Simple Circuits Curriculum

Section 8: Background Information

Introducing the Concept of Electrical Potential

Scientists often reason about a circuit in terms of "electrical potential" or "electrical differential." These concepts explain why electrical currents propagate along the wire, and connect nicely to thinking about the circuit using constraint-based reasoning that takes into account the entire system and how different variables impact it. The phenomenon is referred to as electrical potential because there is potential energy in a circuit as a result of the difference in charge between the positive and negative poles of the battery. Understanding electrical potential requires a basic understanding of concepts related to static electricity.

The concept of electrical potential uses the idea of net excess charge. Before hooking up the wires in a circuit, everything along the wires is balanced. There are electrons and protons all along the wire, as discussed in the Cyclic Simultaneous Model, but they are not charged. There is a charge in the battery because the chemical in the battery carries out "work" to separate protons and electrons. This results in an excess of protons at the positive contact and an excess of electrons at the negative contact. The excess charge propagates through the circuit to the positive terminal. There is a very small transient delay (not noticeable at all) as the circuit gets up to the point where excess negative charge flows along the wire. This point is called "steady state."

The Role of the Battery in Maintaining Electrical Potential

In models based on electrical potential, the battery accomplishes the task of getting the electrons back to the negative contact on the battery, concentrating electrons on the negative contact and leaving a deficit on the positive terminal. This results in the imbalance that causes the electrical flow. The difference in the concentration of electrons between the positive and negative terminals gets distributed along the circuit and causes electrical impulses to move along the circuit. The chemical reaction inside the battery maintains a constant level of imbalance between the positive and negative terminals. Volts are the unit that we use to measure the voltage differential.

The chemical particles inside the battery can each only make a single trip carrying a single electron's worth of charge from one side of the battery to the other. Once it has made its trip, that chemical particle cannot be used again. When does a battery die? When all the chemical material has been moved from one side to the other and there is no more unused chemical left to move electrons and protons. This is why big batteries last longer.

Voltage is always measured as a difference in electron crowding (concentration) between two points. A particular spot in a circuit can't have a voltage. A 1.5 volt battery really means that it will maintain a 1.5 volt difference between its positive and negative terminals. If the concentration goes down between two points, it is referred to as a voltage loss or voltage "drop." If the concentration goes up between two points, it is a voltage gain.

An Underlying Relational Causality

The causality inherent in the concept of electrical potential is a Relational Causal Model. The relationship between two variables rather than one variable or one event causes an outcome. This is the same underlying causal structure involved in thinking about differentials and equilibrium in the topics of pressure or density. This model builds on an understanding of density and knowledge about balance versus imbalance in terms of electrical charge.

Electrical potential focuses on differential and balance. The excess of electrons at the battery's negative contact and the depletion of electrons (resulting in an excess of protons) at the positive contact results in a differential that causes the electrons to flow away from areas of higher concentration and to areas of lower concentration. The chemicals in the battery perform the "work" of concentrating protons on one end of the battery and electrons on the other.

Thinking About a Circuit using Electrical Potential in Comparison to the Cyclic Simultaneous Model

Models that use electrical potential (and the underlying Relational Causality) are less "zoomed-in" than the Cyclic Simultaneous Model, in that they focus less on the behavior of individual particles and more on the behavior of the system as a whole. The Cyclic Simultaneous Model describes the repelling of individual electrons (repelling and being repelled) as the cause of flow. Models based on electrical potential take a different perspective. They look at the behavior of the population or collection of electrons and use net charge as the cause of flow. Like the Cyclic Simultaneous Model, this requires that students look at the circuit as a system and reason about the entire system at once, rather than focusing on portions locally or on one bulb or battery at a time.

A Difficult Distinction that Challenges Understanding

A difficulty in presenting the concept of electrical potential and the underlying Relational Causal Model to students too early in their learning is that it shares aspects of the Cyclic Sequential Model that is so embedded in students' everyday reasoning. In the case of electrical potential, the circuit has electrons all along it before the battery is hooked up, but it is electrically balanced so it does not have net charge. On a surface level, this might fit with a student's idea that it is empty and will be filled with electricity. Although individual electrons don't have to travel to get from battery to bulb in the case of electrical potential, the gradient in electron concentration does propagate through the system. This aspect of its behavior IS cyclic sequential in its causal pattern. These overlaps may lead students back to that model, rather than to a more sophisticated model. One way to get around this is to explicitly point out its similarities and its differences to the Cyclic Sequential Model, reminding students of how the Cyclic Sequential Model is problematic.