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Building students’ understanding of series, parallel, and complex circuits C Matthew E. Vick ircuits are at the heart of cell phones, gaming systems, and even that old lamp in your room. Teaching about circuits can help students understand the underlying principles of many of today’s electronic devices and require them to use quantitative thinking skills. The University of Colorado’s Physics Education Technology (PhET) website (see “On the web”) offers free, highquality simulations of many physics experiments that can be used in the classroom. The Circuit Construction Kit, for example, allows students to safely and constructively play with circuit components while learning the mathematics behind many circuit problems. This article describes my experience using the Circuit Construction Kit with my 11ththrough 12th-grade physics students. S i m u l at i o n s vs . h a n d s - o n l a b s Building circuits often entails the use of breadboards (a construction base for an electronic circuit). Although breadboards present a tactile opportunity for physics students, their use is not always well understood. This is often because the physical layout of resistors (see photo, p. 30) does not look much like the diagrams students draw in class. Also, students who fail to measure current in series often blow the multimeter’s fuses. This adds stress for both students and the teacher, who must continually replace these devices. Finkelstein and colleagues (2005) studied the effects of using the PhET Circuit Construction Kit in place of a traditional circuit-building lab in a college-level introductory physics course. They found that students who used these simulations scored higher on a conceptual set of circuit questions and built physical circuits faster than students who participated in a traditional hands-on lab. Teaching assistants reported that the simulations allowed students to focus on content questions rather than the mechanical questions that result from blown fuses or loose connections. I have found the same to be true in my physics classes: The PhET simulations allow me to focus on the inquiry elements of the lab, rather than the mechanics of circuit construction. Finkelstein and colleagues (2006) also indentify several characteristics that the simulations illustrate in correlation with the National Science Education Standards (NRC 1996). Content Standard A, for example, emphasizes that students develop the “abilities necessary to do scientific inquiry” (NRC 1996, p. 173); using the PhET simulations, students draw conclusions based on their own data. Content Standard B 28 The Science Teacher A Virtual Circuits Lab encourages students to develop an understanding of the “structure of atoms” and “conservation of energy” (NRC 1996, p. 176); the PhET simulations help students visualize Keywords: Electronic circuits at www.scilinks.org the invisible world of electrons and Enter code: TST051002 address the misconception that electrons are “used up” in a circuit. The important thing to remember, though, is that the simulations themselves do not make for a constructivist, inquiry-based lesson—the teacher must use these simulations as a tool for exploration and discussion. Lessons should allow for creativity and problem solving, instead of simple observation. A c i rc u i t s l e a r n i n g c yc l e The PhET Circuit Construction Kit allows students to create circuits that closely resemble schematic diagrams— symbolic representations of the resistors, batteries, and other items in a circuit. Creating circuits that resemble schematic diagrams provides scaffolding for students to connect the symbolic and physical worlds. I use the Atkin and Karplus (1962) learning cycle in my physics class, which can be adapted for other physical science courses. The cycle consists of three stages: concept exploration, concept introduction, and concept application; the 5E Learning Cycle— engage, explore, explain, elaborate, and evaluate—is a similar model. Before using the PhET Circuit Construction Kit with my class, I have students physically connect a single resistor to an adjustable voltage power supply. They then plot the voltage versus the current to introduce the concepts of Ohm’s law and resistance. This physical experience is the part of the lesson designed to “hook” students. It also introduces Ohm’s law in an inquiry-based manner. The lesson then begins with three days of virtual “exploratory” activities that help students discover Kirchoff’s laws: one day for series circuits, one for parallel circuits, and one for complex circuits. Screenshots from the PhET website help guide students through the construction process, but many choose to “play” and build circuits on their own. These students add additional components (e.g., switches) or items (e.g., pencil or coin) from a virtual grab bag. I have found this to be encouraging, as less confident physics students in previous classes did not show interest in “playing around” with the circuits. After completing the virtual exploratories, students physically build the circuits on breadboards. Several students have remarked that this experience got them excited about electronics. When class time is limited, I make sure that students build at least one physical circuit so that those who enjoy working with electronic devices have the opportunity to do so. (Safety I m p o r t a n t t e r m s a n d co n ce p t s . Ammeter: An instrument used to measure the electric current in a circuit. Breadboard: A construction base for