# After completing this chapter, the student should be able to:

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1 Inductance OBJECTIVES After completing this chapter, the student should be able to: Explain the principles of inductance. Identify the basic units of inductance. Identify different types of inductors. Determine the total inductance in series and parallel circuits. Explain L/R time constants and how they relate to inductance. See accompanying CD for interactive presentations and tutorials relating to Chapter 10. When a current flows through a conductor, a magnetic field builds up around the conductor. This field contains energy and is the foundation for inductance. This chapter examines inductance and its application to DC circuits. Inductance is covered in more detail in Chapter 16. INDUCTANCE Inductance is the characteristic of an electrical conductor that opposes a change in current flow. An inductor is a device that stores energy in a magnetic field. Inductance exhibits the same effect on current in an electric circuit as inertia does on velocity of a mechanical object. It takes more work to no start a load moving than it does to keep it moving because the load possesses the property of inertia. Inertia is the characteristic of mass that opposes a change in velocity. Once current is moving through a conductor, inductance helps to keep it moving. The effects of inductance are sometimes desirable and other times undesirable. As noted in Chapter 9, the basic principle behind inductance states, when a current flows through a conductor, it generates a magnetic field around the conductor As the magnetic flux lines build up, they create an opposition to the flow of current. When the current changes direction or stops, or the magnetic field changes, an electromotive force (emf) is induced back into the conductor through the collapsing of the magnetic field. The opposition to the changes in current flow is iden-

2 CHAPTER 10 INDUCTANCE tified as counter electromotive force (counter emf). This effect is summarized by Lenz's law-an induced emf in any circuit is always in a direction to oppose the effect that produced it. The amount of counter emf is in proportion to the rate of change. The faster the rate of change, the greater the counter emf. All conductors have some inductance. The amount of inductance depends on the conductor and the shape of it. Straight wire has small amounts of inductance whereas coils of wire have much more inductance. The unit by which inductance is measured is the henry (H), named for Joseph Henry ( ), an American physicist. A henry is the amount of inductance required to induce an emf of 1 volt when the current in a conductor changes at the rate of 1 ampere per second. The henry is a large unit; the millihenry (mh) and microhenry (ILH) are more commonly used. The symbol for inductance is L. FIGURE 10-1 Schematic symbol for an inductor ~~ FIGURE 10-2 Schematic symbol for a variable inductor. -~- FIGURE 10-3 Several types of inductors used to vary the inductance QUESTIONS 1. Define inductance. 2. What is the unit for measuring inductance? 3. Define a henry. 4. What letter is used to represent inductance? FIXED INDUCTORS ImDINDUCTORS Inductors are devices designed to have a specific inductance. They consist of a conductor coiled around a core and are classifiedby the type of core material-magnetic or nonmagnetic. Figure 10-1 shows the symbol used for inductors. Inductors can also be fixed or variable. Figure 10-2 shows the symbol for a variable inductor. Variable inductors are created with adjustable core material. Figure 10-3 shows several types of VARIABLE INDUCTORS

3 SECTION I DC CIRCUITS FIGURE 10-4 An air-core inductor. FIGURE 10-6 Toroid-core inductor. FIGURE 10-5 Schematic symbol for an iron-core inductor ~~ inductors used for adjusting the core material. Maximum inductance occurs when the core material is in line with the coil of the wire. Air-core inductors, or inductors without core material, are used for up to 5 millihenries of inductance. They are wrapped on a ceramic or phenolic core (Figure 10-4). Ferrite and powdered iron cores are used for up to 200 millihenries. The symbol used for an iron-core inductor is shown in Figure Toroid cores are donut-shaped and offer a high inductance for a small size (Figure 10-6). The magnetic field is contained within the core. Shielded inductors have a shield made of magnetic material to protect them from the influence of other magnetic fields (Figure 10-7). Laminated iron-core inductors are used for all large inductors (Figure 10-8). These inductors vary from 0.1 to 100 henries, the inductance depending on the amount of current flowing through the inductor. These inductors are sometimes referred to as chokes. They are used in the filtering circuits of power supplies to remove AC FIGURE 10-7 Shielded inductor. components from the DC output. They will be discussed further later on. Inductors typically have tolerances of ± 10%, but tolerances of less than 1% are available. Inductors, like resistors, can be connected in series, parallel, or series-parallel combinations. The total inductance of several inductors connected in se-

