Capacitors and Inductors

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DC Principles Study Unit Capacitors and Inductors

By Robert Cecci In this text, you’ll learn about how capacitors and inductors operate in DC circuits. As an industrial electrician or electronics technician, you’ll be likely to encounter capacitors and inductors in your everyday work. Capacitors and induc-

tors are used in many types of industrial power supplies, Preview Preview motor drive systems, and on most industrial electronics printed circuit boards.

When you complete this study unit, you’ll be able to • Explain how a capacitor holds a charge • Describe common types of capacitors • Identify capacitor ratings • Calculate the total capacitance of a circuit containing capacitors connected in series or in parallel • Calculate the time constant of a resistance-capacitance (RC) circuit • Explain how inductors are constructed and describe their rating system • Describe how an inductor can regulate the flow of current in a DC circuit • Calculate the total inductance of a circuit containing inductors connected in series or parallel • Calculate the time constant of a resistance-inductance (RL) circuit

Electronics Workbench is a registered trademark, property of Interactive Image Technologies Ltd. and used with permission.

You’ll see the symbol shown above at several locations throughout this study unit. This symbol is the logo of Electronics Workbench, a computer-simulated electronics laboratory. The appearance of this symbol in the text margin signals that there’s an Electronics Workbench lab experiment associated with that section of the text. If your program includes Electronics Workbench as a part of your

iii learning experience, you’ll receive an experiment lab book that describes your Electronics Workbench assignments. When you see the symbol in the margin of your text, fol- Remember to regularly check “My Courses” low the accompanying instructions in the lab book to on your student complete your Electronics Workbench assignment. If your homepage. Your program doesn’t include Electronics Workbench, you may instructor may post simply ignore the symbol. additional resources that you can access to enhance your learning experience. INTRODUCTION TO CIRCUIT COMPONENTS: CAPACITORS 1

What Is a Capacitor? Contents How Do Capacitors Work? Contents Capacitance Leakage Current Capacitor Types and Ratings Capacitors Connected in Series Capacitors Connected in Parallel RC Time Constants Uses of Capacitors Testing Capacitors Working with Capacitors

INTRODUCTION TO CIRCUIT COMPONENTS: INDUCTORS 49 What Is an Inductor? How Do Inductors Work? Inductor Types and Ratings Inductors Connected in Series Inductors Connected in Parallel RL Time Constants Uses of Inductors

POWER CHECK ANSWERS 65

v Capacitors and Inductors

INTRODUCTION TO CIRCUIT COMPONENTS: CAPACITORS

What Is a Capacitor?

A capacitor is a device that can store and release an electrical charge over a period of time. Capacitors are widely used in electrical and electronic circuits. A basic capacitor consists of two conductive metal plates separated by a thin layer of non- conducting or insulating material called the dielectric. The dielectric may be simple air space, a vacuum, or it may be made of paper, ceramic, tantalum, polyester, polystyrene, polypropylene, or other nonconductive materials. A simplified drawing of the structure of a capacitor is shown in Figure 1. Note that in a real capacitor, the capacitor plates may be flat and rectangular, circular, or tube-shaped.

FIGURE 1—This figure is a simplified drawing of the construction of a capacitor.

1 FIGURE 2—These symbols are used to represent the various types of capacitors.

Figure 2 shows the symbols used to represent capacitors in electrical drawings. All the symbols show the two capacitor plates separated by a space. Note that the symbols for variable capacitors contain arrows. (We’ll discuss the different types of capacitors a little later in this text.)

How Do Capacitors Work?

A capacitor stores its charge of electricity in an electric field located between the capacitor’s conductive metal plates. This electric field is created when unlike charges are placed on the capacitor’s plates. For example, if the negative and positive leads of a power source (such as a battery) are connected to the capacitor plates, the plate connected to the positive lead will receive a positive charge and the plate connected to the negative lead will receive a negative charge. The electrons on the negatively charged plate are attracted to the positive plate, but because of the space between the plates, the electrons won’t be able to reach the positive plate. As a result, the capacitor holds the charge even after the voltage source is removed. This stored energy can then be applied to another load or device until the charge on both capacitor plates is equalized. The basic operation of a capacitor in a DC (direct current) circuit is shown in Figure 3. In the figure, when the switch is closed, electrons flow from the negative battery terminal

2 Capacitors and Inductors FIGURE 3—When the switch is closed, electrons move from the negative battery terminal to the negative plate of the capacitor. Electrons also move away from the positive plate of the capacitor toward the positive terminal of the battery.

toward the upper capacitor plate, giving it a negative charge. At the same time, electrons flow away from the lower capacitor plate toward the positive battery terminal, giving it a positive charge. The upper plate gains electrons until it reaches the same potential as the negative terminal of the bat tery. The lower plate loses electrons until it reaches the same potential as the positive terminal of the battery. At this time, the voltage across the capacitor is the same as the source voltage. Then, even when the source voltage is removed by opening the switch, the capacitor holds or stores the electric charge. When a dielectric other than air or a vacuum is placed between the charged plates of a capacitor, the electric field between the plates is reduced. A dielectric made of insulating material has no free electrons available for current flow. The electrons in the dielectric material are tightly held in their orbits, so none of the electrons can escape from the dielectric and move into the circuit. When a voltage source is applied to the capacitor plates, the positive and negative plates become charged and exert force on the electrons of the dielectric. The positive plate attracts the electrons of the dielectric, and the negative plate repels the electrons of the dielectric. These forces cause the electrons of the dielectric to become displaced. This displacement is shown in Figure 4. In 4A, there’s no charge on the capacitor and therefore no displacement of the electrons. In 4B, a positive charge has been applied to the right-hand plate. You can see how the electrons in the dielec-

Capacitors and Inductors 3 FIGURE 4—The force of the source of potential will cause the orbits of the electrons of the dielectric material to deflect creating a stored charge in the electric field of the dielectric.

The label EP shows the electric field created by the charge on the capacitor plates. The label ED shows the electric field in the dielectric.

tric have been attracted to and displaced toward the positive plate. In 4C, a positive charge has been applied to the left- hand plate. Again, you can see how the electrons in the dielectric have been displaced toward the positive plate. Figures 4B and 4C show that the electric field in the dielectric is in the opposite direction from the electric field created by the capacitor plates. As a result, the net electric field in the dielectric space decreases when a dielectric other than air or a vacuum is placed on the space between the capacitor plates. Since the value of the capacitor is equal to the charge on the plates divided by the electric field between the plates, the value of the capacitor increases when a dielectric is placed between the plates. When the value of a capacitor with a non-vacuum dielectric is divided by the value of a capacitor with a vacuum dielectric, the resulting value is called the dielectric constant of the insulating material, or K. A vacuum dielectric has a dielectric constant of 1, and all other dielectric materials have a dielectric constant greater than 1. Let’s observe the charging and discharging of a capacitor with a simple experiment. Figure 5 shows an experiment involving a small battery, a large-value capacitor (100 microfarads), and a light bulb. To charge the capacitor, touch the capacitor

4 Capacitors and Inductors FIGURE 5—The capacitor shown here can be fully charged in about three seconds.

leads to the terminals of the battery as shown in Figure 5A. Allow the capacitor leads to touch the battery terminals for about three seconds. This time period is sufficient to fully charge the capacitor in this example. After the capacitor has been fully charged, remove the capacitor leads from the battery terminals and touch them to the terminals of the light bulb as shown in Figure 5B. The bulb will glow brightly at first, and will then grow dimmer as the capacitor discharges.

Capacitance

Capacitance is defined as the ratio of the charge of either capacitor plate to the voltage difference between the plates. Capacitance is measured by the amount of electricity needed to raise the capacitor’s charge from zero to maximum. A capacitor’s charge is a static charge; that is, the charge is stationary, not moving. There’s no DC current flow in a capacitor. The basic unit of capacitance is the farad, abbreviated F. One farad of capacitance is produced by a capacitor when one coulomb of electrical charge is stored in the capacitor with a potential of one volt across the plates. (One coulomb is the amount of electricity transferred by a current of one ampere in one second.)

