Exercise 9 Electromagnetism and Inductors EXERCISE OBJECTIVE When you have completed this exercise, you will be familiar with the concepts of magnetism, magnets, and magnetic field, as well as electromagnetism and electromagnets. You will be introduced to solenoids and inductors. You will be able to calculate the reactance of an inductor, as well as the inductance and reactance of series and parallel inductors. You will also be familiar with different applications of inductors. DISCUSSION OUTLINE The Discussion of this exercise covers the following points: Magnetism, magnets, and magnetic field Electromagnetism and electromagnets The solenoid Inductors Operation of inductors in dc circuits. Operation of inductors in ac circuits. Inductance Inductive reactance Equivalent inductance and inductive reactance of series and parallel inductors. Applications of inductors DISCUSSION Magnetism, magnets, and magnetic field Magnetism is defined as the property of a material to exert a magnetic force (attraction or repulsion) on another material from a distance. It is caused by the magnetic field produced by certain types of material, referred to as magnets. The stronger the magnetic field produced by a magnet, the greater the force exerted by that magnet on other materials. The force exerted by a magnet on a material also depends on the nature of that material. Some materials are called ferromagnetic because they are strongly attracted to a magnet. This primarily includes iron, nickel, and cobalt, as well as some rare earth metals. The magnetic force exerted by a magnet is always more concentrated at the extremities of the magnet. These extremities are designated as the north magnetic pole (N) and the south magnetic pole (S) (see Figure 151). By convention, the north magnetic pole aligns with the North Pole of the Earth, while the south magnetic pole aligns with the South Pole of the Earth. This is because the Earth is a giant magnet whose poles attract or repulse other magnets. Festo Didactic 89688-00 185
Figure 151. Example of a magnet with a south magnetic pole and a north magnetic pole (photo courtesy of Aney). When two magnets are placed near one another, similar poles on the magnets repulse each other, while dissimilar poles attract each other, as shown in Figure 152. In Figure 152a, both north poles of the magnets face each other, causing the magnets to be repulsed one from the other. In Figure 152b, the north pole of the first magnet faces the south pole of the other magnet, causing them to be attracted one to the other. (a) Similar poles repulse each other (b) Dissimilar poles attract each other Figure 152. Attraction and repulsion between two magnets. The principle of magnetism illustrated in Figure 152 is the operating principle of a compass. In this device, an arrow with a north pole and a south pole is allowed to rotate around its center. The north pole of the compass arrow (red arrow in Figure 153) is always attracted to (and points toward) the south pole of the Earth. Conversely, the south pole of the compass arrow (blue arrow in Figure 153) is always attracted to (and points toward) the north pole of the Earth. Note that, due to historical reasons, the Earth s geographic South Pole is in fact its north magnetic pole, while the Earth s geographic North Pole is in fact its south magnetic pole. 186 Festo Didactic 89688-00
Figure 153. The arrow in a compass orients itself following the Earth s magnetic field. It is often convenient to illustrate the magnetic field produced by a magnet. This is usually done using magnetic lines of force, as shown in Figure 154. As you can see, the lines of force of the magnetic field exit the magnet through the north pole and enter it through the south pole. Figure 154. Lines of force of the magnetic field produced by a magnet. A common experiment in order to view the lines of force of the magnetic field produced by a magnet is to sprinkle iron fillings onto and around a magnet. As soon as the iron fillings enter the magnetic field of the magnet, they align themselves along the lines of force of the magnetic field, as shown in Figure 155. S N Figure 155. Alignment of iron fillings along the lines of force of the magnetic field produced by a magnet. Festo Didactic 89688-00 187
Electromagnetism and electromagnets In the previous section, you saw that some materials are natural magnets, which means that they naturally have a north pole and a south pole and interact with other magnets. Few materials are naturally found to have this property. However, it is possible to generate a magnetic field around a material by making electrical current flow through it. This is usually achieved by making current flow in a wire, as illustrated in Figure 156. The figure shows that the magnetic field created by a current flowing in a wire is circular and centered on the wire. The orientation of this magnetic field (i.e., the direction of the magnetic field lines) can be determined using the right-hand rule. When placing the right hand on the wire, as shown in Figure 156, with the thumb in the direction of current flow, the other fingers indicate the direction of the magnetic field lines. Magnetic field Wire Right hand Figure 156. The current flowing in a wire creates a magnetic field around the wire. The orientation of this magnetic field can be determined using the right-hand rule. This principle can be taken advantage of by winding the wire in a loop and making current flow in it (see Figure 157). The wire thus produces a magnetic field with north and south magnetic poles, just like a regular magnet. Such a magnet is called an electromagnet. Instead of exhibiting magnetism, electromagnets are said to exhibit electromagnetism. By using the right-hand rule, the direction of the magnetic field inside the electromagnet, and therefore the location of the north and south magnetic poles, can be determined. The higher the current flowing through the loop, the stronger the magnetic field produced in the loop. When the current flow is interrupted, the magnetic field disappears. 188 Festo Didactic 89688-00
