Circuit Analysis Don'ts: Instilling Error Avoidance Skills While Teaching Proper Techniques

Circuit analysis is a discipline that is fraught with pitfalls for the beginning student. Common errors include misidentification of element configurations, unsuccessful efforts to create a simplified equivalent circuit, incorrect application of the source conversion principle, and omission or incorrect formulation of terms when writing a mesh or nodal equation to characterize circuit operation. This paper describes six circuit analysis errors that students frequently make, it suggests some proactive strategies that can be used to help students avoid these errors, and it describes the assessment techniques that have been used to evaluate the effectiveness of these strategies. Introduction Implicit in this discussion is the belief that students are better prepared to solve problems (e.g., to analyze circuits) when warnings about common errors are interwoven into instruction about proper techniques. The essence of this approach is to tell students to "do it this way, but be careful not to do it that way." Warnings about common errors serve to bring proper techniques into clearer focus, which better defines the correct approach. Difficulty Identifying Series and Parallel Elements in a Series-Parallel Circuit One of the most fundamental circuit concepts that students struggle to master is the identification of series and/or parallel circuit elements in series-parallel networks. Students often treat components that are graphically parallel as if they are electrically parallel, and they frequently consider any two elements that share a single common junction to be in series. Some students also have the mindset that components that are not in series must be in parallel, and vice versa. Proactive Strategy Present precise, but concise definitions of series and parallel elements in terms of both connections and circuit parameters: Series elements that are adjacent to one another exclusively share a common junction; all series elements share a common current. Parallel elements span two common junctions; parallel elements share a common voltage. Emphasize that the identification of series and/or parallel element configurations is a critical skill in circuit analysis. Reinforce study in this area by giving students extra practice with series-parallel resistor combination problems. P ge 14322.2 Assessment One course the author has taught on multiple occasions is the second of a three course sequence, which builds on the introduction to series-parallel circuit analysis provided by its predecessor. After observing many of the entering students struggle with concepts they were supposed to have mastered in the previous course, the author instituted a review quiz at the start of the second week of class to assess student competency in fundamental skills and provide students with an incentive to review foundational material. When the review quiz was first administered in Fall 2005, the performance of students on a fourelement series-parallel resistor combination problem was appalling: 70% of the students misidentified at least one resistor configuration as being parallel when it should have been identified as series, or vice versa. The proactive strategy previously described was hastily developed in response to this finding; this strategy has been utilized during the first week of class ever since. Figure 1 records the incidence of misidentified series or parallel elements on similar quiz problems given over the course of four successive semesters. Fall 2005 Spring 2006 Fall 2006 Spring 2007 Students who misidentified element configuration(s) 23 4 11 13 Number of students taking the quiz 33 32 32 32 Percentage of students making this error 70 R E V IS IO N S