Capacitors and Inductors 5 One farad is a very large quantity of capacitance. For this reason, the capacitors used in electric or electronic systems typically have a much smaller value than one farad. The capacitance value of these capacitors is usually measured and expressed in microfarads. One microfarad is equal to 0.000001 farad, or 1 106 farad. You’ll often see microfarads abbreviated using the Greek symbol (µ) and the letter F, like this: µF. So, 10 microfarads would be abbreviated 10 µF. A large-value capacitor would be in the 3,500 µF range. A small-value capacitor would be in the 25 µF range. Capacitors that are smaller than 0.01 µF are rated in picofarads. One picofarad is equal to 0.000000000001 farad, or 1 1012 farad. In notations on electrical or electronic dia- grams, the picofarad is abbreviated pF. So, a capacitor with a value of 100 picofarads would be abbreviated 100 pF. There are four factors that can influence capacitance. These are 1. The area of each capacitor plate 2. The spacing between the plates 3. The addition of a dielectric material 4. The material the dielectric is made of Let’s examine these four factors in more detail. First, one of the greatest influences on capacitance is the area of the capacitor plates. A capacitor with small plates (Figure 6A) has much less capacitance than a capacitor with larger plates (Figure 6B). This increase in capacitance is due to the increased area in which a charge may be present. Another factor influencing capacitance is the space between the capacitor plates. The farther apart the plates are, the lower the capacitance (Figure 7). The addition of a dielectric material (other than air) between the capacitor’s plates will also affect capacitance. As shown in Figure 8, the addition of a dielectric material increases the capacitance of a capacitor. The dielectric material used also influences capacitance. Some dielectric materials increase capacitance more than others. Table 1 shows several different dielectric materials and their dielectric constants.

6 Capacitors and Inductors FIGURE 6—The capacitor shown in 6A has smaller plates and less capaci tance than the larger capacitor shown in 6B.

FIGURE 7—The capacitor plates in 7A are farther apart than the plates in 7B. Therefore, the capacitance of 7A is less than the capacitance of 7B.

A material’s dielectric constant rates how well the material acts as a dielectric as compared to a vacuum. For example, mica has a dielectric constant of 5.0 and paraffined paper has a dielectric constant of 2.5. This means that mica has twice the capacitance of paraffined paper (for an equal area and thickness of dielectric material).

Capacitors and Inductors 7 FIGURE 8—The addition of a dielectric material between the plates of a capacitor increases capacitance.

Table 1 DIELECTRIC CONSTANTS

Dielectric Material Dielectric Constant (K)

Vacuum 1.0

Air 1.001

Paraffined Paper 2.5

Rubber 3.0

Oil 4.0

Mica 5.0

Porcelain 6.0

Glass 7.5

Tantalum Pentoxide 26.0

Distilled Water 80.0

Ceramic 7500.0

The term dielectric strength refers to the maximum voltage that a dielectric can withstand without puncturing. A dielectric material has a very high resistance to current when a low voltage is applied to it. However, the same dielectric may offer little resistance to current when a high voltage is applied.

8 Capacitors and Inductors In a given capacitor, the following quantities have a mathe- matical relationship: • The capacitance of the capacitor

• The area of the capacitor plates

• The dielectric constant

• The distance between capacitor plates

This relationship can be illustrated with this formula:

2.2479 × 10–13 KA C = d In the formula, C stands for capacitance; K stands for the dielectric constant; A stands for the area of the capacitor plates in square inches and d stands for the distance between the capacitor plates in inches.

Leakage Current

No dielectric is a perfect insulator. There will always be a small flow of current that escapes through a dielectric whenever a voltage is applied across a capacitor’s plates. This small amount of current is called leakage current. On an electrical diagram, leakage current is represented by a resistor drawn in parallel with the capacitor (Figure 9).

FIGURE 9—All capacitors have a certain amount of leakage current due to internal resistance. This symbol is used to represent leakage current on an electrical diagram.

The actual value of leakage current is very low due to the extremely high resistance value of the dielectric. The resistance value of capacitors (the insulation resistance) is

Capacitors and Inductors 9 measured in megohms. A typical capacitor has an insulation resistance of 100 megohms or more. However, some capacitors (such as electrolytic capacitors) have a lower resistance value and much larger amounts of leakage current. Leakage current is measured in milliamps (mA) or microamps (µA). Now, take a few moments to review what you’ve learned by completing Power Check 1.

10 Capacitors and Inductors Power Check 1

At the end of each section of your Capacitors and Inductors text, you’ll be asked to check your understanding of what you’ve just read by completing a “Power Check.” Writing the answers to these questions will help you review what you’ve learned so far. Please complete Power Check 1 now.

Indicate whether each of the following statements is True or False.

1. A capacitor is a device that can store and release an electric charge over a period of time.

2. A capacitor’s electric charge is stored in the electric field between the capacitor’s plates.

3. A capacitor’s dielectric is made of conductive metal.

4. When fully charged, a capacitor has one-half the voltage of the power source.

5. The basic unit of capacitance is the farad (F).

Check your answers with those on page 65.

Capacitors and Inductors 11 Capacitor Types and Ratings

There are two basic types of capacitors: fixed and variable. Fixed capacitors have a fixed capacitance value; that is, the capacitance value can’t be changed. However, the capacitance of a variable capacitor can be changed. Variable capacitors have adjustable plates. That is, the surface area of the plates can be varied. The amount of adjustment varies, and the capacitance value varies accordingly. Let’s start by looking at the various types of fixed capacitors: electrolytic, mica, ceramic, paper, tantalum, and polyester film.

Electrolytic Capacitors

One of the most common types of fixed capacitors is the electrolytic capacitor. Electrolytic capacitors may be classified as wet or dry. A wet electrolytic capacitor contains a positive capacitor plate suspended in a metal can filled with dielectric fluid (such as transformer oil). The can serves as the negative plate. A dry electrolytic capacitor is made of a roll of aluminum foil coated with aluminum oxide (an insulator) on one side. The aluminum oxide acts as the dielectric and the aluminum foil is the positive capacitor plate. A layer of paraffined paper is placed between the oxide-coated foil and a second sheet of foil. The second layer of foil is the negative capacitor plate. The layered foil and paper is then tightly wound, and two metal leads are attached. The capacitor is then placed in a sealed metal can to complete the assembly. Electrolytic capacitors typically have capacitance values of between one and several thousand micro farads. With the exception of tantalum capacitors, dry electrolytic capacitors offer the greatest capacitance in the smallest package. Electrolytic capacitors are often termed polarized capacitors. The polar ity of the plates is always plus () and minus (). When the electrolytic capacitor is properly connected to a circuit with the () terminal more positive than the () terminal, the capacitor will charge and have a very small leakage current. However, if an electrolytic capacitor is placed backwards in a circuit (that is, with the negative terminal

12 Capacitors and Inductors more positive than the positive terminal) the aluminum oxide layer won’t act as a dielectric. Instead, a large amount of current can flow through the capacitor—it will functionally act as a low-value resistor. As a result, the capacitor will be destroyed. In fact, older units would often explode under these conditions. However, most modern electrolytic capacitors that are housed in metal cans contain small blowout plugs to release the expanding gases that result from a failed installation. Some electrolytic capacitors are single units. Three single- unit capacitors are shown in Figure 10. An axial lead capacitor is shown in 10A. The term axial lead means that a lead is located at each end of the capacitor. Usually, a black band or a negative sign () is located on the capacitor to indicate its negative plate. Figure 10B shows a radial lead capacitor. A radial lead capacitor contains two leads that exit the bottom of the capacitor. A stripe is used to identify the negative lead. Radial lead capacitors are usually mounted on printed circuit boards. Figure 10C shows a large-value elec-

FIGURE 10—Three common types of electrolytic capacitors are shown here.

Capacitors and Inductors 13 trolytic capacitor. This type of capacitor has solderless, push- on “male” terminals, solder lugs, or screw-type terminals at the top of the capacitor. A typical multiunit electrolytic capacitor is shown in Figure 11. This cylinder-shaped capacitor is actually four capacitors in one. In 11A, note the symbols at the left of each capacitance value: a semicircle, a square, a triangle, and a straight line. In 11B, these same symbols are punched into the insulating disc next to the corresponding solder lug. The upper left hand lug has the value indicated by the straight line in 11A. This value is 30 microfarads (30 µF) with a rating of 300 VDC. The lug with the semicircle symbol means that this lug is for the 50 µF, 450 VDC terminal of the capacitor. All the capacitors in this package are connected to a common ground. The ground is available for connection at the two solder lugs toward the outside of the case.

