Putting Potential at the Core of Teaching Electric Circuits

We believe that some of the learning difficulties described above can be attributed to the fact that voltage is often only a secondary consideration in traditional teaching. For example, voltage is sometimes only introduced as the “energy per charge” or as “the cause of the electric current” towards the end of the teaching unit on circuits. This structure can lead to difficulties in the following ways. Firstly, it fails to address that voltage as a potential difference always refers to a comparison between two distinct points in a circuit. Secondly, it may impede students from understanding the important “relation of cause and effect between pd [potential difference] and current.”⁶ Thirdly, it is likely to make current rather than voltage the students’ primary concept when analyzing circuits. As a result, students tend to reason exclusively with current and resistance when analyzing circuits. For example, they tend to put themselves in the role of the electric current, which they believe to travel sequentially through the circuit, e.g., light bulb by light bulb.⁴ However, it has to be noted that there are also valid arguments to be made in favor of teaching current first, the Physics by Inquiry curriculum perhaps being the best-known example of a successful implementation.⁸ 

A further point of criticism is the often comparatively early introduction of the quantitative relationship V = I R at the example of closed circuits, where voltage and current are always proportional to each other.^9,10 On the one hand, an early focus on a quantitative analysis of Ohm’s law can negatively affect students’ ability to reason qualitatively about electric circuits. On the other hand, the relationship V = I R may seem to suggest that voltage requires an electric current. Such an interpretation is likely to reinforce students’ alternative conception that voltage is a property of the electric current as both quantities are proportional to each other.

In order to avoid some of these difficulties, we believe that potential differences should not only be at the core of teaching but should be introduced even before the electric current.^6,11 Considering the abstract nature of potential differences, we furthermore believe that high school students should be equipped with a qualitative understanding of this physical quantity rooted in their everyday experiences.¹² Such an understanding should allow them not only to recognize the important relation of cause and effect between potential difference and current, but also understand that voltage refers to two points in a circuit.

Since students can only reason effectively about electric circuits if they can easily identify potential differences in a variety of circuits, it is furthermore essential that the electric potential is visually highlighted in circuit diagrams. This can either be done manually or by using suitable computer simulations. However, similar to the criticized focus of traditional teaching on the electric current, many commonly used simulations such as the popular PhET Circuit Construction Kit only illustrate the flow of charge while neglecting a specific visualization of the electric potential.^13,14 In view of this shortcoming, we developed a new easy-to-use simulation to illustrate electric potential differences in simple DC circuits with up to three resistors connected in series or parallel or in combination. The HTML5 simulation can be accessed free of charge via http://www.thomas-weatherby.com/simulation_en.html.

The Electric Pressure Curriculum, as illustrated in Table I and described in this paper, aims to make potential differences rather than current the students’ primary concept when analyzing circuits. Accordingly, air pressure rather than the closed water circuit analogy is used in the curriculum as students lack a conceptual understanding of water pressure in closed water pipe systems and have similar alternative conceptions about closed water circuits as they have about electric circuits.^15,16

After discussing that the electric circuit represents an interconnected system using the bike chain analogy, the curriculum aims to support students in developing an intuitive concept of air pressure as an immediately tangible counterpart to electric potential. Consequently, students investigate a number of everyday objects such as air mattresses and bicycle tires. Building on their experiences with these everyday objects, they then learn that air pressure differences are the cause for air flow and that the bigger the pressure difference, the stronger the air flow. Similarly, students are equipped with a first, qualitative idea of resistance by learning that a piece of fabric (e.g., a scarf) impedes an air flow.