an electric circuit (see photo, p. 30). Current: A flow of electric charges through a conductor; measured with an ammeter. Kirchoff’s laws: Rules for finding current and voltage in a series or parallel circuit. Multimeter: An electronic device used to measure voltage, current, and resistance that combines several measurement functions into one unit. Noncontact ammeter: A bull’s-eye that is placed over any area of a circuit to read its current. Ohm’s law: The current through a conductor between two points is proportional to the voltage across the two points and inversely proportional to the resistance between the two points, or Current = voltage/ resistance or I = V/R. Resistance: The property of a material that resists the flow of electric charges through it. Voltage: A measure of the difference in electric potential between two points in a space, material, or electric circuit. Voltmeter: A device used to measure the voltage in an electric circuit. note: Students should be reminded to keep the voltage reading on their power supply at 4 V or less and asked not to touch uninsulated wires; safety glasses are required for this activity.) S e r i e s c i rc u i t e x p l o rat o r y The lesson’s first exploratory requires the most class time, since students are still learning how to use the PhET website and Circuit Construction Kit. In this activity, students construct a virtual series circuit with three resistors. I provide them with short written instructions to guide them through the simulation, since previous classes complained that they did not have enough support to use the Summer 2010 29 Pa ra l l e l c i rc u i t s e x p l o rat o r y The second virtual exploratory, on parallel circuits, moves faster than the first since it “parallels” the format. It is important to include screenshots in the instructions for this activity because the parallel circuits need “extra wire” to allow for the measurement of current in each branch of the circuit. It is also important that the resistance values are different so that the current through each branch will also be different. This helps avoid the misconception that current is always equal in each branch of a parallel circuit. Once again, students form their own data tables for voltage and current. I ask them to use the noncontact ammeter to record the total voltage across the battery and the total current right next to the battery. When measuring resistance, I have students use Ohm’s law with the total voltage and current, 30 The Science Teacher Photo courtesy of the author PhET site. Instructions for changing the default values of the resistors are particularly important—this helps students develop accurate generalizations. If all resistance values are left at the default of 10 Ω, the voltage across each resistor will be equal, which can lead to the misconception that voltages across series resistors are always equal. The written instructions for each exploratory activity and an application lab can be found online (see the “Editor’s note” at the end of this article). The interface in the Circuit Construction Kit includes a voltmeter with leads, so students can connect opposite sides of the resistors with a power supply for measuring voltage. Internal resistance and resistance in the wires are modeled to make the simulation more realistic. To measure current, students use either the ammeter or the “noncontact ammeter,” a bull’s-eye that is placed over an area of the circuit to read its current. I use the noncontact ammeter to avoid the difficulty of “breaking” circuits when inserting the ammeter. Other instructors may choose to use the ammeter so that their students can model the skill of inserting this device. Students explore the lesson’s concepts by drawing conclusions from their data, instead of through open-ended circuit building. The exploratory instructions I provide ask them to construct a data table of voltages across and currents through each of the resistors. Students share their data tables with the class and discuss the concepts that voltage drops in one circuit add up to the total voltage drop in an entire circuit and that current is the same throughout a series circuit. When using the Circuit Construction Kit, teachers should be aware that the simulation shows the charges moving faster with higher current. To avoid misconceptions, ask students to explain the ways in which the animated charge carriers are not like actual electrons. For example, current is the measure of the movement of charge, not of individual electrons— electrons continue to drift in a random pattern that moves more in the direction of the current than against it. Breadboard with a series circuit and multimeter. rather than focusing on the complex relationship between total resistance and the individual values. My intention is for students to realize that the total resistance is less than any of the individual resistance values. As students share their data with the class, they quickly realize that voltage drops are equal in each branch of a parallel circuit and that the current through each branch adds up to the total current. I have students discuss why they initially think that the total resistance is less than the individual resistors. Students often complain, “But that doesn’t make sense!” The visualization of electron flow that the simulations provide aid in this discussion; it allows me to ask questions about how the simulation shows the charge flow in each branch. C o m p l e x c i rc u i t s e x p l o rat o r y During the third exploratory, students construct