY) thea Tire (8) Decreasing voltage 'g. 11-3 Polarity of counter electromotive force (coma Yo History of : aa Electronics Heinrich Lenz In 1834 Russian physicist Heinrich Lenz stated his law concerning the polarity of induced voltages. converts electric energy into magnetic en- ergy. When the current increases, more elec- tric energy is converted into magnetic energy. ‘The inductor’s magnetic field now processes ‘more energy than it had before the current in- creased. When current through an inductor de- creases, its magnetic field decreases. Magnetic energy from the field is converted back into electric energy in the inductor. Thus, an in- ductor stores energy when its current jncreases and returns stored energy when its current decreases. Inductance converts no electric energy into heat energy. Only resistance is ca- pable of converting electric energy into heat energy. Thus, if an inductor ith absolutely no resistance could be constructed, its net use of energy would be zero, For the two quarters of the ac eyele when the current is increasing (first and third quarter), it would take energy from the system. For the other two quarters of the cycle (Second and fourth) when the current is decreasing, it would return the same amount of energy to the system. Notice that inductance stores and returns energy in much the way capacitance does. During the first and third quarter-cycle, in- ductance converts electric energy to mag- netic energy and stores the magnetic energy, whereas capacitance directly stores electric energy. During the second and fourth quarter- cycle, inductance converts its stored magnetic energy back to electric energy and returns it, whereas capacitance just returns its stored electric energy. Inductance Chapter 14 Back electromotive force (hem#) Lenz's lawEE Answer the following questions. 1, The electric property that opposes changes in current is called ‘The physical device that opposes changes in current can be called a(n) or 2 3. ‘Truc or false. A straight wire possesses inductance. 4, True or false. A straight wire can be called an inductor, 5, True or false. Inductance converts electric energy to heat energy. 11-2 Unit of Inductance— The Henry The base unit of inductance is the fienry, This unit, named in honor of an American scientist, is abbreviated H. The henry is defined in terms of the amount of cemf produced when the cur- rent through an inductor is changing amplitude. One henry of inductance develops 1 V of cemf when the current changes at a rate of 1 A/S. This definition of a henry is shown graphically Henry (#) in Fig, 11-4, 4 3 by & 1 . 1 2 3 Seconds 4Votcemt Fig. 114A 4-H inductor produoes 1 V of cemt when the current changes at a rete of 1 Als, 288 Chapter 11. inductance 6. True or false. The cemf aids the source voltage when the current in an inductive circuit is increasing 7, True of false. Transformers operate on the principle of setf-inductance. 8. The symbol ot abbreviation for indue- tance is ; 9. Jaw can be used to find the polarity of the cemf in an inductor. 10. Another abbreviation for cemt is 11, When current in an inductor is increasing, ‘energy is being converted to energy. ‘A wide range of inductances are used in elec- tric and electronic circuits. Inductances in cir- cuits of very high frequency aro often less than 1 WH. For low-frequency circuits, inductors with ‘more than 5H of inductance are common. A formula for determining inductance (2) in henrys (H) is Loa where Viageeg = the cemf in volts AI = the change in coil currentin —j amperes At = the time in seconds required for the current to change EXAMPLE 11 Deterinifie the inductance of ‘an inductor: (coil) that produces 5.V. of cemf when the: current changes from 300 mA to 800 mA in two seconds, 4 Given: Vigeg = 5V AT = 800 mA - 300 mA = 500 mA = 0.54 At=2s é Find: “Inductance (L) = Y, Known: | L'= 538 AT/AG- i:=_35v 025475 ‘The inductance is 20 hearys, 11-3 Factors Deter Inductance The inductance of an inductor is. primarily determined by four factors: 1. The type of core material 2. The number of tums of wire 3. The spacing between turns of wire 4. The diameter of the coil (or core) ‘The core of an inductor is the material that ‘occupies the space enclosed by the turns of the ‘inductor. ‘The amount of current in an iron-core indue- tor also infiuences its inductance. This is because the magnetic properties of the iron core change as the current changes. Ultimately, the amount of inductance is de- termined by the amount of cemf produced by a specified current change. Of course, the amount of cemf depends on how much flux interacts with the conductors of the coil. Hf all other factors are equal, an iron-core inductor has more inductance than an air-core inductor, This is because the iron has a higher permeability; that is, it is able to carry more flux, With this higher permeability, there is more flux change, and thus mote cemf, for a given change in current, Adding more turns to an inductor increases its inductance because each turn adds more p Answer the following questions. 12. The base unit of inductance is the 15. ‘The abbreviation for the base unit of © inductance is the. . 14. Interms of the base units of voit- age, current, and time, the base unit of 7. inductance is equal to a(n) : & Joseph Henry American physicist Joseph Henry did extensive research on eleotro- ‘magnetism and discovered the principles that made the devel- ‘opment of the telegraph possible, The fundamental unit for induc- tance, the henry is named for him, History of ‘magnetic field strength to the inductor, Increas- ing the magnetic field strength results in more flax to cut the turns of the inductor, ‘When the distance between the turns of wire in a coil is increased, the inductance of the coil decreases. Figure 11-5 illustrates why this is 0. With widely spaced turns (Fig. 11-5(@], many Of the flux lines from adjacent turns do not link together, Those Hines that do not link together produce a voltage only in the turn that pro- duced them. AAs the tums come closer together (Fig. 11-50), fewer lines of fux fai to link up, ‘When other factors gre equal, the inductor with the largest-diametet'core will have the most inductance. This is because all the flux has to go through the core of an inductor. Thus a large- diameter core can handle more flux, ata specified flux density, than a small-diameter cove can. 15. Does the amount of inductance increase or decrease when more turns are added to an inductor? 