FIGURE 11—A typical multiunit electrolytic capacitor is shown here.

Almost all large electrolytic capacitors have a voltage rating that must never be exceeded. For example, if a capacitor has a rating of 25 WVDC (or 25 VDC), then no more than 25 volts may be applied across the capacitor. If the voltage rating is exceeded, the capacitor may be damaged. In this rating, WVDC stands for “working volts DC.” Typical working voltages can range from five volts to many hundreds of volts DC.

14 Capacitors and Inductors Electrolytic capacitors are most often used in electrical or electronic power supplies. They’re used to filter the alternating current or AC ripple that can appear at the output of the rectifier in the DC power supply. They’re also used as charge storage devices, since their large capacitance values can hold a voltage level constant as the demands on the power supply vary.

Mica Capacitors

Mica capacitors are frequently used in both commercial and industrial electronic circuits. Mica capacitors are high-voltage capacitors that are commonly used in high-voltage transmitters and other types of oscillators that are used in the induction heating of metal products. Figure 12 illustrates several typical mica capacitors. Small mica capacitors are shown in 12A, larger rectangular shapes are shown in 12B, and a large tubular mica capacitor is shown in 12C.

FIGURE 12—Shown here are three different styles of mica capacitors.

Smaller mica capacitors are formed by alternating sheets of mica with sheets of metal foil as shown in Figure 13. Here each alternate layer of foil connects to a lead that exits the capacitor body. Tubular mica capacitors are made much like electrolytic capacitors. However, in the tubular mica capacitor, the dielectric is a thin sheet of mica rolled up between the foil layers.

Capacitors and Inductors 15 FIGURE 13—A mica capacitor is made by placing thin sheets of mica between alternating layers of foil.

Mica capacitors usually have capacitance values from a few picofarads to about 0.2 µF. The voltage values range between 100 volts and several thousand volts. Mica capacitors are very stable, and their capacitance values don’t change greatly as their temperatures rise or fall. Also, their leakage currents are very low, with a typical insulation resistance of about 1,000 megohms or 1,000 MΩ. Larger mica capacitors are stamped with their capacitance value and voltage rating. However, a color-coding system is used to indicate the capacitance values of smaller mica capacitors. The color codes for small mica capacitors are shown in Table 2. This is called the 6-dot color code. The values calculated by the table are in picofarads. A typical six-dot color pattern for a mica capacitor is shown in Figure 14. The arrow across the center of the capacitor indicates the direction in which you must read the dots. In 14A, you can see that digit 1 is located at the top center of the capacitor. Digit 2 is located to the right of digit 1. The decimal multiplier is located at the bottom right (digit 3). The remaining two dots (digits 4 and 5) specify the capacitor’s tolerance and temperature coefficient. This color code system is also used with disk-shaped capacitors as shown in Figure 14B. Note the position of digits 1 through 5 on the disk- shaped capacitor.

16 Capacitors and Inductors Table 2 SIX DOT COLOR CODE FOR MICA CAPACITORS

Dot Number 1,2 3 4 5

Significant Decimal Tolerance Temperature Dot Color Figure Multiplier % Coefficient ppm per °C

Black 0 1 20 1,000

Brown 1 10 1 500

Red 2 100 2 200

Orange 3 1,000 3 100

Yellow 4 10,000 4 20 to 100

Green 5 — 5 0 to 70

Blue 6 — 6—

Violet 7 — 7—

Gray 8 — 8—

White 9 — 9—

Gold — 0.1 — —

Silver — 0.01 10 —

FIGURE 14—Two examples of the six-dot color code for mica capacitors are shown here.

Now, imagine that you have a capacitor with dot colors brown, black, and orange. These colors relate to the values 1,0, and the multiplier 1,000. Write the digit 1 followed by the digit 0 (10) and then multiply 10 by 1,000. The result is 10,000, so the capacitor has a value of 10,000 picofarads. We

Capacitors and Inductors 17 can convert 10,000 picofarads to farads by dividing. Since one picofarad is equal to 0.000000000001 or 1 10-l2 farad, multiply 10,000 by 0.000000000001. This capacitor has a value of 0.00000001 farad (1 108 F) or 0.01 µF.

Table 3 SIX DOT COLOR CODE FOR MILITARY MICA CAPACITORS

Dot 1,2 3 4 5

Significant Decimal Tolerance Temperature Color Figure Multiplier % Coefficient ppm per °C

Black 0 1 20 —

Brown 1 10 — —

Red 2 100 2 200

Orange 3 1,000 — 100

Yellow 4 10,000 20 to 100

Green 5 — — 0 to 70

Blue 6 — — —

Violet 7 — — —

Gray 8 — — —

White 9 — — —

Gold — 0.1 5 —

Silver — 0.01 10 —

If the left-most third dot in the upper row is a black dot, the mica capacitor has been manufactured to military specifica- tions. The color code chart for this type of capacitor is given in Table 3. This is also in picofarads.

Ceramic Capacitors

Ceramic capacitors are often termed disk capacitors due to their shape. Ceramic capacitors consist of layers of metal foil with deposits of ceramic material on them. Alternate layers of foil are connected to the leads that exit the capacitor body. A special insulating resin coating is then applied over the capacitor to seal it.

18 Capacitors and Inductors Ceramic capacitors produce very little leakage current, much like mica capacitors. Typical capacitance values range from a few picofarads to about 2 µF. Ceramic capacitors can operate in circuits with voltages up to 5,000 volts, depending on the markings on the capacitor. Ceramic disk capacitors are usually marked with a set of code num bers. These numbers can be looked up in a manufacturer’s manual to determine the capacitance and working voltage of the capacitor. Ceramic disk capacitors may also be color- coded as in the examples shown in Figure 15. Table 4 lists the values that correspond to the color markings on these capacitors. The values listed in the table are in picofarads.

FIGURE 15—If a ceramic disk or tubular capacitor isn’t marked with code numbers, you can use these dot patterns to decode its capacitance value.

Capacitors and Inductors 19 Table 4 COLOR CODE FOR CERAMIC DISK CAPACITORS

Dot or Band 1,2 3 4(A) 4(B) 5

Tolerance Tolerance Temperature Significant Decimal % 10 pF % 10 pF Coefficient ppm Color Figure Multiplier or Less or Greater per deg C

Black 0 1 2 20 0

Brown 1 10 — 1 30

Red 2 100 — 2 80

Orange 3 1,000 — 2.5 150

Yellow 4 10,000 — 220

Green 5 — 0.5 5 330

Blue 6 — — — 470

Violet 7 — — — 750

Gray 8 0.01 0.25 — 30

White 9 0.1 1.0 10 —

Paper Capacitors

Molded paper capacitors are an inexpensive type of capacitor. Like electrolytic capacitors, paper capacitors are composed of two layers of foil separated by a paper dielectric. Paper capacitors are available in capacitance ranges from about 250 picofarads to about 1 microfarad. Some typical paper capacitors are shown in Figure 16. Typically, paper capacitors are stamped with their capacitance value and working voltage. Also, a dot or band indicates the ground side of the capacitor. Some paper capacitors are color-coded, like mica capacitors. This coding is shown in Figure 17. In 17A, note the six color bands on the capacitor. Bands 1 and 2 refer to the first two digits of the capacitance value. Band 3 is the multiplier. Band 4 refers to the tolerance, and bands 5 and 6 indicate the voltage. Table 5 lists the values that correspond to these color codes, in picofarads.

20 Capacitors and Inductors FIGURE 16—This illustra- tion shows some typical paper capacitors.

FIGURE 17—Some types of paper capacitors have color bands or dot patterns such as those shown here.

In Figure 17B, note that the flat paper capacitor contains only four dots. Unlike a mica capacitor, the dots on a paper capacitor appear underneath the arrow. The first two dots (digits 1 and 2) correspond to the first and second digits of the capacitance value, and the third dot (digit 3) indicates the multiplier. The single dot in the top row (digit 4) indicates the tolerance of the capacitor. No voltage rating is given on this type of capacitor, unless the case is stamped with a value or the case has color bands for voltage ratings.

Tantalum Capacitors

In a tantalum capacitor, tantalum pentoxide is used for the dielectric. Tantalum capacitors are available in three forms: foil, wet electrolyte, and solid electrolyte.