a virtual complex circuit. At this point, they are often proficient with the PhET program. In this activity, students construct two complex circuits and then measure voltage and current values. They often look for broad generalizations, so the lab should include questions that focus on the series and parallel components of the circuit separately. This lesson requires the most scaffolding on the teacher’s part. Students want to be “given” the complex circuit rules, A Virtual Circuits Lab rather than work through the realization that series circuit rules are used in some parts of the circuit and parallel circuit rules are used in others. C o n ce p t d eve l o p m e n t After at least three days of building virtual (and possibly physical) circuits in series, parallel, and complex structures, students are prepared to work on more abstract problems. At this point, they often want to memorize specific circuit arrangements. I give students a labeled list of “series” and “parallel” circuit equations each time we do this activity. Undoubtedly, one student will ask why the complex circuit equations are not provided. Giving students ample practice, both in groups and as individuals, is vital to helping them discover how to apply the series and parallel voltage and current relationships in a non–simple circuit case. I find it necessary to lead a daily discussion to remind students that complex circuits do not have one set of equations. As a class, students fall back on the expectation for a single set of equations for complex circuits almost every day. Application lab: Build a complex circuit Finally, students are assigned a specific total resistance for which they are to construct their own complex circuit given certain resistance values. I have created a spreadsheet that generates possible values from the combinations given. As an extension, students can physically create the circuit on a breadboard and then check the total resistance using a multimeter. The PhET simulations focus students on connecting the concepts that resistors in series add to the total resistance and that resistors in parallel generally decrease the total resistance. The benefit of the physical construction is that it often serves as a “hook” for students who want to study electronics further. A formal lab report can be required, but I like to emphasize the “play” and problem solving inherent in the activity, so students receive credit when they complete the task successfully and show me their final product. Conclusion The PhET website has many simulations that allow students to create, observe, measure, and analyze—instead of simply watching an animation over which they have no control. This learning cycle guides students through experiences that help them develop an understanding of how current is divided through parallel circuits and how voltage is divided in series circuits. The virtual lab allows students to construct circuits that look like the diagrams found in textbooks and tests; the physical lab allows students to manipulate real objects and deconstruct electronic circuits—so they become more than just “black boxes.” The use of both a virtual lab and a physi- cal lab provides scaffolding for students, allowing them to connect the physical and symbolic worlds. The Atkin and Karplus learning cycle approach (1962) works well with the virtual labs provided by PhET. The Circuit Construction Kit makes the exploration less repetitive for students since they can easily construct new circuits. The application phase allows students to create a circuit using their own creative thinking. In my classes, students gave positive feedback about the use of the simulations and showed much less frustration than previous students who had only worked with breadboards. In this series of activities, virtual labs can be used to support inquirybased instruction in concert with a physical lab—allowing teachers and students to reap the benefits of both methods. n Matthew E. Vick ([email protected]) is an assistant professor in the Department of Curriculum and Instruction at University of Wisconsin–Whitewater. Editor’s note The full instructions for each of the three exploratory activities and the application lab are available on The Science Teacher’s website at www.nsta.org/highschool/connections.aspx. NSTA connections For more information on circuits, check out the “Electric and Magnetic Forces: Electrostatics and Current Electricity” NSTA Science Object. NSTA Science Objects are online, inquiry-based content modules for teachers that are free of charge. For more information, visit http://learningcenter.nsta. org/products/science_objects.aspx. On the web Physics Education Technology website: http://phet.colorado.edu/ index.php References Atkin, J. M., and R. Karplus. 1962. Discovery or invention? The Science Teacher 29 (5): 45. Finkelstein, N.D., W.K. Adams, C.J. Keller, P.B. Kohl, K.K. Perkins, N.S. Podolefsky, S. Reid, and R. LeMaster. 2005. When learning about the real world is better done virtually: A study of substituting computer simulations for laboratory equipment. Physical Review Special Topics— Physics Education Research 1 (1): 010103(1)–010103(8). Finkelstein N.D., W.K. Adams, C.J. Keller, K.K. Perkins, C. Wieman, and the Physics Education Technology Project Team. 2006. High-tech tools for teaching physics: The physics education technology project. Journal of Online Learning and Teaching 2 (3): 110–121. National Research Council (NRC). 1996. National science education standards. Washington, DC: National Academies Press. Summer 2010 31