16. List four ways to increase the inductance of an inductor, TERRE ETT oe Electronics Core Tron-core inductor Air-core inductor Inductance Chapter 11 287Air-core inductor Variable inductor Iron-core inductor current Fig. 11-5 Effect of turn spacing. (2) Widely spaced tums provide less Inductance then (6) closely speced turns do. 441-4 Types of Inductors One way of classifying inductors is by the type of material used for the core of the inductor. ‘The core may be either a magnetic material or a nonmagnetic material. The symbols for induc- tors with these materials are shown in Fig, 11-6. Inductors are also classified as either fixed or variable, Figure 11-7 shows two symbols used to indicate a variable inductor, The most com- mon way of varying inductance is by adjusting the position of the core material. In Fig. 11-8 the position of the ferrite core material (called a slug) is adjustable within the coil form. Maxi- ‘mum inductance ocoars when the slug is po- sitioned directly in line with the coil of wire, (2) ron-core (magnet) ig. 11-6 Fixed-value inductor symbols, (0) Alrcore (onmagnatic) Fig. 11-7 Variable inductor symbols, Either symbol ‘cen be used for magnetic or nonmagnetic cares. Ghapter 11 Inductance Some variable inductors use a brass sing. Brass hhas more reluctance (opposition to flux) than air does, Therefore, the brass slug decreases induc- tance when it is centered in the coil. Air-Core Inductors ‘An air-core inductor, used as part of a high- frequency circuit, is shown in Fig. 11-9. This {inductor is self supporting and requires no coil form. However, many inductors that are rep- resented by the air-core symbol are wound on a coil form. The form may be either solid or hollow. These forms have about the same reluc- tance (opposition to magnetic flux) as air does. ‘Therefore, the inductor is much like an air-core inductor; its core is nonmagnetic, These indue- tors may be wound on such core materials as ceramic or phenolic. They often look like the coil in Fig. 11-10(@). These inductors seldom have more than 5 mH of inductance. Ferrite and Powdered-iron Cores ‘The coil shown in Fig. 11-10(a) may also be’ an iron-core inductor. In this case the core me terial would be ferrite or powdered iron, correct symbol would then be the iron-c symbol of Fig. 11-6(a), (On some schemati diagrams, the two solid lines in the iron-cot symbol are replaced by two broken lines tore resent a ferrite or powdered iron core.) Mo} inductors of this type have less than 200 miThreaded brass shat “Threaded cll form _- = (aper or plastio) eae Colt form 14 (papar et plastic) Ferite sug ‘Colo wi (@) Threaded shat (8) Threaded ohug Fig. 11-8 Methods of adjusting inductance. Fig. 11-9 Aircore inductor of inductance. They are used primarily at frequencies above the audio (sound) range. Fig. 11-10(6) shows another style of inductor wound ona ferrite core. Toroid Cores ‘The cores of the inductors discussed so farhave all been straight. The magnetic fux loops must extend through the air a3 well as through the ore material. With a toroid core, the flux loops all exist within the core. Toroid cores (Fis, N-10(6)] are doughmut-shaped, Each tum of Wire is threaded throngh the center of the core, 8 shown in Fig. 11-10(c). Inductors made with x toroid cores are called toroidal inductors. The toroid core is usually made from powdered iron or ferrite, Toroidal inductors can have high in- f doctance values for their size. ‘Surface Mount Chip Inductor Fi. 11-10 Mitre ihre aes a ee i. 11-10 Mnisture high-frequency inductor, hip inductors are available in the aH and (a) Either nonmagnetic or ferrite core, KH range of inductance. Fig. 11-11 shows a (b) Ferrite core. 1H chip inductor positioned inside the end (21 Torvid core. | ‘Toroid Core © Inductance Chapter 11 288Molded inductors Eandt laminations Fig. 11-111 Surface mount inductor positioned in the end of a small paper clip. of a small paper clip. This inductor is approxi- mately 1 mm thick, 12 mm wide, and 2 mm tong. Notice in Fig. 11-11 that the connecting ends aré tinned so they can be readily soldered in place on a circuit board. Malded Inductors Some inductors look like resistors (Fig. 11-12). ‘These inductors are enclosed in an insulat- {ng material to protect the inductor winding, ‘Molded inductors can have cores of air, ferite, or powdered iron. Some of the resistors discussed and pictured in Chap. 4 (See, 4-11) are constructed similarly to the inductors wound on a nonmagnetic core. ‘Thus, some resistors have significant induc- tance and some inductors have significant resis- tance. Resistors use high-tesistance materials to minimize the number of tums needed to obtain the desired resistance. Conversely, inductors use low-resistance materials to minimize the sesistance of the tums required to obtain the de- sired inductance. The quality (Q) of inductors {and capacitors) is improved by minimizing the resistance. Fig, 11-42 Molded inductors. Chapter 11 Inductance Fig. 11-12 Shielded inductor. Special. wire-wound resistors are wound so that the cemf of half of the tums cancels | the cemf of the other half of the turns that are required to obtain the desired resistance. ‘These resistors are referred to as noninductive resistors, Shielded Inductors Inductors are often shielded to protect them from the influence of magnetic fields other than their own. The shield is made from a magnetic material, Figure 11-13 shows an exploded view of the parts of a shielded, adjustable coil forma, ‘The coil winding is not shown. It would be wound on the cylindrical tube, or bobbin, The coil form shown in Fig, 11-13 is the type used ‘on printed circuit boards. Some miniature chokes (inductors), like those in Fig. 11-12, are also shielded. Their shields are encased underneath the outside molding. Laminated Iron Gore Nearly all the large inductors used at power frequencies (60 Hy, for example) use laminated fron cores. These inductors have inductances ranging from about 0.1 to 100 H. ‘The typical laminated core uses laminations’ “like those in Fig. 11-14. From this illustrai tion it is easy to see why these laminations are called E and I laminations. The B laminatio are stacked together to the desired thicknes as are the I laminations. The winding is put o the center leg (Fig. 11-15) of the E stack, Th stack is then positioned aoross the open end: the E stack. /tamination lamination ‘11-14 E and | laminations. These leminetions are stacked in various configurations to form cares for electromagnetic devices laminations Etaminatons Winding Fig. 11-15 Laminated-iran-core inductor, The coil fits over the center lag of the E laminations, As seen in Fig, 11-16, the E and I lamina- tions form two parallel paths for flux. The center leg of the E lamination is twice as wide as either of the outside legs because it has to carry twice as much flux. For a given amount and rate of current change, the laminated- iron-core inductor creates more flux than other types of inductors. This changing fiux, in turn, creates cemf. This is why laminated. iron-core inductors can provide large amounts of inductance. «The inductance of an iron-core inductor is seen from Fig. 11-17, which illustrates the Winging (Cross-sectional view Fig. 19-48 Flux paths in a laminated core, creases as the magnetic field strength increases. ‘The magnetic field strength of an inductor is a function of the amount of current lowing in the winding, Refer to Fig. 11-17, Suppose the cur- rent through the inductor changes from point A to