Capacitors and Inductors 21 Table 5 COLOR CODE FOR PAPER CAPACITORS

Dot or Band 1,2 3 4 5,6

Significant Decimal Tolerance Voltage Significant Color Figure Multiplier % Figure

Black 0 1 20 0

Brown 1 10 — 1

Red 2 100 — 2

Orange 3 1,000 30 3

Yellow 4 10,000 40 4

Green 5 100,000 55

Blue 6 1,000,000 — 6

Violet 7 — — 7

Gray 8 — — 8

White 9 — 10 9

Gold — — — 10

Silver — — 10 20

No color — — 20 —

A foil tantalum capacitor is made of two layers of tantalum foil. One of the foil layers is oxidized to produce a thin deposit of tantalum pentoxide on its surface. The tantalum pentoxide acts as the dielectric. The entire assembly is rolled and sealed in an aluminum case to complete the capacitor. The typical capacitance range for foil tantalum ca pacitors is between 0.5 µF to 2,500 µF, with voltage ratings of up to 630 VDC. A wet electrolyte tantalum capacitor is made from pellets of tantalum powder with a wire lead attached. The pellets are then purified and welded into a porous mass. A thin layer of tantalum pentoxide is formed on the surface of the pellets by passing a current of electricity through the pellets. Finally, the entire assembly is sealed in a tantalum or silver can con-

22 Capacitors and Inductors taining an electrolyte solution. Wet electrolyte tantalum capacitors are available in capacitance ranges from 0.1 µF to 2,200 µF. Working voltages range from 3 VDC to 150 VDC. A solid electrolyte tantalum capacitor is constructed much like the wet electrolyte version. The pellets of tantalum are coated with dry graphite, manganese dioxide, and silver powders. This assembly is then sealed in a metal can or dipped in plastic resins to complete the capacitor. The solid electrolyte form of tantalum capacitor is available in capaci tance ranges of 0.005 µF to 1,000 µF. Working voltages are in the range of 3 VDC to 125 VDC. All types of tantalum capacitors offer the advantage of capacitance stability. Also, tantalum capacitors are up to three times smaller than many conventional electrolytic capacitors. A tantalum capacitor can be made so small that it can be used as an IC chip capacitor or a surface-mount capacitor. This type of capacitor is used on standard and miniature electronic circuit boards.

Polyester Film Capacitors

The final type of fixed capacitor we’ll look at is the polyester film capacitor. This type of capacitor is constructed of two layers of metal foil separated by a film of polyester. Another layer of polyester is then added to the outside of the capacitor to act as an insulator between the capacitor and case. The bodies of polyester, polystyrene, and polypropylene capacitors are usually marked with their capacitance ratings. Small circuit-board capacitors may be marked with a color code similar to those used on mica capacitors.

Variable Capacitors

Variable capacitors were once widely used in tuning circuits for oscillators, transmitters, and receivers. However, modern advances in solid-state electronics have virtually eliminated variable capacitors from these types of circuits. A variable capacitor contains a series of metal plates that mesh into or apart from one another when a knob at the front of the capacitor is turned. Because the effective plate

Capacitors and Inductors 23 area can change, the capacitance can vary. Another type of variable capacitor called a trimmer capacitor contains a mica sheet between a stationary and an adjustable metal plate. Now, take a few moments to review what you’ve learned by completing Power Check 2.

24 Capacitors and Inductors Power Check 2

Fill in the blanks in each of the following statements.

1. Another name for an electrolytic capacitor is a capacitor.

2. Ceramic capacitors are often called capacitors because of their shape.

3. capacitors are seldom used in modern circuits.

4. The plate of an electrolytic capacitor is marked with a band.

5. capacitors are often much smaller than conventional electrolytic capacitors.

Check your answers with those on page 65.

Capacitors and Inductors 25 Capacitors Connected in Series

Just like resistors, capacitors may be connected in series or parallel arrangements. A typical series arrangement of two capacitors is shown in Figure 18. As you can see, this circuit contains a 0.5 µF capacitor and a 0.4 µF capacitor connected in series. Connecting the capacitors in series is the same as increasing the distance between the capacitor plates. Therefore, when capacitors are connected in series, the total capacitance of the circuit decreases. To determine the total capacitance of two capacitors connected in series, use the following formula:

C1 × C2 CT = C1 + C2 Now, using this formula, calculate the total capacitance of the circuit in Figure 18.

FIGURE 18—This simple circuit contains two capacitors connected in series.

C1 × C2 Write the formula. CT = C1 + C2

0.5 µF × 0.4 µF Substitute the values of C and C . CT = 1 2 0.5 µF + 0.4 µF

26 Capacitors and Inductors Multiply (0.5 0.4 0.2). Add (0.5 0.4 0.5 × 0.4 0.9). Note that we’ve dropped the µF CT = 0.5 + 0.4 symbols here to simplify. You can only do this when all the units in the problem are the same. 0.2 CT = Divide (0.2 0.9 0.222). 0.9

CT = 0.222 µF Answer: The total capacitance of the circuit is 0.222 µF. Note that we’ve included the units symbol µF in the answer. If three or more capacitors are connected in series, use the following formula to calculate the total capacitance: 1 CT = 1 + 1 + 1

C1 + C2 + C3

Figure 19 illustrates a circuit containing three capacitors connected in series. The three capacitor values are 0.5 µF, 0.2 µF, and 1.0 µF. Use the formula to calculate the total capacitance of this circuit.

1 Write the formula. CT = 1 + 1 + 1

C1 + C2 + C3 FIGURE 19—This circuit contains three capacitors connected in series.

1 C = T Substitute the values of C1j, C2, and 1 + 1 + 1 C3. 0.5 µF + 0.2 µF + 1 µF

Capacitors and Inductors 27 1 C = T Divide to find the values of each 1 + 1 + 1 of the three fractions (1 0.5 2; 1 0.5 + 0.2 + 1 0.2 5; 1 1 1).

1 Add in the denominator of the frac- CT = tion (2 5 1 8) 2 + 5 + 1

1 Divide (1 8 0.125). CT = 8 CT 0.125 µF Answer: The total capacitance of this circuit is 0.125 µF. If capacitors with equal values are connected in series, it’s easy to calculate the total capacitance of the circuit. When the capacitors are of equal value, the total capacitance value is equal to the value of one capacitor divided by the number of total capacitors that are connected in series. C CT = n In the formula, n stands for the total number of equal value that capacitors are connected in series. Figure 20 shows a circuit in which two equal capacitors are connected in series. Using the formula, calculate the total capacitance of this circuit.

C Write the formula. CT = n

Substitute the value of either capaci- 2 µF C T = tor (2 µF) for C. The number of 2 capacitors that are connected in series is 2, so the value of n is 2. 2 CT = Divide (2 2 1). 2

CT = 1 µF Answer: The total capacitance of this circuit is 1 µF.

28 Capacitors and Inductors FIGURE 20—When two capacitors of equal value are connected in series, the capacitance value is equal to one-half the value of either capacitor.

Capacitors Connected in Parallel

When capacitors are connected in parallel, the total capacitance of the circuit increases. The effect is the same as when the plate area of a single capacitor increases. When capacitors are connected in parallel, the total capacitance is equal to the values of capacitors added together. You can use the following formula to calculate the total capacitance in a parallel circuit:

CT C1 C2 C3 C4 . . .

Figure 21 displays two capacitors in a parallel arrangement.

One capacitor is 1 µF (C1) and the other capacitor is 3 µF

(C2). Calculate the total capacitance of the circuit. CT C1 C2 Write the formula. CT 1 µF 3 µF Substitute the values for Cl and C2. CT 1 3 Add (1 3 4). CT 4 µF Answer: The total capacitance of this circuit is 4µF. Let’s look at another example problem. Figure 22 shows a circuit containing a parallel arrangement of four capacitors. Calculate the total capacitance of the circuit.

Capacitors and Inductors 29 FIGURE 21—This circuit contains two capacitors connected in parallel.

CT C1 C2 C3 C4 Write the formula.

FIGURE 22—This circuit contains four capacitors connected in parallel.

30 Capacitors and Inductors CT 1 pF 30 pF 15 pF 2 pF Substitute the values of C1,

C2, C3, and C4 into the formula.

CT 1 30 15 2 Add (1 30 15 2 48). CT 48 pF Answer: The total capacitance of this circuit is 48 pF.