Magnetic field direction When current flows through the loop, the wire loop forms an electromagnet Figure 157. A loop of wire through which current flows (an electromagnet) produces a magnetic field, which makes it the equivalent of a standard magnet. The solenoid As stated in the previous section, an electromagnet is created by making current flow through a loop of wire. However, the strength of the magnetic field produced by a single loop of wire is rarely sufficient for any application. To increase the strength of the magnetic field, it is common to wind a wire regularly in the form of a helix. The resulting device is called a solenoid. Figure 158 shows an example of a solenoid. The orientation of the lines of force of the magnetic field produced by a solenoid can be determined just like in a single wire loop using the righthand rule. Since the magnetic field produced by each wire loop in a solenoid is oriented in the same direction, they add up together. The resulting magnetic field of the solenoid is thus equal to that of one of its loops multiplied by the total number of loops. South pole (magnetic field lines enter) North pole (magnetic field lines exit) Current exits Current enters Figure 158. Solenoid. Festo Didactic 89688-00 189
The center of a solenoid is called the core. The core of the solenoid in Figure 158 is simply air. It is possible to greatly increase the strength of the magnetic field produced by a solenoid by replacing its air core with a core made of a ferromagnetic material, typically an iron core, as shown in Figure 159. Solenoids with iron cores are very common and are often simply designated as electromagnets. Figure 159. Solenoid with an iron core. Electromagnets made of iron-core solenoids have many applications. One of the most important is their use in motors, where the interaction between the electromagnet in the rotor and the magnet in the stator results in a rotary motion used to produce mechanical work. Electromagnets made of iron-core solenoids are also found in electromechanical devices using the principles of the solenoid with a plunger (see Figure 160). A plunger is simply a removable iron core. The solenoid is designed so that the plunger can be moved in and out of its center. When current flows in the solenoid, a magnetic field is produced that strongly attracts the plunger toward the center of the solenoid. When the current no longer flows, the plunger is released (springs are often used to return the plunger to its original position). This enables the force exerted by the magnetic field of the solenoid to be transformed into linear mechanical motion. This linear motion is used for control in a wide variety of applications, such as door bells, magnetic locks, circuit breakers, relays, valves, and magnetic breakers. The electrical diagram symbol for a solenoid is shown in Table 17. Figure 160. Solenoid with plunger. The magnetic field produced by the solenoid attracts the plunger inside its core, thus producing a linear motion used in many applications. 190 Festo Didactic 89688-00
Table 17. Solenoid and associated symbol. Component Symbol Solenoid Inductors In ac circuits, a coil of wire such as a solenoid or a motor coil is a type of component referred to as an inductor. Inductors are commonly found in ac circuits. Just like capacitors, the energy supplied to an inductor is not used to produce any immediate work. Instead, inductors store energy in their magnetic field and oppose current variations in a circuit. Table 18 shows the general electrical diagram symbol for an inductor, as well as the electrical diagram symbol for an inductor with a magnetic core (such as an iron core), the most common type of inductor. Table 18. Inductor symbols. Component Symbol Inductor Inductor with a magnetic-core Operation of inductors in dc circuits The operation of inductors in ac circuits is different than that in dc circuits. However, to better understand their operation in ac circuits, it is necessary to first study their operation in dc circuits. Consider the circuit in Figure 161. When the toggle switch is closed, a current flows through the circuit. A certain proportion of this current flows in the resistor, while the rest flows in the indicator light. The proportion between the current flowing in the resistor and the current flowing in the light depends on their respective resistance. However, the current flowing in each is constant. Therefore, as soon as the toggle switch is closed, the light lights up, which stays constant until the toggle switch is opened, at which point the light turns off immediately. Festo Didactic 89688-00 191