point B, The flux density would change from A’ to B” and produce a certain amount of emf, This amount of cemf would, of course, represent a certain amount of inductance, Now suppose the current ia the inductor was ‘greater and the current changed from C to D in Fig. 11-17. Although C to D is the samme amount of change as A to B, it produces a much smaller change (C’ to D’) in flux. Thus, the inductor has less cemf and inductaneg at the higher current. Points Z and F in Fig, 11-17 show what happens when the core of an inductor is saturated, Since ‘change in current from Eto F produces almost. no change in flux, there is very litle inductance, Except for special applications, inductors are never operated in the saturation region of the permeability curve, Filter Chokes Laminated-iron-core inductors are often re- ferred to as filter chokes. These chokes are used in the filter circuits of power supplies in a wide variety of electrical and electronic equip- ‘ment. The power supply is often the part of the ‘equipment which converts alternating to diregt current. The filter circuit, which includes the inductor, smooths out the fluctuating or pulsat- ing direct current until it is nearly pure direct current. Saturated Filter choke Inductance Chapter 11 =Smoothing choke Swinging choke Ohmic resistance RF coils, Quality 292 Chapter 14 Fux density (8) “ eo Magnate fad stongth(H) ‘11-11 Permeability curve. Permeability decreases as flux density and ‘magnetic field strength increase ‘There are two types of filter chokes: the smoothing choke and the swinging choke. The swinging choke is one in which the I and E iaminates are butted together so that there is a minimum ait gap between them. This makes the amount of inductance vary with the amount of current (Fig. 11-17). A typical swinging choke may be rated 20 H at 50 mA and 5 H at 200 mA. ‘The smoothing choke frequently has @ small (0.1 mm) air gap between the I and E lamina- tions. This makes the inductance less depen- dent on the amount of current because air does not saturate as easily as iron, Radio-Frequency Chokes or Coils Inductors that are used at higher frequencies are often called RF chokes or RF coils. Since radio was one of the early popular uses of high- frequency inductors, they became known as radio-frequency, or RF, coils. An RF coil or choke may have an air, powdered iron, or ferrite core, It may be either fixed or variable, 41-5 Ratings of Inductors ‘We have seen so far that one of the main rat- ings of an inductor is its inductance, Inductors are also rated for de resistance, current, voltage, quality, and tolerance. The de resistance specifies the resistance of the wire in the winding of the inductor. ‘This is the resistance between the terminals of the inductor that one would measure with Inductance an ohmmeter, Therefore this de resistance is sometimes called the ohmic resistance. The current rating of an inductor is impor- tant because it indicates how much current the inductor can continuously carry without over- heating. With laminated-core inductors, the current rating also indicates the current level at which the inductance was measured, At lower current levels, the inductance is greater than the specified value. ‘The voltage rating indicates how much volt- age the insulation on the inductor winding can continuously withstand, Exceeding this voltage rating may not result in instantaneous break: down of the insulation. However, it will shorten the life expectancy of the inductor’s insulation. Voltage ratings are used mostly with laminated- core inductors, With these inductors, the core is often physically and electrically connected to the chassis of an electric device. However, the winding may be hundreds of volts positive or negative with respect to the chassis. ‘The quality of an inductor refers to the ratio of its reactance to its resistance. Generally it is de- sirable to have a high-quality inductor. All other factors being equal, the lower the de resistance, the higher the quality of the inductor. Detailed information on quality is provided in Sec. 11-8. Like all other components, inductors have ‘manufacturer's tolerances. Precision inductors can be obtained with tolerances of less than 1 percent. However, they are expensive. ‘Typical inductors used in mass-produced elec tric and electronic devices have tolerances of 10 percent or more. 4 /11-6 Inductors in DC Circuits The behavior of an inductor in a pure de citeuit is contrasted to that of a resistor in Fig. 11-18, With a resistor (Fig. 11-18(¢), the current jumps to its maximum value almost the instant the switch is closed. When the switeh is opened, it Grops back to zero just as fast. An inductor in a de circuit (Fig, 11-18@6)} forces the current to rise more slowly. This is due to the inductor’s emf. The time required for the current to reach its maximum value is dependent on the amount of inductance and resistance. With inductors of ‘typical quality, the time is much less than 1 s. Once the current reaches its peak vaiue, the only opposition the inductor offers is its de resistance, When the switch in Fig. 11-18(6) is opened, the ccemf of the inductor prevents the cutrent from instantaneously dropping to zero. It does this a toa 0.05 4 g “switch SP soiten pane closes Tim ——> (2) Curent rise ina resistve circuit |b SH Jand 100.0 7 2.05 A £ 3 (8) Curent tsa ina esistve-induotivectcuit ‘Fi 1-18 Comparison of e resistive and 2 i resistive-inductive de circuit, The inductor opposes changes in current, I by ionizing the air between the switch contacts as the switch opens, As the energy stored in the inductor's magnetic field is used up, the switch ‘contacts deionize and current stops. ‘When the switch in Fig. 11-18() is opened, the cemf of the inductor becomes much greater than the source voltage. The high voltage (cemf) generated when an inductive circuit is opened is known as an inductive kick. It is the voltage that ionizes the air between the switch contacts ‘and causes the contacts to arc and burn, The in- ductive kick of an inductor is very high because the current drops very rapidly when the switch is opened. The difference between the source ‘Voltage and the cemt is dropped across the ion- ized air between the switch contacts. Kirchhof?’s voltage law still applies. That is, the voltage across the switch plus the inductor’s cemf still equal the source voltage. Notice the polari- ties in Fig, 11-19. The induetor’s cemf and the Yoltage across the switch are series-opposing. Thus, they both can be much greater than the battery voltage. The exact value of the cemf in Fig. 11-19 when the switch opens depends ‘upon two factors: the amount of inductance and the amount of current in the circuit before the switch is opened. The inductive kick of an in- ductor can be many thousands of volts, Induc- tive kick is the principle on which the ignition oil in an automobile operates, ‘The relationship between the current and Voltage (cemf) in an induetor is illustrated in Fig. 11-20. The resistarice Rh this figure is very high relative to the olimic resistance of the in- ductor. Therefore, the voltage across the induc- tor is almost zero once the current reaches its ‘maximum value. Notice in Fig. 11-20 that the voltage across the inductor is maximum when the current through it is minimum and rising, Also, the voltage is minimum when the current is maximum and steady. Further, notice that the resistive current and voltage rise together. Fig. 11-18 Voltage polarities when an indvetive circuit is opened, Inductive kick Inductance Chapter 11, 283Ideal inductor Inductive reactance UX) Voltage and current Tie—> Fig. 11-20 Current and voltage relationshis in en inductar. Maximum inductive voltage occurs before maximum current is reached, Answer the following questions. 