RC Time Constants

A resistance-capacitance circuit or RC circuit is a circuit that contains both resistors and capacitors. In an electric or electronic circuit, a capacitor opposes voltage changes across its terminals or leads. For this reason, a capacitor doesn’t instantly become fully charged when a voltage is applied. Instead, it takes a certain time period for the capacitor to reach full charge. The length of time required for a capacitor to reach full charge de pends on the size of the capacitor and the amount of resistance that’s in series with the capacitor. For the same series resistor value, a large-value capacitor will take longer to charge than a small-value capacitor. Also, if the resistance value of a circuit is high, it will take longer to charge the capacitor than if there were little or no resistance in the circuit. Figure 23 is a graph illustrating the effect of resistance on an RC circuit.

FIGURE 23—The effect of resistance on an RC circuit is shown in this graph.

Capacitors and Inductors 31 The vertical line axis of this graph shows voltage, starting at 0 volts and increasing as you move up the line. The horizontal line shows time, starting at 0 and increasing as you move to the right on the line. The diagram shows that when the circuit resistance is low, it takes little time to charge the capacitor. As resistance increases, the charging time increases proportionally. Now, let’s see what happens if we keep the resistance value constant and increase the size of the capacitor. Figure 24 shows a diagram of another RC circuit.

FIGURE 24—Changing the capacitance will have this type of effect on an RC circuit.

The vertical and horizontal lines of this graph represent the same quantities of voltage and time as the previous diagram. The graph shows that the voltage across the plates of a small capacitor increases much quicker than the voltage across the plates of a large capacitor. Therefore, in an RC circuit with a fixed resistance, the charging rate is inversely proportional to the size of the capacitor. You might think that increasing the applied voltage would make the capacitor charge quicker. However, this isn’t true. A high voltage charges the capacitor in the same amount of time as a low voltage. In an RC circuit, the length of time required for a capacitor to reach full charge is determined by the time constant of the circuit. The time constant in an RC circuit is equal to the

32 Capacitors and Inductors capacitance times the resistance of the circuit. Therefore, the formula used to find the time constant of an RC circuit is the following: TC R C In this formula, TC stands for the time constant in seconds. The letter R stands for the resistance in ohms and C stands for the capacitance in farads. A capacitor will charge to about 63 percent of the supply voltage in one time constant, and reach its full charge in about five time constants. A simple RC circuit with a voltage source and a switch is shown in Figure 25. In this circuit, the applied voltage is 100 VDC, the resistance is 100 kΩ, and the capacitance is 0.01 µF. Let’s calculate the time constant for this circuit. Note that before we can substitute these values into our formula, we’ll need to convert kilohms to ohms and microfarads to farads.

FIGURE 25—This circuit illustrates a simple RC circuit.

TC R C Write the formula.

100 kΩ 100,000 Ω To convert 100 kilohms to ohms, multiply 100 by 1,000 (100 1,000 100,000).

0.01 µF 0.00000001 F To convert .01 microfarads to farads, divide 0.01 by 1,000,000 (0.01 1,000,000 0.00000001).

TC 100,000 Ω 0.00000001 F Substitute the values for R and C in the formula.

TC 0.001 s, or 1 ms Multiply. Answer: The time constant for the circuit is 0.001 seconds, or 1 millisecond.

Capacitors and Inductors 33 The time constant of this circuit is 1 millisecond. This means that one millisecond after the switch is closed, the capacitor has charged to 63 percent of the supply voltage (63 volts in our example circuit). After five time constants, the capacitor reaches its full charge (100 percent of the supply voltage, or 100 VDC). When the switch is opened, the capacitor will remain charged. The time the capacitor remains charged depends on the rate of internal leakage in the capacitor. Capacitors that have a high internal resistance and therefore, low leakage, will remain charged for a longer period of time than a capacitor with low internal resistance and high leakage. The graph in Figure 26 illustrates the charging rate for the capacitor in Figure 25. In this graph, you can see voltage and current values in the circuit at one millisecond intervals. After one millisecond, the voltage on the capacitor is approximately 63 percent of its final value, and the voltage across the capacitor is 63 VDC. In the graph, the line that starts at zero and curves upward shows the increase in voltage across the capacitor. In the graph, the line that starts at 100 and curves down- ward shows the decrease in voltage across the resistor. After one millisecond, the voltage across the resistor drops to approximately 37 percent of its initial voltage. After two milliseconds, the capacitor has charged up to 86.5 VDC and the voltage across the resistor has dropped to 13.5 VDC. The capacitor’s voltage increases while the resistor’s voltage drops at the same rate. Because the resistor and capacitor are connected in series, the sum of the resistor voltage and the capacitor voltage must equal the voltage of the power source at each point in time. After five time constants (five milliseconds in this example) the capacitor can be considered to be fully charged. In the graph, the capacitor is charged to 99.3 percent of its full voltage. The voltage across the resistor has simultaneously dropped to 0.7 VDC. In reality, a capacitor never charges to exactly 100 percent of power supply voltage. Internal resistance in the capacitor always keeps the capacitor’s voltage slightly below the value

34 Capacitors and Inductors FIGURE 26—This graph shows how the voltages across the capacitor (EC) and resistor (ER) change for each one millisecond of time after the circuit closed. of the applied voltage. You can see that after the sixth time constant (six milliseconds in this example) the voltage of the capacitor is at 99.7 percent of full charge. Table 6 displays the current and voltage relationship for the circuit illustrated in Figure 25. The first column lists the time periods up to 6 milliseconds. The column labeled EC lists the voltage across the capacitor for each time period. The column labeled ER lists the voltage across the resistor for each time period. The column labeled I (mA) lists the circuit current for each time period. We learn the following three things from this chart: 1. The voltage across the capacitor increases as the capacitor charges 2. The voltage across the resistor drops as the capacitor charges

Capacitors and Inductors 35 Table 6 VOLTAGE AND CURRENT FOR A SERIES RC CIRCUIT

TIME EC ER I (mA)

0 msec 0.0 100.0 1.000

1 msec 63.0 37.0 0.370

2 msec 86.3 13.7 0.137

3 msec 94.9 5.1 0.051

4 msec 98.1 1.9 0.019

5 msec 99.3 0.7 0.007

3. The circuit current starts at its maximum possible value and then falls to zero as the capacitor charges The fully charged capacitor can be discharged using the circuit shown in Figure 27. This is the same circuit you saw in

Figure 25, with the addition of a switch (S2) and resistor (R2).

The discharge of the capacitor occurs through the switch S2

and the resistor R2. Note that the discharge resistor (or load resistor) in this example has the same value as the charging

resistor (R1) had—100 kΩ This means that the discharge rate of the capacitor will be equal to, but opposite to, the charging

rate. In this circuit, the switch S1 must be opened to discon- nect the 100 VDC power supply from the circuit. This allows the capacitor to completely discharge.

FIGURE 27—This figure is a modification of the circuit shown in Figure 25. Note that this circuit has been modified to give the capacitor a path for discharge.

36 Capacitors and Inductors The arrows in the figure show the direction of current flow through the circuit. The direction of current flow is clockwise, and the capacitor is the source of voltage. Figure 28 shows a universal time constant graph. This graph shows the voltage of a capacitor as it charges and discharges. The left side of the graph indicates the percent of the final voltage across the capacitor. The bottom of the graph indicates the time in time constants. To find the capacitor and resistor voltages for any time constant, simply multiply the applied voltage by the percentage of the final capacitor voltage at any given time constant. Let’s look at an example problem. Suppose that an RC circuit contains a 0.1 µF capacitor and a 20 kΩ resistor. The RC circuit is supplied with 24 VDC. First, we’ll calculate the time constant.

TC R C Write the formula.

20 kΩ 20,000 Ω To convert 20 kilohms to ohms, multiply 20 kilohms by 1,000 (20 1,000 20,000).

FIGURE 28—This universal time constant graph shows the voltage of a capacitor as it charges and discharges.

Capacitors and Inductors 37 0.1 µF 0.0000001 F To convert .1 microfarads to farads, divide 0.1 by 1,000,000 (0.1 1,000,000 0.0000001).

TC 20,000 Ω 0.0000001 F Substitute the values for R and C in the formula.