Toggle switch DC power source Resistor Indicator light Figure 161. DC power source connected to a resistor in parallel with an indicator light. Now, consider the circuit in Figure 162, in which the resistor in the circuit of Figure 161 is replaced by an inductor. When the toggle switch is closed, a current circulates in the inductor, which causes a magnetic field to build up around the inductor. This has the effect of opposing the flow of current in the inductor. As a result, initially, less current flows in the inductor and more current flows in the indicator light. At this point, more current flows in the inductor and less current flows in the indicator light. Therefore, when turning on the switch, the light at first glows brightly, then its intensity decreases until it is constant. Conversely, when the toggle switch is opened, the magnetic field around the inductor collapses (loses strength). As this happens, a current circulates in the inductor in the same direction as the current of the now disconnected dc power source. As the inductor magnetic field collapses, the current decreases. Therefore, when turning off the switch, the light at first glows very bright, then its intensity fades until it ceases glowing. Toggle switch DC power source Magnetic-core inductor Indicator light Figure 162. DC power source connected to an inductor in parallel with an indicator light. 192 Festo Didactic 89688-00
Operation of inductors in ac circuits AC inductors are basically the same as dc inductors. Their operation, however, is slightly different due to the properties of ac circuits in comparison to dc circuits. Consider the circuit in Figure 163 consisting of an ac power source connected to an inductor in parallel with an indicator light. When the switch is closed, a current circulates in the inductor. During the positive half-wave of the current sine wave, the magnetic field produced by the inductor builds up, then it collapses as the current sine wave returns toward zero. During the negative half-wave, the magnetic field produced by the inductor builds up again, but current circulates in the opposite direction. The above process repeats at every cycle produced by the ac power source. Inductors in ac circuits have the effect of opposing current, just like resistors and capacitors. Inductors achieve this by storing energy in their magnetic field as current increases, then releasing it as current decreases. Toggle switch AC power source Magnetic-core inductor Indicator light Figure 163. AC power source connected to an inductor in parallel with an indicator light. a Once again, it is important to note that not all ac circuits produce sine waves. In addition to that, not all sine waves produced by ac crcuits have polarity changes. Finally, not all ac circuits produce periodical waves. Inductance The fundamental characteristic of an inductor is its inductance. The inductance is the measurement of the magnetic field created by a current flow. The higher the inductance, the higher the amount of energy it can store. Inductance is measured in henries (H) after American scientist Joseph Henry, who discovered the electromagnetic phenomenon of self-inductance and developed practical applications of the electromagnet. Inductance is usually denoted using the letter. Just like resistors and capacitors, inductors have a certain tolerance, which indicates by how much their inductance can vary from the nominal rating. The tolerance of an inductor is generally expressed as a percentage of its nominal inductance, and can be low or high depending on the precision of the inductor. Festo Didactic 89688-00 193
Inductive reactance As stated previously, ac inductors oppose current variation by storing energy in their magnetic field, then releasing it. This has the effect of opposing current flow in ac circuits, just like resistors and capacitors. The opposition to current flow of an ac inductor is referred to as its inductive reactance and depends on its inductance, as well as on the frequency of the ac power source. The inductive reactance of an ac inductor is calculated using the following equation: (20) where is the inductive reactance of the ac inductor, expressed in ohms ( ) is the frequency of the ac power source, expressed in hertz (Hz) is the inductance of the inductor, expressed in henries (H) As you can see from Equation (20), the inductive reactance of an ac inductor is expressed in ohms ( ), just like the resistance of a resistor and the capacitive reactance of a capacitor. Because of this, in ac circuits containing an inductor, the inductive reactance of the inductor replaces the resistance when using Ohm s law to calculate the voltages and currents in the circuit. Ohm s law thus becomes: (21) where is the current flowing in a conductor, expressed in amperes (A) is the voltage applied across the conductor, expressed in volts (V) is the inductive reactance of the ac inductor, expressed in ohms ( ) Consider, for example, the ac circuit in Figure 164 containing an inductor. The ac power source has a voltage of 220 V and operates at a frequency of 50 Hz, while the inductance of the inductor is equal to 3.5 H. AC power source Inductor Figure 164. AC circuit containing an inductor. 194 Festo Didactic 89688-00