17. Draw the symbols for a. A fixed iron-core inductor ». A fixed air-core inductor c. A variable inductor 18. True or false. A slug-type core is used in an iron-core inductor. 19. True or false. When a brass core is cen- tered inside a coil winding, the coil will have maximum inductance. 20. True or false. The ait-core inductor symbol is used for all inductors that use nonmagnetic core material, 21. True or false. A ferrite-core inductor would be represented by using the symbol for an iron-core inductor, 22, True or false. A 50-mH inductor would most likely have an air core. 23. True or false. To provide maximum in- ductance, a ferrite core should be centered in the coil winding. 24, What type of core would be used in a 5-H inductor? 25. What is the shape of a toroidal core? 26. Why is the center leg of an E lamination wider than the outside legs? 27. Why does an inductor have a current rating? 28, What is meant by the quality of an inductor? 29. What is an RF choke? 30. What type of core does a filter choke have? 31. What is meant by inductive kick? 32. An inductive circuit and a resistive circuit have equal currents, When the switch is opened in each circuit, which circuit produces more arcing across the switch contacts? 33. Does the cemf exceed the source volt- age when an inductive de circuit is opened? 34, Does an inductor’s voltage (cemf) reach its maximum value before the current reaches its maximurn value? 41-7 {deal Inductors in AC Circuits ‘An idea! inductor is an inductor that has no re- sistance. It does not convert any electric energy into heat energy, and it has infinite quality. In the discussions that follow, we assume that we have ideal inductors. 288 Ghapter 11. Inductance Inductive Reactance 2 Inductance, like capacitance, controls i current without using power, Therefore, the position of an inductor to alternating current, also called reactance X, To distinguish in tive reactance from capacitive reactance, use the symbol X, for inductive reactance.Inductive reactance is the result of the cemf of the inductor. The inductor lets just enough ac flow to produce a cemf that is equal to (and ‘opposite to) the source yoltage. This idea is illustrated in Fig. 11-21. During each half cycle of the source (an ac generator), the cemf of the inductor produces a matching half- cycle of sinusoidal voltage. At any instant of time the two voltages (source and cemf) are equal. The teason for this can be ascertained by referring to Fig. 11-22, which shows that the voltage leads the current by 90° in an in- ductive circuit. Notice from the figare that the current is changing direction at the instant the source voltage is at its peak value. When the current changes direction, two things happen: (1) the polarity of the mmf and the direction of the fiux change, and (2) the flux changes from a collapsing flux to an expanding flux (or vice versa). Either of these happenings would change the polarity of the cemf; but when they occur simultaneously, the polarity cannot change. Also, notice from Fig, 11-22 that the rate of current change,,and therefore the rate of fux change, is greatest as the cur- rent crosses the zero reference line. Thus, the cemf is greatest as the current is changing direction, ‘The reactance of an inductor can be calcu- lated with the following formula: X,~ 2nfl. = 6.28/L ‘The inductive reactance is in ohms when the frequency is in hertz and the inductance is in henrys. Vottage Voltage a \/ - - “S\Roterence point (2) Posttve haitcycto my . . \ i e } p “SReteronce port (0) Nogative haltoycle Fig. 11-21 Source end inductor 30 voltages, The inductor’s cemt ‘opposes the source voltage, ABOUT ELECTRONICS serious injuries. From the above formula it can be seen that in- dactive reactance is directly proportional to both frequency and inductance. Doubling either doubles the reactance. This direct proportional relations makes sense when one recalls two things: 1, ‘The higher the frequency, the more rapidly the current is changing, Thus ‘more cemf and mote reactance are produced 2. The higher the inductance, the more fux change per unit of current change. Again, more cemf and reactance are produced. EXAMPLE 11-2 — ‘What is the reactance of a 3-H inductor when the frequency is 120 Hz? Given:. Inductance L = Frequency f= 120 Hz ind: Inductive reactance (X,) Known: 6.28fL + Solution: 6.28 X FX L 6.28 X'120 Hz X 3H = 2261.0 Answer: The 3-4] inductor has 2261 0 ‘of reacistnce at 120 Hz, Voltage 7 Inductence Chapter 14, Stay Calm in Shocking Situations A worker's sudden ‘movement in response to a mild eleotrie shack can resuit inthe current {deal inductor Vojage Current Fig. 11-22 Alternating current end valtage in an inductor. The voltage leads the current by 20°, EXAMPLE 11-3 ‘A’2.5-mH inductor is placed ‘in: circuit where the frequenicy is 100 kHz. What is its inductive reactance? Given: b= 2.5 mH Pes 100 kHz Finds" * X, X,= 6:28/L 2.5 mH = 0.0025 H 100 kHz = 100,000 Hz 5.28 X 100,000 Ha, x 0.0025 H: = 1570.0 ‘The 2.5-mH inductor has 1570 Q.of reactance at 100 kHz. X ‘Answer: In solving example 11-3, we could have left the inductance in millihenry and the frequency inkilobertz, Then, the 10 of millikenry would have canceled the 10° of kilohertz, ‘When the inductor’s current and voltage are known, its reactance can be calculated by using ‘Ohm's lave, EXAMPLE 11-4 ‘The aé voltage measured across an inductor is 40 V. The current measured through the inductor is 10 mA. What is its reactance? Given: ~ V,=40V 1,=10mA Find: x, : ¥, Known: X,= 75 ee ai Solution: x, = OY = 4000.0 ‘The inductor has 4000 9 of “reactance. P Answer: 298 Chapter 11. Inductsnce If the frequency of the voltage in exam- ple 11-4 is known, or measured, the inductance ‘could then be calculated using the reactance formula. EXAMPLE 11-5 Determine the inductance of the inductor in’example 11-4 when the frequency is 500 Hz. Given: f= 500 Hz X, = 4000.0 (from © example 11-4) Find: L : Known: . X, = 6.28/L rearranged, givés. Solution: Answer: Phase Relationships of / and V The sinusoidal cemf of the inductor in Fig. 11-21 is produced by a sinusoidal current through the inductor. This current wave, shown. in Fig. 11-22, is 90° out of