TC 0.002 s, or 2 ms Multiply. Answer: The time constant for the circuit is 0.002 seconds, or 2 milliseconds. The time constant in this circuit is 2 milliseconds. Figure 29 shows the universal time constant graph marked with 2 millisecond time constant intervals. Now, let’s suppose that we need to calculate the voltage across the capacitor at 4 milliseconds (two time constants). Looking at the graph, start at the 4 millisecond point on the bottom line of the graph. Trace upward until you reach the A curve. Now, look across to the left to find the percentage. You can see that you’re slightly above the 86 percent line, so let’s

FIGURE 29—This universal time constant graph indicates the voltage of a capacitor over 2 millisecond intervals.

38 Capacitors and Inductors estimate the percentage at about 86 percent. You now have all the information you need to calculate the voltage. Multiply the supply voltage by the percentage. EC 24 V 86% Write the problem. Multiply the supply voltage by the percentage. EC 24 0.86 Convert 86 percent to the decimal value 0.86.

EC 20.64 VDC Multiply (24 0.86 20.64). Answer: The voltage across the capacitor at 4 milliseconds is 20.64 VDC. The voltage across the resistor in this circuit can be found in two ways. You could use the graph to determine the voltage, but it’s easier to simply subtract the capacitor voltage from the source voltage. ER ES EC Write the problem. Subtract the capacitor voltage from the supply voltage. ER 24 V 20.64 V Substitute the values for ES and EC. ER 24 20.64 Subtract (24 20.64 3.36). ER 3.36 VDC Answer: The voltage across the resistor at 4 milliseconds is 3.36 VDC. Now, take a few moments to review what you’ve learned by completing Power Check 3.

Capacitors and Inductors 39 Power Check 3

Indicate whether each of the following statements is true or false.

1. An RC circuit is a circuit that contains only resistors.

2. A capacitor charges to about 37 percent of the supply voltage in one time constant.

3. When capacitors are connected in parallel, the total capacitance of the circuit increases.

4. A capacitor charges to 100 percent of the supply voltage in three time constants.

5. When capacitors are connected in series, the total capacitance of the circuit decreases.

6. When capacitors of equal value are connected in series, the total capacitance value across the capacitors is equal to the value of one capacitor divided by the number of capacitors connected in series.

Check your answers with those on page 65.

40 Capacitors and Inductors Uses of Capacitors

In both electrical and electronic work, you’ll see capacitors used in many ways. Many circuit boards contain large numbers of capacitors that perform a variety of functions in the circuit. A typical industrial power supply is shown in Figure 30. Several capacitors are visible on the circuit board. Note the large capacitor mounted to the back of the circuit board.

FIGURE 30—A typical industrial power supply is shown here.

The large capacitor’s purpose is to store charges of DC voltage between the cycles of power that are applied to the capacitor. Without this large electrolytic capacitor, the output of the power supply would pulse instead of flowing steadily. A simplified diagram of the power supply is shown in Figure 31.

A load resistor (RL) is connected to the power supply output voltage. Also shown are two measurement points, A and B. If an oscilloscope is connected at these two points, the two waveforms shown in Figure 32 would result. Note that an oscilloscope measures voltage on the vertical axis of a graph and time across the horizontal axis.

Capacitors and Inductors 41 FIGURE 31—Shown here is a simplified drawing of a power supply with two test points.

When the oscilloscope is connected to measurement point A, waveform 1 can be seen. Waveform 1 is a typical 60-cycle (60 Hz) alternating current (AC) waveform. This waveform is called a sine wave. The sine wave shows how the voltage rises to a positive peak, drops down to zero, drops further to a negative peak, rises back to zero, and then rises again to a positive peak. (The term 60-cycle means that the sine wave repeats itself 60 times per second.) At point B in Figure 31, the power supply output voltage has been rectified, or changed to DC. When the oscilloscope is connected to measurement point B, waveform 2 can be seen. Waveform 2 is the rectified DC voltage. The rectifier in this example allows current to flow only in a positive direction. This happens as the AC waveform rises to a positive peak. When the current flows through the rectifier, the capacitor charges to a positive voltage that’s almost equal to the positive peak of the AC waveform. As the AC voltage starts to decrease toward the negative peak, the current stops flowing in the rectifier. During the negative portion of the AC cycle, the charged capacitor provides the current for

the resistor load (RL) until the AC waveform becomes positive again and current flows through the rectifier. Since the voltage supplied by the capacitor isn’t as great as that supplied at the peak of the AC waveform, there’s a slight dip or ripple in the voltage level during each cycle. This dip is referred to as ripple voltage. Larger capacitance values will supply longer time constants and reduce the ripple in the voltage.

42 Capacitors and Inductors FIGURE 32—This figure shows the waveform that results when an oscilloscope is connected to points A and B In the circuit shown in Figure 31. Waveform 1 represents the AC voltage that can be measured at point A of Figure 31. Waveform 2 represents the rectified DC voltage that can be measured at point B of Figure 31.

A circuit board with various types of capacitors is shown in Figure 33. This circuit board also contains many resistors, diodes, integrated circuits, and other semiconductor devices. This circuit board controls the speed of a DC motor. The power supply circuit for the motor-driver board contains a large capacitor (C1). This capacitor smoothes out the ripples in the output voltage. This circuit board contains several other capacitors as well. There are five ceramic disk capacitors, seven encapsulated ceramic capacitors, and two tantalum capacitors. Some of these capacitors are used in RC timing circuits. When this

FIGURE 33—This is a typical industrial speed controller for a small DC motor.

Capacitors and Inductors 43 circuit board is connected to a motor, these circuits trigger semiconductor devices to control the speed of the motor. Other capacitors filter or smooth out the DC voltage on the circuit board to prevent false triggering of the semiconductor devices. Capacitors are also used to allow the passage of an AC signal while at the same time preventing a DC voltage from moving further in the circuit. This is useful in amplifiers where the DC voltage on one stage of an amplifier can upset the voltage on another stage. A diagram of an amplifier circuit is shown in Figure 34.

FIGURE 34—An amplifier uses capacitors to prevent DC voltages from passing from stage to stage.

There are three stages of amplification in this amplifier. The first stage is powered by 12 VDC and is a preamplifier stage. A second stage is powered by 24 VDC and provides an inter- mediate stage of amplification. The output of the second stage is used to drive high-voltage semiconductor devices in the final stage. If capacitors weren’t used between the stages, voltage from the high-voltage stage would feed back into the second and first stages, upsetting the operation of the amplifier and pos- sibly damaging the lower-voltage components in the first two stages. By using capacitor coupling between the stages, the AC signal can easily pass from stage to stage, but the DC voltages can’t. Capacitors are used in many types of integrated-circuit memory circuits and systems. In some systems, a capacitor holds a charge that’s used to keep memory information intact during power interruptions. In other systems, the memory cells themselves are tiny capacitors that store the charge. When

44 Capacitors and Inductors voltage is applied to the capacitor, one bit of memory information is stored. These memory chips contain millions of tiny transistors and capacitors that store millions of bits of data.

Testing Capacitors

Before reading the information in this section, be sure to remember the following important safety tip.

Warning: Always discharge a capacitor before measuring, by passing, touching, or otherwise working with it. A capacitor can hold a substantial charge for hours after circuit power has been removed.

Capacitors can be tested easily with a volt-ohm-milliamp meter (VOM) that’s set to measure resistance. When testing a capacitor, use the highest resistance scales and touch the meter’s test leads to the capacitor’s wire leads. For a large value capacitor, you’ll initially see a low value of resistance that increases gradually until the meter reads an open circuit. This reading change occurs as the capacitor charges to the internal battery voltage of the meter. Smaller value capacitors charge more quickly. Very small capacitors read infinity resistance. Any capacitor that produces a reading of under one megohm after it’s charged can be considered faulty and should be replaced. When you’re testing a capacitor with a meter, the capacitor should be removed from its circuit. Other components in the circuit can influence your readings with a VOM. A special meter called an inductor/capacitor/resistor meter or an LCR meter is used to directly measure the capacitance of a capacitor. An LCR meter is shown in Figure 35. To use an LCR meter, the capacitor is disconnected from the circuit, the meter’s leads are connected to the capacitor leads, the meter is turned on, and the range selector switch is set to the proper range. The capacitance value is read directly from the display on the front panel.