To calculate the current flowing in the circuit, it is necessary to first calculate the inductive reactance of the inductor: Using the inductive reactance of the inductor, it is then possible to calculate the current flowing in the circuit: Equivalent inductance and inductive reactance of series and parallel inductors The equivalent inductance of series inductors is calculated using the following equation: (22) where is the equivalent inductance of all inductors in the series circuit, expressed in henries (H) is the inductance of each inductor in the circuit, expressed in henries (H) The equivalent inductance of parallel inductors is calculated using the following equation: (23) where is the equivalent inductance of all inductors in the parallel circuit, expressed in henries (H) is the inductance of each inductor in the circuit, expressed in henries (H) It is then possible to convert the calculated equivalent inductance of the circuit into an equivalent inductive reactance value for the series or parallel circuits. Alternatively, it is possible to obtain the equivalent inductive reactance of a series or parallel circuit using the individual inductive reactance of each inductor in the circuit. In this case, the equivalent inductive reactance of series inductors is calculated using the following equation: (24) where is the equivalent inductive reactance of all inductors in the series circuit, expressed in ohms ( ) is the inductive reactance of each inductor in the circuit, expressed in ohms ( ) Festo Didactic 89688-00 195
The equivalent inductive reactance of parallel inductors is calculated using the following equation: (25) where is the equivalent inductive reactance of all inductors in the parallel circuit, expressed in ohms ( ) is the inductive reactance of each inductor in the circuit, expressed in ohms ( ) As you can see, the equivalent inductive reactance of series and parallel inductors is calculated in exactly the same way as when calculating the equivalent capacitive reactance of series and parallel inductors. Applications of inductors Inductors are found in a multitude of applications. One of the most common applications of inductors is in rotating machines such as motors and generators. The windings of these machines are essentially inductors. The interaction between the magnetic field produced by motor windings and other components in the rotating machine is the basic principle behind the operation of motors and generators. Another common application of inductors is in transformers. Transformers are important components of ac circuits that allow the voltage and current of the circuit to be varied. They basically consist of two inductors whose magnetic fields interact one on the other. Transformers are covered later in this manual. Figure 165. Transformers are basically two inductors interacting one on the other through their magnetic fields (photo courtesy of Fizped). 196 Festo Didactic 89688-00
Exercise 9 Electromagnetism and Inductors Procedure Outline PROCEDURE OUTLINE The Procedure is divided into the following sections: Setup Troubleshooting an inductor using an ohmmeter Calculating the inductive reactance of an inductor Connecting a circuit containing an inductor Calculating the reactance of inductors connected in series Calculating the reactance of inductors connected in parallel PROCEDURE High voltages are present in this laboratory exercise. Do not make or modify any banana jack connections with the power on unless otherwise specified. Setup In this section, you will install the training system modules in the workstation. 1. Refer to the Equipment Utilization Chart in Appendix A to obtain the list of equipment required to perform this exercise. Install the equipment required in the workstation. Make sure that all fault switches are set to the O (off) position. Troubleshooting an inductor using an ohmmeter In this section, you will measure the resistance of an inductor using an ohmmeter and verify that there is continuity between its terminals. 2. Set up the circuit shown in Figure 166. Use the inductor in the Capacitors / Inductor module to implement the inductor in the circuit. Inductor Figure 166. Circuit for measuring the resistance of an inductor. Festo Didactic 89688-00 197
Exercise 9 Electromagnetism and Inductors Procedure 3. Using the ohmmeter function of the multimeter, measure the resistance of the inductor. Record the value below. Inductor resistance 4. Does the resistance value you measured in the previous step indicate that there is continuity between the terminals of the inductor? a Yes No The resistance measured across inductors is caused by the resistance of the wire used to build the coil. Calculating the inductive reactance of an inductor In this section, you will calculate the inductive reactance of the inductor in the Capacitors / Inductor module using its nominal inductance. 5. Calculate the inductive reactance of the inductor using the nominal inductance shown on the faceplate of the Capacitors / Inductor module. a The inductive reactance of an inductor is calculated using the following equation: Inductive reactance Connecting a circuit containing an inductor In this section, you will set up an ac circuit containing an inductor. You will measure the inductor voltage and the current flowing in the circuit, and calculate the inductive reactance of the inductor using the measured values. You will compare the inductive reactance obtained from circuit measurements to the inductive reactance calculated using the nominal inductance in the previous section. 6. Make sure that the main power switch on the Power Source module is set to the O (off) position, then connect it to an ac power outlet. Set up the circuit shown in Figure 167. Note that the Control Transformer module is not required in this circuit. The circuit operates at the ac line voltage and is powered by the Power Source module. Use the inductor in the Capacitors / Inductor module to implement the inductor in the circuit. 198 Festo Didactic 89688-00