phase with the cert and the source voltage. The current must be 90° out of phase because the cemf can be zero only when the current is not changing. The only instant when the current is not changing is when it is exactly at its peak value. That is, at the instant the current has just stopped rising and has not yet begun to fall, itis effectively a constant value. This is the instant at which zero cemf ocours. It can be seen from Fig. 11-22 (and Fig. 11-20) that the voliage leads the current in an inductor circuit. More precisely, the voltage leads the current by exactly 90° in | an ideal inductor. Power in an Inductor The ideal inductor uses no power because its current and voltage are 90° out of phase. (Re- member, P = IV cos 8, and cos 90° = 0.) Thus, in a pure inductance (ideal inductor) both cur rent and voltage are present but there is no net’ conversion of energy.Current Current (0) Expanding magnete tele to the source. From an energy point of view, one can say that ‘energy is vansferred back and forth between the source and the inductor, During the quarter-cycle in which current is rising [Fig. 11-23(@), energy is taken from the source (generator). The energy from the generator is converted into magnetic energy and stored in the inductor's field. Dur- ing tho next quarter-cycle (Fig. 11-23@), when the current is decreasing, the field of the induc- tor collapses. Its stored energy is converted back to electric energy and returned to the generator. (0) Collapsing magnet fle n 6 fh. a (A) Cottapsing magnetic le Current ‘VH3S Power in n duct. Every othar quarter cycle (b and cf the Inductor retums its stored energy As shown in Fig, 11-23(0), energy is again taken from the generator during the third. quarter cycle, This energy is again returned during the fourth quarter-cycle [Fig. 11-23(@)]. Notice in Fig. 11-23() and (©) that the polarity of the cemf remains the same. Yet the magnetic field changes from a collapsing field to an expanding field. As previously explained, this is because the polarity of the magnetic field also changes [between Fig. 11-236) and ©] when the direction pf the cur. rent reverses. Answer the followirig questions. 35. Does an ideal inductor possess any resistance? 36. What causes inductive reactance? 37. The symbol for inductive reactance is 38. ‘The formula for calculating the reactance of an inductor is : 39. Doubling the frequency of an inductive circuit causes the reactance to : 40. Determine the reactance of the following inductances at the frequencies specified: a. 6Hat 60 Hz . 150 mH at 10 kHz, ©. 30 wH at 250 MHz 41. What is the reactance of an inductor that drops 20 V ac when 0.5.A ze flows through it? 42. Inductance causes current to voltage by___ degrees. 43, ‘The power consumed by an ideal inductor that draws 2.A from a20-V ac source is 44, How much inductance is needed to provide 3600 0 of reactance to a 30-V, 400-Hz source? 45. What is the frequency when a 3-mif inductor produces 4200 01 of reactance? Inductance Chapter 142 al Skin effect Effective resistance Impedance (2 11-8 Real Inductors in AC Circuits Real (nonideal) inductors use some power be- cause all inductors possess resistance as well as reactance, The quality of teal inductors is less than infinite. - GED A... that quality is defined as reactance { divided by resistance and that itis frequency | For an inductor, the formula for quality Q is EXAMPLE 11-6 What is'the quality of a 10-ml¥ coil (induc (or) at 150 Kia if its resistance is 60.0? Given: Hand X, = 6.28/L 28 XX Lo” 6.28 X 150,000 Hz 2 00LH. 9420 0 Answe ‘The @Q of the coil is 157. ‘The quality of iron-core inductors used at low frequencies is often less than 10, With air-core inductors operating at high frequen- cies, the quality can be more than 200. Typical RF chokes have a quality ranging from 30 to 150, The higher the quality of the coil, the less power the inductor uses. Also, the higher the quality, the farther the current and voltage are out of phase. Current and voltage are 90° out of phase only when there is no resistance. ‘The combined opposition offered by resistance and reactance is called impedance, Since an in- ductor has both resistance and reactance, it offers impedance to an ac current, To be technically Chapter 11 Inductance correct, we should specify the impedance of an inductoc. However, the dominant form of oppo- sition of an inductor is reactance, Therefore, we usually talk about its opposition in terms of re- actance only. When the quality of the inductor is above 5, the difference between its reactance and its impedance is less than 2 percent. Thus, the use ‘of reactance instead of impedance when caleulat- ing the current in an inductor is quite reasonable, It is especially reasonable when you consider that the inductance may be 20 percent above or below its rated value, Power Losses in Inductors It has already been emphasized that real in- ductors use power because of their resistance. However, their resistance may actually be greater than the resistance measured by an ohmmeter, This higher-than-measured resis tance is the resuit of the skin effect. The skin effect is caused by the tendency of electrons to travel close to the outer surface of a conductor Fig. 11-24). The higher the frequency, the more pronounced the skin effect becomes. Because of the skin effect, the center of a conductor does not contribute to the current-carrying capacity of the conductor. Thus, the effective resistance of the conductor at high frequencies is greater than that measured by an ohmameter Sold Elgorone conductor (a) OC end low frequencies sold Electrons conductor (0) Higher trequencies Fig. 11-24 Shin effect. At high frequencies, the current concentrates near the Surface 3 ofthe conductorThe skin effect can be minimized by using fitz wire, which is a multiple-conductor cable, Each conductor in litz wire has a very thin in- sulation on it. The conductors are very small in diameter (about 44 gage). These small, in- sulated conductors are twisted together to form. very small cable. When litz wire is used, the individual conductors are soldered together at the ends of the coil. This connects all the con- ductors in parallel to effectively make a single wire out of the multiple-conduetor cable. For a given overall diameter, litz wire provides more surface area than a single-strand conductor. Be- cause of this greater surface area, litz wire has 2 lower resistance at high frequencies, Answer the following questions. 46. Does an iron-core inductor or an air-core inductor have a higher quality rating? 47. What isthe quality of a 0.3-H inductor at 20 Kiiz if it has an effective resistance of 100.07 48, What is impedance? Tton-core inductors have power losses in their core material as well as in their winding. ‘Two actions cause the core to convert electric energy info heat energy. First, the magnetic field of the winding induces a voltage in the core material. The induced voltage causes a ‘smail current to flow in the core. This current, Produces heat in the core. The second action that causes power loss in the core isthe periodic reversal of the magnetic field, Every time the polarity ofthe magnetic fcid reverses, it creates ‘a small amount of heat in the core, Methods of ‘minimizing these core losses are discussed in the chapter on transformers, 49. What causes the resistance of a ‘conductor to be greater at high frequencies than at Jow frequencies? 