Aiding Student Understanding of Applying Kirchoff’s Voltage LawTrevor Register1, David Rosengrant2 1Physics Teacher, River Ridge High School

2Associate Professor, Department of Physics, Kennesaw State University

PERC 2015 – College Park, MD July 30th, 2015Abstract

Students struggle with both a conceptual understanding and the mathematical application of Kirchoff's Voltage Law (KVL). The highly abstract nature of potential and electricity creates difficulties in students differentiating between and simply understanding such topics as charge, current, potential difference, and power1,3. I have developed a diagram that builds conceptual understanding of potential and potential difference and also aids in generating a system of equations adhering to KVL. The diagram relates electric potential to a position along the circuit and incorporates all loops within that circuit on a single diagram. Though this work is in its initial phases in a high school classroom it has favorable results with students.

Limitations

The diagram’s primary advantage is in generating equations according to KVL without knowing anything quantitative about the circuit. The diagram is meant to be a stepping stone towards such an analysis. Given this, without any quantitative information, the relationship between the magnitudes of different potential differences cannot be known. However, since the height of a line clearly represents absolute potential, students could mistakenly conclude that one potential drop is more, less, or equal to another. In the first example, the drop in height of the line is shown to be the same, but without any additional information, it cannot be known that is equal to . Therefore, this limitation must be explicitly discussed with students. Additionally, the slope of slanted lines do not yet provide any information about the circuit.

AcknowledgementsThis work has been supported in part by National Science Foundation Grant #1035451.

The Diagram

At it’s core, the diagram is a qualitative potential vs. position graph that incorporates all loops within the circuit. Electric potential at any point is represented by the height of the line on the diagram. Different loops within the circuit are represented by different branches on the diagram. To generate a diagram, the following guidelines should be followed:

• Draw a horizontal dashed line to represent the ground potential, 0 V.• Pick a point on the circuit to begin. The battery or other source is best.• Upward slanted lines represent the rise in potential provided by a source.• Flat lines represent the wire between elements in the circuit.• Downward slanted lines represent the drop in potential that charges experience when

passing through a load in the circuit.• Choose a single loop to follow and complete each loop one at a time.• After the final element in a circuit is reached in a loop, make sure the line drops to the 0 V

dashed line.• For additional loops, simply extend a horizontal flat line from the first loop at the point at

which the paths diverge.

ΔV B ΔV 1

ΔV 2

0𝑉

ΔV 3

ΔV B

ΔV 1

ΔV 2

¿ ΔV B∨¿∨Δ𝑉 1∨+¿ Δ𝑉 2∨¿

0𝑉

A

B

C

D

E A

B C

D

E

ΔV B ΔV 1 ΔV 2

¿ ΔV B∨¿∨Δ𝑉 1∨¿∨Δ𝑉 2∨¿

0𝑉A

B

C

D

F

E

A

B C D

EF

A

B

C D

E

FG

A

BC

E

D

FG References

1Cohen, R., Eylon, B., and Ganiel, U. (1983), “Potential Difference and Current in Simple Electric Circuits: A Study of Students’ Concepts,” Am. J. Phys. 51, 407.

2Hieggelke, C. J., Maloney, D. P., Kanim, S. E., & O'Kuma, T. L. (2015). TIPERs: Sensemaking Tasks for Introductory Physics. Glenview, IL: Pearson Education, Inc.

3McDermott, L. C., and Shaffer, P. (1992), (a) “Research as a Guide for Curriculum Development: An Example from Introductory Electricity, Part I: Investigation of Student Understanding,” Am. J. Phys. 60(11), 994.

Student Work Samples

The following pictures show examples of student work using the KVL diagram. These were taken from an AP Physics 1 class during the Spring 2015 semester.

Students worked on the problems2 below in groups of 2-3. Students were asked to rank the magnitude of the potential difference between points M and N. All of the bulbs and batteries in each circuit are identical.

Students were not given any of the typical “rules of thumb” for circuits, such as the potential drops across parallel elements are equal. Through working problems like these, this was done to allow students to discover such relationships on their own as well as to be a soft test of the diagram’s effectiveness in developing conceptual understanding. Anecdotally, students found the diagrams useful, especially in differentiating between current and potential difference. The work to the right shows an example of one of the discussed limitations. In actuality, the potential difference across points M and N increases as more bulbs are added in parallel; yet, the student erroneously thought the potential differences were the same.

ContactRead about this and more on my blog, Time-Variant Teaching.

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