Exercise 9 Electromagnetism and Inductors Procedure Inductor Figure 167. Circuit for measuring the inductive reactance of the inductor. 7. Turn the power source on. Measure the voltage across the source and the current flowing in the circuit. Record the values below. Inductor voltage V Current A 8. Using the voltage across the inductor and the current flowing in the circuit you measured in the previous step, calculate the inductive reactance of the inductor. a The inductive reactance of the inductor can be calculated using the following variation of Ohm s law: Inductive reactance 9. Turn the power source off. Is the inductive reactance of the inductor you calculated from measured circuit parameters in the previous step close to the inductive reactance you calculated using the nominal inductance in step 5? Yes No Calculating the reactance of inductors connected in series In this section, you will calculate the equivalent inductance and equivalent inductive reactance of a circuit containing three inductors connected in series. You will then calculate the current flowing in the circuit. 10. Consider the circuit shown in Figure 168. Festo Didactic 89688-00 199
Exercise 9 Electromagnetism and Inductors Procedure 0.1 H 0.3 H 0.4 H AC power source Figure 168. Circuit containing three inductors connected in series. 11. Knowing that the inductances,, and of the circuit are equal to 0.1 H, 0.3 H, and 0.4 H, respectively, calculate the equivalent inductance of the circuit. a The equivalent inductance of series inductors is calculated using the following equation: Equivalent inductance H 12. Knowing the equivalent inductance of the circuit, calculate the equivalent inductive reactance. Consider that the frequency of the ac power source is equal to 60 Hz. a The inductive reactance of an inductor is calculated using the following equation: Equivalent inductive reactance 13. Knowing the equivalent inductive reactance of the circuit, calculate the current flowing in it. Consider that the voltage of the ac power source is equal to 24 V. a The current flowing in the circuit can be calculated using the following variation of Ohm s law: Current A 200 Festo Didactic 89688-00
Exercise 9 Electromagnetism and Inductors Procedure Calculating the reactance of inductors connected in parallel In this section, you will calculate the equivalent inductance and equivalent inductive reactance of a circuit containing three inductors connected in parallel. You will then calculate the current flowing in the circuit. 14. Consider the circuit shown in Figure 169. AC power source 1.5 H 2.5 H 3 H Figure 169. Circuit containing three inductors connected in parallel. 15. Knowing that the inductances,, and of the circuit are equal to 0.6 H, 0.8 H, and 1 H, respectively, calculate the equivalent inductance of the circuit. a The equivalent inductance of parallel inductors is calculated using the following equation: Equivalent inductance H 16. Knowing the equivalent inductance of the circuit, calculate the equivalent inductive reactance. Consider that the frequency of the ac power source is equal to 50 Hz. Equivalent inductive reactance 17. Knowing the equivalent inductive reactance of the circuit, calculate the current flowing in it. Consider that the voltage of the ac power source is equal to 220 V. Current A Festo Didactic 89688-00 201
Exercise 9 Electromagnetism and Inductors Conclusion 18. Turn off the power source and the measuring instruments. Disconnect your circuit. Return the leads to their storage location. CONCLUSION In this exercise, you were introduced to magnetism and inductors. You became familiar with the operation of inductors, both in dc and ac circuits, as well as with the concept of inductance. You learned how to calculate the reactance of an inductor, as well as the inductance and reactance of series and parallel inductors. You also learned different applications of inductors. REVIEW QUESTIONS 1. Define what inductance is. 2. What does the inductive reactance of an inductor represent and in which unit is it expressed? Briefly explain. 3. Calculate the inductive reactance of an inductor, knowing that its inductance is equal to 0.3 H and that the ac power network to which it is connected operates at a frequency of 50 Hz. 202 Festo Didactic 89688-00
Exercise 9 Electromagnetism and Inductors Review Questions 4. Consider the circuit shown in Figure 170. Calculate the current flowing in the circuit from the indicated parameters. Inductor AC power source Inductor Inductor Figure 170. Circuit for review question 4. 5. Name two applications of inductors in ac circuits. Festo Didactic 89688-00 203