50. What is lit wire? 51. What causes the core of a Jaminated-iron- core inductor to heat up? 11-8 Inductors in Parallel Parallel inductors (with no mutual inductance) can be treated just like: parallel resistors. The formulas used with resistors can be used with in- ‘ductors by substituting Z for R. The formalas are General method: Le 1 ane LtE tp tee Two inductors in parallel: LXL, L+t, equal inductors in parallel: - 1 te EXAMPLE 1 Se ‘What is the inductance of a 0.4-H induc- ‘or and a 600-mH{ inductor connected in parallel? Given: L-= 04 L, Find: eee & LX, own Ls aT EI 04H XO6H_ 0.24 Solution: Le= O28 = OCH Tat = 0.241 Answer: The total (or equivalent) * inductance is 0,24 H, ot 240 mH : ite wire Parallel inductors Inductance Chapter 11Total inductive reactance Parallel inductive reactances 300 Chapter 41 Inductance Notice that the total inductance is less than ‘the smallest of the parallel inductances. It al- _ Given: ‘ways is with parallel inductors, ‘The total inductive reactance of parallel im ductors can be found by either of two methods, Find: ve ‘The first method is to find the total inductance, Kmown: | X,= 6.28/1, as in example 11-7 and then find the total reac- X, xX, tance by using the reactance formula, The sec- ‘ond method is to determine the reactance ofthe 4 Me individual inductors and then, using the parallel Solution: 6.28 X 20,000 x 0.4 formula, combine the individual reactances to 50,2400 6.28 X 20,000 x 0.6 find the total reactance. The formulas for com- bining parallel inductive reactances have the 75,360 0 same structure as those used for parallel resis- 50,240 x 75,360 tances and parallel inductan Sep z 75,360 = 30,1 Cae melee ‘Answer: The total inductive reactance is 30,144 0. : X, T So yore Two parallel inductive reactances: As you might expect, the two methods used in examples 11-8 and 11-9 give exactly the same 2 Xu X He answer. i In parallel-inductor circuits the total current splits up in inverse proportion to the inductance of the individual inductors. The lowest indue- tance carries the highest current (Fig. 11-25). ‘The exact value of the current in each branch of the circuit can be found by using Obm’s law. EXAMPLE 14-8 Just replace the Rin Ohm's law with X,, The currents recorded in Fig. 11-25 were calculated Using the first method, find the total induc by using the reactances in example 11-9: tive reactance for example 11-7 when the ca quency is 20 kHz. ave n 40V ee LX. 502000 Given: Vy _40v Find: X,, 75,3608 Known: =053mA Solution: 6.28 "20,000 Hz. x 0241 4.99104 059mA = 30,1446. Answer: ‘The total inductive reactance is 30,1440, or 30.144k0. 4ov 4 QW) zo ez O84, EXAMPLE 14-9 Using, the second method, find the total Tama oR mA inductive reactance for example 11-7 when ig. 44-85 Currents in perolel inductors, The the frequency is 20 kHz. smaller inductor carries the greeter current.y, te 40V fom = ag gay ~ 0.00133 A = 133mA OF course, J, can also be found by using Kirchhoff's current law. For the citeuit of Fig. 11-25, we have hal, th, = 0.8 mA + 0.53 mA 33 mA, The current-divider formula used with par- allel resistors and resistances can also be used With parallel inductors and reactances. If J, in Fig, 11-25 was not known, it could be caleulated with the current-divider formula in either of these two ways: I,XX, % 7%, = 1.33 mA x 75.36 KO 50.24 KO + 75.36 KO 1X I, 1th 11-10 Inductors in Series ‘Treat series inductances and series reactances the same way you treat series resistances. The formula for series inductances is L,=L, +L, +L, + et, For inductive reactance in series the formula is X, 2X, +X, +X, + et. Again, the total reactance can also be determined. by the reactance formula if the total inductance is known. That is, X,,= 6.28/L, = 0.8 mA. 1.33 mA X0.6H_ O4HF 06H ~O8mA EXAMPLE 11-10 Using the reactance formula, find the total feactance at 60 Hz of a 3-H choke and a H choke connected in series. Gives: 1, =3H L,=5H F=.60 He uid: Xx, H+SH=8H 28 X 60 Hz X 8H. = 30140 : ‘The total inductive reactance is 3014.0. Answer: EXAMPLE 14-14 ——— Find the total reactance for example 11-10 ‘without first finding the total inductance. Given: 1, = 3H H 0 Hz Find: : Known: x, +X, 63851, 6.28 fL, Solution: X,''= 6.28 X 60 Hz X 31H 1130.9 6:28 X 60 Hz X SH 1884.0 X,,= 11300 + 1884.0, 3014.0 Answer: The total reactance is 3014.0) g # inductances As shown in Fig, 11-26, the total voltage in a Series series inductor circuit spits in direct proportion to the individual inductances: y, 3B oo = 125v 8H 4, Ea 7sv 20v eon CY Le Bi n25V Fig. 11-26 Voltages in series inductors, The larger inductor drops the greatar voltage. Inductance Chapter 11 reactances am~ u aie | a2 Chapter 11 ‘The exact voltage values can also be found by using Ohm's law and the reactances of example Il-I1, Again, Kirchhoff’s laws apply. The total voltage equals the sum ofthe individual cireuit voltages, 11-11 Time Constants for Inductors wo CRED a A. .... that in the previous chapter we looked { at time constants for resistor-capacitor (R-C) combinations. ‘The concepts developed there can easily be extended to cover resistor-inductor (R-L) com- binations. The only modification needéd is to think in turns of current rather than voltage. ‘The time constant for an R-L circuit is defined as the time required for the current through the resistorinductor to rise to 63.2 petcent of its final value, For an increasing ‘current, such as that shown in Fig, 11-27(a), % of fat current ‘of stating current Fig. 11-27 FEL time constants. Inductance the final value is the value determined by the resistance in the circuit and the voltage applied to the circuit, For a circuit in which the current is decreas- ing, the time constant is defined as the time re- quited for the inductor’s current to be reduced by 63.2 percent of its starting value. As shown in Fig, 11-270), itis also the time it takes for the current to decay to 36.8 percent of its former value, The time constant of an R-L cireuit can be calculated using the formula ‘The time constant is in seconds when L is in henrys and R is in ohms. Why the time is in seconds is shown by substituting equivalent base units into the formula, remembering that = —_volts Henrys = Sraperes/seconds and volts ‘Ohms = amperesThus, = inductance _ henrys eee eee aga ipbres/seconds volts X seconds _ _amperes ~—“volts ‘amperes = seconds EXAMPLE 11-12 TF Assume that the inductor in Fig. 11-27 is an ideal inductor rated at:10 H, If the resistor is 50.0, what is the time constant of the circuit in Fig, 11-272 Give Find: Known: i t i i Solution: Answer: The time constant is 0.2, It should be noted that 7 for practical values of R and L is usually in fractions of a second, Even if the resistor is removed from the circuit, the ohmic (4c) resistance of maltihenry inductors ‘keeps the time constant small. 