Capacitors and Inductors 45 FIGURE 35—The LCR meter shown here can directly measure the value of an inductor, capacitor, or resistor. (Photo Courtesy of Quad-Tech, Incorporated)

Working with Capacitors

As mentioned earlier, always discharge a capacitor before working on the circuit. A capacitor can hold a substantial charge for hours after circuit power has been removed. This is especially true of large-value electrolytic capacitors in power supplies, motor drivers, or other such industrial circuits. To discharge a capacitor, first use a DC voltmeter to measure the voltage across the capacitor. Make sure that there are zero volts in the capacitor before working with it. Then, connect a low resistance value, high-wattage resistor across the capacitor leads. Before working on any equipment, always measure the voltage across the capacitor with a DC voltmeter to be sure there’s no voltage present in the capacitor. Some circuits contain a resistor called a bleeder resistor which is located across the terminals of the capacitor. A bleeder resistor is a very high-value resistor that bleeds or removes the charge across a capacitor in a few minutes after power has been removed from the circuit. Even if a capacitor has a bleeder resistor, you can’t be sure that the capacitor is completely discharged. If a bleeder resistor fails, a capacitor can hold a lethal charge of electric energy for hours. Always discharge a capacitor yourself to be sure that it’s safe. Always replace a failed capacitor with the exact same device. This is especially important when a capacitor is located in a timing circuit.

46 Capacitors and Inductors If you suspect that a capacitor has failed open, clip an external capacitor across the faulty capacitor with a pair of jumper wires to test the circuit. If the test capacitor solves the circuit problem, the original capacitor should be replaced. Now, take a few moments to review what you’ve learned by completing Power Check 4.

Capacitors and Inductors 47 Power Check 4

Fill in the blanks in each of the following statements.

1. To discharge a capacitor, touch the capacitor leads to a .

2. You should always a capacitor before measuring, testing, or otherwise working with it.

3. A special meter called an is used to directly measure the capacitance of a capacitor.

4. Some circuits contain resistors called resistors, which are connected across the capacitor leads.

Check your answers with those on page 65.

48 Capacitors and Inductors INTRODUCTION TO CIRCUIT COMPONENTS: INDUCTORS

What Is an Inductor?

An inductor is an electrical or electronic circuit device that operates in the opposite manner from a capacitor. While a capacitor stores a charge in the electric field between its plates, an inductor stores a charge as a magnetic field sur- rounding the conductor. Although in ductors aren’t as common as capacitors on electronic circuit boards, inductors are still widely used in industrial circuits.

How Do Inductors Work?

When current flows through a conductor, a magnetic field is gener ated in the area around the conductor. The strength of the magnetic field is directly related to the strength of the current flowing in the conductor. The magnetic field remains as long as current continues to flow through the conductor. When the source of current is removed, the magnetic field disappears. However, the magnetic field doesn’t disappear instantly. Instead, the magnetic field collapses over time. If the strength of the current flowing in a conductor changes, the strength of the magnetic field also changes. When a change in current occurs, the magnetic field generates a voltage in the conductor that’s called a self-induced electromotive force, or self-induced EMF. A self-induced EMF is generated whenever a magnetic field changes. If the magnetic field is steady or at zero, then the self-induced EMF is also zero. The polarity of the self-induced EMF opposes the external voltage source that’s trying to change the current flow in the conductor. The effect is that the conductor current can’t change its value instantly. Energy is stored in the magnetic field around the conductor. If the current source in a conductor is suddenly removed, the magnetic field will generate a self-induced EMF or voltage of sufficient value to create an arc across the ends of the con-

Capacitors and Inductors 49 ductor which were connected to the current source. The arc allows the current to flow in the conductor and to decay to zero as the magnetic field is reduced to zero. All conductors have the property of inductance. However, in a straight conductor, the inductance is very small and can be neglected, except in high-frequency circuits. In standard DC circuits, the inductance produced by a straight conductor has very little effect on circuit current flow. If a straight conductor is formed into a coil, the inductance of the wire increases. This is because the magnetic lines of force around each turn of the wire join together to create a large magnetic field around the entire coil. The inductance of the coil can be further increased by winding the coil of wire around a frame or core of iron or steel. Typical inductors are shown in Figure 36.

FIGURE 36—Shown here are several different inductors.

Inductors that are used in low-frequency circuits are generally composed of an iron core with many turns of heavy gauge wire. These inductors resemble transformers. Iron core inductors, in combination with capacitors, are often used in

50 Capacitors and Inductors AC to DC power supplies to provide a constant DC output voltage. Higher frequency circuits use smaller inductors that are wound on insulated tubes. These inductors are termed air core inductors. Variable inductors are also available. These inductors are used in the tuning circuits of oscillators and receivers.

Inductor Types and Ratings

Figure 37 shows the symbols used for inductors in electrical drawings. The general inductor symbol is also widely used for an air core inductor. The iron core and ferrite core symbols contain two solid or broken lines next to the coil to signify the presence of iron or ferrite. The final symbol represents a variable inductor. Variable inductors are used in tuning circuits in transmitters or receivers.

FIGURE 37—These are the standard symbols for inductors used in electrical drawings and industrial schematics.

Figure 38 shows a special type of inductor that’s used in very high frequency circuits. This type of inductor has no coil of wire. Instead, a small ferrite bead is placed around a conductor. The tiny ferrite bead has the same effect as placing an inductor in series with the conductor. A high-frequency inductor may also be sealed in a case as shown in Figure 39. The purpose of the case is to provide a grounded shield around the inductor to prevent the produc- tion of a magnetic field that would disturb other circuit components.

Capacitors and Inductors 51 FIGURE 38—This type of inductor is used in high-frequency circuits.

FIGURE 39—Illustrated here is a shielded inductor that’s used in high-frequency circuits. (Courtesy of JFD Electronics Corporation)

Inductors are rated using the unit of measure called the henry (H). An inductor has an inductance of one henry when a voltage of one volt is produced across the inductor when the current in the inductor changes at the rate of one ampere per second. A large iron-core inductor generally has an inductance of 50 to 100 henries (50 H to 100 H). High-frequency air-, plastic-, or ceramic-core inductors have much less inductance and are rated in millihenries (mH) or microhenries (µH). A number of factors can influence the inductance value of a coil. These factors are as follows: • The number of turns of wire on the coil

• The shape of the coil

• The material on which the coil is wound

52 Capacitors and Inductors Inductors Connected in Series

Connecting inductors in series is much the same as connecting resistors in series or connecting capacitors in parallel. To calculate the total inductance of a circuit containing two or more inductors in series, simply add the values of the inductors together using the following formula: LT L1 L2 L3 L4 . . . Note that the letter L is used to stand for inductance in this formula. An inductive circuit is shown in Figure 40. The circuit contains two inductors connected in series. Calculate the total inductance of this circuit. LT L1 L2 Write the formula. LT 2 H 4 H Substitute the values for L1 and L2. LT 2 4 Add (2 4 6). LT 6 H Answer: The total inductance of this circuit is 6H.

FIGURE 40—This circuit contains two inductors connected in series.

Figure 41 illustrates a circuit containing four inductors connected in series. Let’s calculate the total inductance of this circuit. First, however, note that this circuit contains two inductors rated in millihenries (mH) and two inductors rated in microhenries (µH). To calculate the total circuit inductance, we must first convert all the inductors to the same units. It’s easiest to convert the larger units into the smaller units.

Capacitors and Inductors 53 FIGURE 41—This circuit contains four inductors connected in series.

LT L1 L2 L3 L4 Write the formula. 2 mH 2,000 µH 4 mH 4,000 µH Convert the values of the two inductors from millihenries to microhenries. To do this, multiply each value by 1,000 (2 1,000 2,000; 4 1,000 4,000). LT 2,000 µH 4,000 µH 150 µH 200 µH All the inductors are now rated in microhenries, so we can add them. Substitute

the values of Ll, L2, L3, and L4 into the formula. LT 6,350 µH Add (2,000 4,000 150 200 6,350). Answer: The total inductance of the circuit is 6,350 µH, or 6.35 mH. If the inductors connected in series are of equal value, simply count the number of inductors, then multiply that number times the value of one inductor. So, suppose a circuit contains five inductors connected in series. The value of each inductor is 200 µH. What is the total inductance of the circuit? LT 5 200 µH Set up the problem. Multiply the number of inductors (5) times the value of one inductor (200 µH).

LT 5 200 Multiply (5 200 1,000). LT 1,000 µH Answer: The total inductance of the circuit is 1,000 µH.