4 CHAPTER 10 INDUCTANCE FIGURE 10-8 Laminated iron-core inductor. 5. What is the total inductance of a circuit with three inductors, 10 H, 3.5 H, and 6 H, connected in parallel? L/R TIME CONSTANTS A time constant is the time required for current through a conductor to increase to 63.2% or decrease to 36.8% of the maximum current. An RL circuit is shown in Figure LlR is the symbol used for the time constant of an RL circuit. This can be expressed as: L t =- R ries (separated to prevent their magnetic fields from interacting) is equal to the sum of the individual inductances. I,. = L1 + L2 + L Ln If two or more inductors are connected in parallel (with no interaction of their magnetic fields) the total inductance is found by using the formula: where: t = time in seconds L = inductance in henries R = resistance in ohms Figure charts the growth and decay (or increase and decrease) of a magnetic field, in terms of time constants. It takes five time constants to fully transfer all the energy into the magnetic field, or to build up the maximum magnetic field. It takes five full-time constants to completely collapse the magnetic field QUESTIONS 1. What are inductors? 2. Draw the symbols used to represent fixed and variable inductors. 3. What is another name for a laminated iron -core inductor? 4. What are the formulas for determining total inductance in: a. Series circuits? b. Parallel circuits? FIGURE 10-9 Circuit used to determine UR time constant. GROWTH DECAY

5 114 SECTION I DC CIRCUITS FIGURE Time constants required to build up or collapse the magnetic field in an inductor. I- 100 z w a: 80 o ::2! ~ 60 X «::2! 40 u... o -ן m 20 o a: w ~... I----GROWTH ---~~I... / ~ \9.301< 98.2% 95% / 86.5% \ J " 63.2% \ 1\:% I i "~ CL o 1 2 TIMECONSTANTS I---- DECAY j ~1 5.0% 1.8% ~ % 10-3 QUESTIONS 1. What is a time constant for an inductor? 2. How is a time constant determined? 3. How many time constants are required to fully build up a magnetic field for an inductor? 4. How many time constants are required to fully collapse a magnetic field for an inductor? 5. How long does it take to fully build up a magnetic field for a O.I-henry inductor in series with a IOO,OOO-ohmresistor? SUMMARY Inductance is the ability to store energy in a magnetic field. The unit for measuring inductance is the henry (H). The letter L represents inductance. Inductors are devices designed to have specific inductances. The symbol for fixed inductance is: ----~~~-- The symbol for a variable inductor is: Types of inductors include: air core, ferrite or powdered iron core, toroid core, shielded, and laminated iron core. The total inductance for inductors connected in series is calculated by the formula: LT = L J + L2 + L Ln The total inductance for inductors connected in parallel is: 1 1 III --= L J L2 L3 r., A time constant is the time required for current to increase to 63.2% or decrease to 36.8% of the maximum current.

6 CHAPTER 10 INDUCTANCE A time constant can be determined by the formula: L t =- R It takes five time constants to fully build up or collapse the magnetic field of an inductor. CHAPTER 10 SELF-TESr \ ".' 1. How can the magnetic field be increased for a particular inductance? 2. What is the total inductance for the circuit shown? 3. A 500-mH inductor and a 10-kilohm resistor are connected in series to a 2S-volt source. What will be the voltage across the inductor 100 microseconds after energizing the circuit?.' c-. ~= 800 /1H L4 = 125 /1H

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