In a next step, this intuitive understanding is applied to electric circuits. By initially using accessible vocabulary, the aim is to scaffold a transition to the concept of potential and potential difference. To this end, the electric potential is introduced as an “electric pressure” in the wires analogous to students’ intuitive concept of air pressure.¹⁷ In order to help students easily identify “electric pressure differences” or “potential differences,” the “electric pressure” can be visualized even in open circuits using the color coding feature of the computer simulation as shown in Fig. 1. Furthermore, students are encouraged to also manually color code the “electric pressure” in printed circuit diagrams, e.g., using crayons. In contrast to the CASTLE curriculum,¹² however, only open circuits are examined at this stage so that students can first develop a conceptual understanding of voltage before examining closed circuits, where voltage and current exist simultaneously. We also recommend discussing how voltmeters can be used to measure potential differences in electric circuits at this point. By initially considering only open circuits, the curriculum also circumvents some of the objections that were raised against the air pressure analogy from a physical perspective.¹⁸ 

In the simulation, a high potential is displayed in red and a low potential in blue by default, although this color scheme can also be inverted. In the curriculum, the color coding is based on the way in which values are often illustrated in everyday life as it aims to build on students’ prior experiences with color coding temperatures, e.g., on weather charts or water taps. On such everyday objects, red typically stands for a high and blue for a low (temperature) value. Similarly, red is used in the curriculum to illustrate a high electric pressure at the negative terminal while blue stands for a low electric pressure at the positive terminal. For a more in-depth discussion of key design decisions of the curriculum, as well as the physics behind the concept of “electric pressure,” please refer to Burde and Wilhelm.¹⁹ 

Next, students are asked to analyze closed circuits consisting of a battery and a light bulb. Based on the air pressure analogy, it is discussed that the “electric pressure difference” across a light bulb causes an electric current just as air pressure differences cause an air flow and that a resistor impedes the electric current. This intuitive, qualitative relationship is first illustrated in the form of a diagram (see Fig. 2, left) in order to facilitate a better understanding of the equation I = V/R, which is only introduced towards the end of the curriculum (see Fig. 2, right). To help students better remember the formula symbols, they learn that V stands for “Variation in Pressure,” R for “Resistance,” and I for “Intensity of Electron Flow.”

Furthermore, students learn that an (ideal) battery—in contrast to the initially discussed air pressure examples such as air mattresses or bicycle tires—maintains this “electric pressure difference.” Classroom experience shows that students easily accept this difference between the source domain (air pressure) and the target domain (electric circuits) of the analogy, maybe also because the idea is visually indicated by color coding. After introducing the concept of resistance, this idea is then applied to parallel circuits. This

• helps students realize that a battery is a source of constant voltage rather than constant current.

• helps students understand the central relationship of cause and effect between voltage and current.

• makes voltage rather than current the students’ primary concept when analyzing circuits.

For this purpose, e.g., using the computer simulation, students first analyze a simple electric circuit with one resistor (see Fig. 3, left), to which another resistor is connected in parallel (see Fig. 3, right). At the example of the computer simulation, teachers should point out that the first step in any analysis of circuits is to draw in the “electric pressure” using color coding as it illustrates that batteries are a source of constant potential difference and not constant current. Next, teachers should focus students’ attention on the fact that adding a second resistor does not change the current through the first resistor since the “electric pressure difference” across it stays the same. Similarly, it is important to argue that the second resistor now means an additional current due to the applied “electric pressure difference,” which needs to be supplied by the battery. At the same time, teachers should avoid a statement like “the current divides at the fork in the wires” as it implies that the battery is a source of constant current and may also reinforce students’ tendency to analyze circuits sequentially from the perspective of the flow of charge.²⁰ To help students understand this important aspect of parallel circuits, the electric current is visualized in the computer simulation by arrows whose thickness corresponds to the current intensity (see Fig. 3).

When using the simulation, teachers are not limited to color coding the electric potential. Instead, the electric potential in circuits can also be visualized using a height analogy. As shown in Fig. 4, this has the advantage that the linear potential reduction through a resistor can be discussed using the simulation. Furthermore, the simulation allows users to choose between the physical and the conventional direction of current and set the voltage of the battery. In the height representation, it is moreover possible to specify whether the high potential is assigned to the positive or the negative terminal to ensure that the current always flows “downhill.”

An empirical evaluation in the area of Frankfurt, Germany, with 790 middle school students (grades 7 and 8) showed that students who were taught based on the ideas described in this article developed a significantly better conceptual understanding of simple circuits than their traditionally taught peers.²¹ A slightly modified English version of this curriculum, suitable for use in public schools, can be downloaded free of charge from https://www.talkingcircuits.com/bookdownload.html.