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 elec- tronics 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 cur- rent 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 mar- gin signals that there’s an Electronics Workbench lab experiment associated with that section of the text. If your program includes Elec tronics 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 Work bench, 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 vari- able 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 posi tive 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 volt- age 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, elec- trons move from the negative battery termi- nal to the negative plate of the capacitor. Electrons also move away from the positive plate of the capacitor toward the positive ter- minal of the battery. toward the upper capacitor plate, giving it a negative charge. At the same time, electrons flow away from the lower capaci- tor 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 elec- trons of the dielectric material to deflect creating a stored charge in the elec- tric 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 dielec- tric 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 dielec- tric, 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 dielec- tric constant greater than 1. Let’s observe the charging and discharging of a capacitor with a sim ple experiment. Figure 5 shows an experiment involving a small bat tery, 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 sec- onds. 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 capac- itor 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 electri cal charge is stored in the capacitor with a potential of one volt across the plates.