11-12 Preventing Mutual Inductance ae) - that mutual inductance occurs when mag- hetic flux from a component induces a volt~ ‘ge in an electrically isolated component. Mutual inductance can be reduced ot prevented y the following methods: 1. Axis orientation E 2. Physical separation 3. Shieiding uppose the center axes of two coils are at 90° y° each other, as shown in Fig, 11-28(@). Under (2) Very ite mutual rcuotanca ] U (©) High mutual incuetanee ig. 11-28 Axis orientation and mutual inductance, this condition, very little of the flux from one oil cuts the other coil. We say that very little : coupling occurs between the coils (inductors). Coupling When the axes of the coils are lined up and close together, as in Fig. 11-28(b), mutual in- ductance results. When inductors are physically separated, ‘mutual inductance is reduced, The farther apart the inductors are, the less mutual inductance (Coupling of flux) they have, An inductor that is enclosed in a magnetic shield has very little mutual inductance with surrounding inductors. The flux from surround- ing inductors passes throilgh the low reluctance (high permeability) of the shield rather than through the inductor. 11-13 Undesired Inductance As mentioned earlier, all conductors possess +, inductance. The inductance of a single wire, | although low, is significant at very high frequen. { cies. Often this inductance is undesirable because | of Bs efet onthe electie or ectronie cnet, [ermal SE Ta high-frequency circuits, imerconnecting leads are keptas short as possible to reduce inductance, Career ‘and other ‘Whenever possible, the inductance of the leads information is used as part of the required inductance of the 8" be found at ee sews for As mentioned in See. 11-4, wire-wound and 8 Eectroris : ind ndusries fepositedflm resistors may have an apprec- pSMSUS ble amount of inductance, Their resistive cle- ‘ments are coils of conductive material wound on @ nonmagnetic insulator form. In de and Inductance Rhantew 44 anoNoninductive wire-wound resistors low-frequency ac circuits, this undesired in- ductance has very little reactance and can be ignored. However, at higher frequencies the reactance becomes greater and the total oppo- sition (impedance) of the resistor significantly exceeds its resistance. In many electronic cir- cuits this is undesirable and unacceptable. ‘To minimize the above problem, special non- inductive wire-wound resistors are produced. In Answer the following questions. 52, A03-H inductor and a 0.6-H inductor are connected in parallel. They are connected toa 15-V, 150-Hz source. a. What is their total, or equivalent, inductance? '. What is the total reactance? c, What is the total current? 4. What is the current through the 0.6-H inductor? 53, Suppose the inductors in question 52 are now connected in series rather than parallel a. What is the total inductance? b. What is the total reactance? . What is the total current? . What is the voltage across the 0.6-H inductor? these resistors, half the turns of wire are wound clockwise and half are wound counterclockwise. ‘Thus the magnetic field of half of the turns can- cels the field of the other half of the turns. These resistors are often used in high-power circuits ‘when the load on the circuit must be independent of the frequency, 54, How can you minimize the mutual inductance between two coils? 53. How is a wire-wound noninductive resistor constructed? 56. Determine the time constant of a 30-H ideal inductor connected in se- ries with a 60-0 resistor and a 10-V de source. 57. A 4-mH inductor is connected in series with a 6-mH inductor to a 30-V source. Determine the voltage across the 4-mH inductor. 58. Assume the inductors in question 57 are in parallel instead of series. Determine the current through the 6-mH inductor if 1,.is 10 ma. 304 Chapter 11. InductanceChapter 11 Summary and Review SE 1. Inductance opposes changes in current. 2. Inductance results from induced voltage. 3, Inductors are devices that provide inductance, Chokes, coils, and reactors ate other names for inductors. 4, The symbol for inductance is L. 5. The induced voltage in an inductor is known 4s counter electromotive force (cemf) or back electromotive force (bem). 6. Lenz’s law is concerned with the polarity of an induced voltage (cemf), 7. A cemf opposes the change that created it. 8. Inductors convert energy back and forth between the magnetic form and the electrical form. 9. The henry is the base unit of inductance. The abbreviation for hency is H. 10. Inductance is determined by (1) core material, (2) number of tums, (3) spacing of turns, and (4) diameter of turns, 11. Inductors are rated for inductance, de resistance, current, voltage, quality, and tolerance. 12. The de resistance of an inductor is also called ohmic resistance, 13, The quality Q of inductors ranges from less than 10 to more than 200. 14, Current in a de inductive cireuit rises more slowly than in a de resistive circuit. 15. Ina de inductive circuit, voltage (cemf) reaches its peak value before the current does. 16. Inductive kick causes arcing in switch contacts ‘when an inductive cirenit is opened. 17. 18. 19. 20. 21. 22. 23. 24, 2s, 26. 21, 28, 29, 30. 31. 32, Inductive reactance is the opposition of an inductor to alternating current, ‘The symbol for inductive reactance is X,, Inductive reactance is directly proportional to both frequency and inductance. ‘Ohm's law can be used in inductive circuits by replacing R with X,. In an inductive circuit, current lags voltage by 90°. deal inductors use no power or energy. Real inductors have resistance; therefore, they do use some power, : Impedance is the combined opposition of reactance and resistance, ‘The skin effect increases the effective resistance of a conductor at high frequencies. Litz wire is multistrand wire designed to reduce the skin effect, Core losses are cafsed by induced currents in the core and by periodic reversal of the magnetic field. Inductors (and inductive reactances) in parallel behave like resistors in parallel. The same formulas are tised éXcept that R is replaced by L or X,. Inductors (and inductive reactances) in series behave like resistors in series ‘The lowest series inductance drops the least voltage, ‘Mutual inductance can be reduced by axis, orientation, physical separation, and shielding, Undesired inductance occurs in conductors and resistors. Trees) Inductance: ‘The quality Q for en inductor: Time constant: ieee TOR Vissios ‘Alfat Inductive reactance: x, 6.28fL Inductance Chapter 11 305Related Formulas...continued For series inductors: For parallel inductors: Lp=L, +L, + et A 1 = roped X,,=%,, +X, + ete Ltt Chapter Review Questions For questions 11-1 to 11-12, determine whether each 11-15, The