54 Capacitors and Inductors Inductors Connected In Parallel

When inductors are connected in parallel, you can calculate the total inductance of the circuit the same way you calculate for resistors connected in parallel or capacitors connected in series. If there are only two inductors in parallel, use the following formula:

L1 × L2 LT = L1 + L2

Figure 42 shows a circuit that contains two inductors connected in parallel. The values of the inductors are 7 µH and 8 µH. Let’s calculate the total inductance of this circuit.

FIGURE 42—This circuit contains two small inductors connected in parallel.

L × L 1 2 Write the formula. LT = L1 + L2

7 × 8 Substitute the values for L1 and L2. LT = 7 + 8

Multiply in the numerator (the top) of the 56 fraction (7 8 56). Add in the denomi- LT = 15 nator (the bottom) of the fraction (7 8 15).

Capacitors and Inductors 55 LT 3.7 Divide (56 15 3.7). LT 3.7 µH Answer: The total inductance of the circuit is 3.7 µH. Note that the total inductance is approximately half the value of the original inductor. This is the same result that occurs when you work with resistors connected in parallel and capacitors connected in series. Now, suppose a circuit contains more than two inductors connected in parallel? To find the total inductance of such a circuit, you can use the following formula:

1 LT = 1 + 1 + 1

L1 + L2 + L3

Figure 43 shows a circuit that contains three inductors connected in parallel. The values of the inductors are 50 µH, 100 µH, and 2 µH. Find the total inductance of the circuit.

FIGURE 43—This circuit contains three small inductors connected in parallel.

56 Capacitors and Inductors 1 L = T Write the formula. 1 + 1 + 1

L1 + L2 + L3 1 LT = Substitute the values of L1, L2, and 1 + 1 + 1 L3. 50 µH + 100 µH + 2 µH

1 Divide to find the values of each of L = T 1 + 1 + 1 the three fractions (1 50 0.02; 1 50 + 100 + 2 100 = 0.01; 1 2 0.5).

1 Add in the denominator of the frac- LT = 0.02 + 0.01 + 0.5 tion (0.02 0.01 0.5 0.53). 1 Divide (1 .53 1.886). LT = 0.53 LT 1.886 µH Answer: The total inductance of the circuit is 1.886 µH.

RL Time Constants

Just as with the RC timing circuits seen earlier in this text, a resistor may be connected in series with an inductor to create a resistance-inductance circuit or RL circuit. When voltage is applied to an RL circuit, the current flow won’t reach its maximum value immediately. This is because the inductor tends to oppose a change in current flow in a circuit. Instead, the current flow will build up over a period of time until it reaches its steady state value. Remember that there’s no voltage drop across an inductor if the current flowing in the conductor doesn’t change. In the steady state condition, all of the applied voltage appears across the resistor in series with the inductor. The steady state current can be found by applying Ohm’s law: E I (steady state) = R Therefore, varying the resistance of an RL circuit changes the value of the steady state current in the inductor.

Capacitors and Inductors 57 The time it takes for the current to reach its steady state value in an RL circuit depends on the value of the resistor and the inductor. When the resistance is large, it takes a shorter time for the current to reach its maximum value. The influence of resistance on an RL circuit is shown in Figure 44.

FIGURE 44—This graph shows how the size of the series resistor influences the RL time constant.

If the resistor value in an RL circuit remains the same, the time constant of the circuit can be modified by changing the inductor value. The current in a large inductor takes much longer to reach its steady state value than in a small inductor. Since the value of the inductor doesn’t affect the value of the steady state current, varying the inductor value only changes the time required to reach the steady state current, and not the value of the current. The influence of an inductor in an RL circuit is shown in Figure 45.

FIGURE 45—This graph shows that a large inductor takes longer to reach its steady state current than a small inductor.

58 Capacitors and Inductors As the graph shows, resistor and inductor values affect the time it takes for current to reach its steady state. We therefore need some way to calculate the time constant for circuits using various resistance and inductance values. Use the following formula to calculate the time constant of an RL circuit: L TC = R

In this formula, TC stands for the time constant in seconds; L stands for the inductance in henries; and R stands for the resistance in ohms. Let’s look at an example circuit. Figure 46 shows a typical RL circuit. In this circuit, a 100 Ω. resistor is connected in series with a 1 mH inductor. A supply voltage of 100 VDC is applied to this circuit when the switch (S1) is closed. Calculate the time constant for this circuit. L TC = Write the formula. R

1 mH 0.001 H Convert 1 millihenry to henries. To do this, divide 1 by 1,000 (1 1,000 0.001). 0.001 H TC = Substitute the values for R and L into the 100 Ω formula.

TC 0.00001 s, or 10 µs Divide (0.001 100 0.00001). Answer: The time constant for this circuit is 0.00001 sec onds, or 10 microseconds.

FIGURE 46—This simple RL series circuit is supplied with 100 VDC and con- trolled by a switch.

Capacitors and Inductors 59 The time constant for this circuit is 10 microseconds. This means that in 10 µs, the circuit current reaches 63.2 percent of its steady state value. You can see the similarity and difference between an RL and an RC circuit. An RL circuit allows a current flow of 63.2 percent of the steady state value in one time constant. An RC circuit achieves 63.2 percent of its steady state voltage across the capacitor in one time constant. The discharge of an RL circuit also follows the time constant principles seen in RC circuits. A chart of currents and voltages in RL and RC circuits is shown in Figure 47.

RL CIRCUIT L (H) TC (sec) = R (Ω) Current Buildup: Curve 1—Inductor Current or Resistor Voltage Curve 2—Inductor Voltage Current Decay: Curve 2—Inductor Current or Resistor Voltage

RL CIRCUIT TC (sec) = C (F) × R (Ω) Charge: Curve 1—Capacitor Voltage Curve 2—Capacitor Current or Resistor Voltage Discharge: Curve 2—Capacitor Current or Resistor Voltage

FIGURE 47—This chart shows a universal time constant that’s referred to both RL and RC circuits.

60 Capacitors and Inductors The left side of the graph shows the percentage. This is either the percentage of voltage in an RC circuit or the percentage of current in an RL circuit.

Uses of Inductors

Inductors are widely used as filtering components in industrial DC power supplies. A typical power supply is shown in Figure 48. This arrangement of capacitors and inductors is called a filter network or a pi () network. In this circuit, an inductor is connected between two capacitors. The first capacitor (C1) is located at the left of the filter section. C1 stores DC pulses and bypasses any AC ripple to ground. The inductor adds to the capacitor’s efficiency by preventing current changes (such as those from AC ripple) from bypassing the first capacitor. The second capacitor (C2) also stores a charge and helps maintain the power supply’s output voltage at a constant level, even when the load on the power supply varies.

FIGURE 48—This power supply has a special filter attached that contains two capacitors and an inductor.

Inductors are also widely used in DC motor-drive systems. The drive system is designed so that one driver can power various sizes of DC motors. However, the inductance of the coils of wire inside the DC motor changes greatly as motor size increases. The best way to match the output of the motor driver to the motor being used is to connect an inductor in series with the motor (Figure 49). The inductor matches the inductance of the system to the output impedance of the drive system. This

Capacitors and Inductors 61 FIGURE 49—In this circuit, an inductor is connected in series with a DC motor to improve the motor’s response.

matching allows the DC motor to respond quicker to driver signals. DC motor-drive manufacturers can provide inductors for various motor types if fast motor response is required. Now, take a few moments to review what you’ve learned by completing Power Check 5.

62 Capacitors and Inductors Power Check 5

Fill in the blanks in each of the following statements.

1. A high-frequency inductor can be made by placing a bead over a straight conductor.

2. An inductor is used in a DC or low-frequency circuit.

3. Inductors store energy in a .

4. An inductor opposes a in current flow.

Check your answers with those on page 66.

Capacitors and Inductors 63 NOTES

64 Capacitors and Inductors Power Check Answers 1

1. True Answers

2. True Answers 3. False 4. False 5. True

Power Check Answers 2

1. polarized 2. disk 3. Variable 4. negative 5. Tantalum

Power Check Answers 3

1. False 2. False 3. True 4. False 5. True 6. True

Power Check Answers 4

1. low value, high wattage resistor 2. discharge 3. inductor/capacitor/resistor meter (LCR) 4. bleeder

65 Power Check Answers 5

1. ferrite 2. iron core 3. magnetic field 4. change

66 Power Check Answers