Most Physics courses that cover the topic of electric circuits will typically spend time comparing series and parallel circuits to one another. Part of the discussion pertains to the effect of adding resistors upon the overall resistance. The concept of equivalent resistance typically emerges during that discussion. This Concept Builder makes an effort to provide students with a conceptual feel of equivalent resistance. In each question, three to four circuits are presented to students and they must identify the one circuit that has an equivalent resistance that is not like the others. The mathematical burden is very low in this exercise. Whenever there are two resistors in a circuit, their resistance values are always the same. They are also integer values that can be easily divided by two or multiplied by two without the need for a calculator. This allows students to easily determine the equivalent resistance.

We recommend providing students with several simple examples of determining the equivalent resistance before attempting this Concept Builder. We also recommend choosing numerical values for the resistances such that the equivalent resistance can be determined without a calculator and without a formula. 

This Concept Builder consists of 54 different questions that are grouped into 18 different Question Groups and spread across three different activities. Those three activities are described as follows:

• Series Circuits: Question Groups 1-6. Learners are presented with three circuits showing a power source and one or more resistors. Two of the circuits have the same resistance and the third circuit has a different one. Learners must identify the circuit whose resistance does not match the other two.
• Parallel Circuits: Question Groups 7-12. This activity is similar to the first activity but all three circuits are parallel circuits. Learners must identify the circuit that has an equivalent resistance that is not equal to the other two.
• Both Types of Circuits Question Groups 13-18. Learners are presented with four different circuits; they are a mix of series and parallel circuits. One of the circuits has an equivalent resistance that is not like the others. 

Before using the Concept Builder with your classes, we recommend that teachers attempt each of the activities in order to evaluate their appropriateness for your classes and what pre-requisite understanding a student must have in order to complete it. Alternatively, the questions are provided in a separate file for preview purposes. 

In order to complete an activity, a student must correctly analyze each question in that activity. If a student's analysis is incorrect, then the student will have to correctly analyze the same or very similar question twice in order to successfully complete the activity. This approach provides the student extra practice on questions for which they exhibited difficulty. As a student progresses through an activity, a system of stars and other indicators are used to indicate progress on the level. A star is an indicator of correctly analyzing the question. Once a star is earned, that question is removed from the cue of questions to be analyzed. Each situation is color-coded with either a yellow or a red box. A red box indicates that the student has incorrectly analyzed the question and will have to correctly analyze it twice before earning a star. A yellow box is an indicator that the question must be correctly analyzed one time in order to earn a star. Once every question in an activity has been analyzed, the student earns a Trophy which is displayed on the Main Menu. This system of stars and trophies allows a teacher to easily check-off student progress or offer credit for completing assigned activities.

The most valuable (and most overlooked) aspect of this Concept Builder is the Help Me! feature. Each Question Group is accompanied by a Help page that discusses the specifics of the question. This Help feature transforms the activity from a question-answering activity into a concept-building activity. The student who takes the time to use the Help pages can be transformed from a guesser to a learner and from an unsure student to a confident student. The "meat and potatoes" of the Help pages are in the sections titled "How to Think About This Situation:" Students need to be encouraged by teachers to use the Help Me! button and to read this section of the page. A student that takes time to reflect upon how they are answering the question and how an expert would think about the situation can transform their naivete into expertise. 

 

 

There are numerous resources at The Physics Classroom website that serve as very complementary supports for the Which One Doesn't Belong? - Equivalent Resistance Concept Builder. These include:
 

 

 

Additional resources and ideas for incorporating this Which One Doesn't Belong? - Equivalent Resistance Concept Builder into an instructional unit on Electric Circuits can be found at the Teacher Toolkits section of The Physics Classroom website.  Visit Teacher Toolkits.