abbreviation for the base unit of inductance statement is true or false. is ai-2) 11-1. A straight length of conductor has no induc- 11-16. The base unit for inductive reactance is the tance. (11-1) see CLL a 11-2, A 2-H inductor would most likely have a lami- 11-17. The symbol for inductive reactance is nated iron core. (11-4) ——_ 1) 11-3, Magnetic shields for inductors ae usually made ‘11-18. When current in an inductor is increasing, the from high-reluctance materials. (11-12) cemf ______ the source voltage. (11-1) 11-4, The reactance of an inductor can be measured 11-19. Another name for cemf is __. (11-1) with an ohmmeter. (11-7) 11-20. Inductive reactance i proportional 11-5. The core material in a variable inductor is often to frequency. (11-7) called a toroid. (11-4) 11-21. When one coil induces a voltage in another coil, 11-6. Maximum inductance in a variable inductor oc- the process is called —_.. (11-1) curs when the brass slug is centered within the 11-22. Voltage _______ current by coil core, (11-4) degrees in an ideal inductor. (11-7) 11-7, The cemf exceeds the source voltage when an. 11-23. Inductors are also known as. inductive circuit is opened. (11-6) and —___. (11-1) 11-8. The iron core of an inductor converts some 11-24. The center leg of an iron-core cazries electric energy into heat energy. (11-8) as much flux as an outside leg does. (11-4) 11-9. The quality of a coil is frequency-dependent, 11-25. The polarity of the cemf can be determined by (11-8) applying __ law. (11-1) 11-10. A small induced current flows in the core of an 11-26. The electric quantity that opposes change in iron-core inductor. (11-8) current is __. (11-1) 11-11. The lowest-value inductor drops the most volt- 11-27. An inductor converts ____ energy to age in a series-inductor circuit. (L1-10) ———— energy while the current is increas- 11-12. The lowest-value inductor draws the most cur- ing. (11-1) rent in a parallel-inductor circuit. (11-9) 11-28. The resistance of the tars of wire in an indue- ; toris called _ or For questions 11-13 to 11-30, supply the missing word or resistance. (11-5) Pee 11-29. Arcing between the switeh contacts when an 11-13. wire is used to reduce the skin inductive citcuit is turned off is caused by effect. (11-8) (11-6) 11-14. The base unit of inductance is the : 11-30. The combined opposition of regetance and a-12) resistance is called (1-8) 308 Chapter 11 InductanceCI omecnae Neen questions: 11-31. What are three techniques used to minimize or eliminate matual inductance? (11-12) 11-32. What four factors determine the inductance of ‘an inductor? How can inductance be increased ‘using each of these factors? (11-3) eTUa made 11-1, What is the time constant of a 500-miH ideal indue- tor connected in series with a 10-0 resistor? (L1-11) 11-2, What are the reactance and current in a circuit that consists of a 300-mH inductor connected 10 a.20-V, 7.5-KHz source? (11-7) 11-3, Determine the quality of a 70-mH inductor that hhas a resistance of 125-01 at 35 kHz, (11-8) 1-4, Determine the total inductance and the circuit cur- Tent of a 4-H inductor and a 6-H inductor series ‘connected to a 400-Hz, 80-V supply. Also deter- mine the voltage across the 4-H inductor. (11-10) 11-5, Whats the inductance of a 5-mH inductor and a 7-mH inductor connected in parallel? (11-9) 11-6. How much inductance is needed to limit the current from a 50-V, 200-Hz source to 25 mA? (il-7) CORI ke teeny 11-1, Two variable inductors are identical except that cone has a brass slug, and the other a ferrite slug, Which inductor would have the larger range of inductance? 11-2, Why aren’ inductor shields made from nonfer- ous materials such as tin or plastic? 11-3, Ata given current, would a swinging choke or ‘a smoothing choke have the larger inductance if the choke had identical coils and the same size and shape of core? Why? 11-4, Why is the total inductance of two series inductors agreater than the inductance of the larger inductor? 11-5, Why are parallel inductive reactances treated like parallel resistances when figuring the total reactance? 11-6. Why does periodic reversal of the magnetic field cause a magnetic core to produce heat? a alee) 11-33. What electrical ratings are used to completely specify an iron-core inductor? (11-5) 11-34. What happens to Q when the resistance of an inductor increases? (11-5) 11-7, Two inductors are connected in seties to a 35-V source. Determine V,, if L, = 0.36 Hand 1, = 0.54 H. (11-9) 11-8, Determine the value of L needed to produce a time constant of 0.003 s when R = 20.0 and V,= SOV. (11-1) 11-9. An inductor produces 4 V of cemf when its cure ent changes at a rate of 1.2 amps in 0.5 s, What is its inductance? (11-2) 11-10. The inductor in problem 11-9 above is con- neeted to a 24-V, 400-Hz source. Determine its Feactanoe and current. (11-7) 11-11, How much voltage is required from an 300-Hz source to force 0,06 A through a 0.8-H inductor? (11-7) 11-7. What is the frequency of the source voltage when a 0.13-A current drops 20 V across a 0.04-H inductor? 11-8. Why can we use either the values of X, or the Values of L in the current-divider formula for parallel inductor circuits? 11-9. A 200-mH (L,) and a 0.15H (L,) inductor are ‘connected in parallel and draw 46 mA from the power source, Determine, 11-10. Would you expect the current and voltage to be in phase in a circuit containing impedance? Why? 11-11, An inductor produces 0.5 V of cemf when the current is increased at a uniform rate from 20 mA to 60 mA in2 ms. Determine the inductance of the inductor. Show your calculations, Inductence Chapter 14 3071. inductance 2. choke, coil, reactor, inductor Denon 9. Lena's 10. bef IL, electric, magnetic 12, henry 13, H 14, volt per ampere per second 15, increase 16, Use a core with higher permeability or less reluc- tance, inerease the number of tums, put the turns closer together, increase the diameter of the turns. 17. a. See Fig, 11-6). b. See Fig. L1-6(6). ©. See Fig. 11-7. Sopa sn 24, laminated-iron core 25. doughnut-shaped 26. Because it carries twice as much ux. 27. Because too much current will cause the winding to overheat, 28. the ratio of reactance to resistance 29. an inductor or coil designed to be used at radio frequencies 30. laminated-iron 31. the high cemaf that occurs when an inductive circuit is opened 32, inductive 4. 42, 43. 1.43 45. 47, 48. 49. 50. 51 52. 53. 54, 55, 56, 37, 38. . nO the cemf of the inductor ae X, = 6.28/L, double 2, 2262.0, 9425.0, ©. 471240 400 lag, 90° 10 223 ki air-core inductor 37 Impedance is the combined opposition of resistance and reactance, skin effect Litz wire is multistrand wire used to reduce the skin effect, induced currents and magnetic polavity reversal a. 0.2H b. 188.50 ©. 79.6 mA 4.26.5 mA. a09H 848.0 177 mA 4.10V Orient the axes 90° to each other, separate the coils, and shield them. Half the turns ere wound in one direction and the other half are wound in the opposite direction. 05s Rv 4mA+ Inductance | Chapter 11