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# Series, Parallel, & Complex Resistor Combinations

Lesson 8 of 10

## Objective: Students will be able to calculate the equivalent resistance and apply Ohm's Law to series, parallel, and complex resistor circuits.

In a previous lesson, students were introduced to Ohm's Law and explored series and parallel resistor combinations when they built circuits. After I refresh students' memory of Ohm's Law with a ranking task, students take notes on series, parallel, and complex resistor combinations. Today's goal is to calculate the equivalent resistance in different circuits and use that equivalent resistance to calculate current and voltage (HS-PS3-5). Class ends with students applying their new knowledge to a practice AP Physics 1 problem (SP5 & SP8).

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When students walk into class, today's ranking task is already projected onto the screen at the front of the room. I choose this task because it asks students to apply their knowledge of circuits, specifically how current is proportional to voltage and inversely proportional to resistance. This introduction is meant to get students thinking about current, voltage, and resistance as a part of Ohm's Law.

Once the students are settled, I read the instructions from the top of the activity. My reading of the instructions is to ensure students understand that class has started. I emphasize to students that they should work individually and take about five minutes to rank the circuits, explain their reasoning, and then assess their level of confidence. During these five minutes of work time, I walk around the room and informally assess how students are doing with simple glances at their work. My changes in location help students stay quiet and focused.

When the five minutes are over, I reveal the answers to the students by writing them onto the front screen: C, B=E, A, D, F. I then ask if anyone has all of the answers in the correct order. At least one student has the correct solution and is willing to share with the rest of the class. He starts by highlighting Ohm's Law and reminding the class that V=IR. Then, he explains that since each resistor equals two ohms, it is just a matter of looking at the resistance within and voltage supplied to the circuit. After he completes his explanation and shares a few examples, I end the introductory activity by asking if anyone requires further clarification. Because this activity reviews material from the previous class that we apply in today's lesson, the students keep their work to use as a reference.

#### Resources

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It's time for students to take out a sheet of paper and get ready to learn about different resistor combinations. My students are operating under the expectation that they must write down key points from the presentation. This expectation of how to take notes has been outlined and ingrained in their learning since freshman year.

I display the Series, Parallel & Complex Resistor PowerPoint (also available as a pdf) to help the students understand what they need to write down. As I'm showing the slides on the front board, I have a hard copy of the PowerPoint which includes teacher notes (viewable when the file is downloaded). These notes help me to stay focused and ensure I mention the highlights as we progress through each slide.

The presentation starts with an explanation of how to calculate the total resistance when resistors are connected in series. After students work through an example of finding the equivalent resistance in a series circuit, we then repeat the process for a circuit that has resistors connected in parallel. The presentation ends with an explanation of complex resistor combinations. After I show students how to simplify such a circuit, they then work through an example. When we get to the final slide, I give students about five minutes to think about, work on, and discuss the problem with those around them. Then, I go through the solution by writing on the white board (next to the projected problem).

While I describe this section as "direct instruction," I usually have a lot of interaction with my students throughout the presentation and am constantly moving throughout the room to change my proximity. The students ask questions, participate in problem-solving, and connect to real-world examples to stay engaged the entire time. I use the lights in the room to show how different switches control different strands of lights and also reference holiday lights.

For each of the example problems that are included in the presentation (key is viewable when the file is downloaded), students are encouraged to collaborate with those students seated around them. I'm also walking around to answer questions and provide assistance when needed. While I don't collect or grade the work or their notes, students know the importance of working through them and understanding the solutions. Homework problems and the unit test contain similar problems, so at this point in the course students usually embrace the ability to have guided practice time.

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Because students are already familiar with my suggestions for solving AP Physics 1 free response questions, I simply tell students to put everything away except for their calculators and equation sheets. Once everyone is situated and quiet, I give each student a copy of an AP Physics Problem that applies Ohm's Law. It's my goal to simulate the environment of the AP Physics 1 test, so students are limited in time and must have the problem completed at the end of class. I maintain absolute silence throughout their work time, and walk around the classroom to ensure students aren't cheating. I purposely choose this AP problem so students can apply their newly-learned knowledge of complex resistor combinations. The problem also gives students the opportunity to practice Ohm's Law and drawing schematics.

At the end of the class hour, when the bell rings, students come forward and show me their work. I'm standing at the door, so I quickly scan each student's work before handing them a copy of the rubric. Providing students with the rubric as they leave the room allows them an opportunity for immediate feedback. My students understand that they need to take the rubric, compare it to their solution, and score their work appropriately.

Scoring their own work offers students insight into how well they grasp the material. It also shows students what AP Physics 1 readers are looking for in a strong answer, and gets students thinking about how they might score on the AP exam at the end of the year. Not only is self assessment a powerful learning opportunity for the students, but it also takes some of the burden off of the teacher. Students turn in their scored problems at the start of the next class period and I record their grade.

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- LESSON 1: Charge Fundamentals
- LESSON 2: The Static Lab
- LESSON 3: Coulomb's Law
- LESSON 4: Electric Fields
- LESSON 5: Drifting Into Current
- LESSON 6: Ohm's Law
- LESSON 7: Constructing Circuits
- LESSON 8: Series, Parallel, & Complex Resistor Combinations
- LESSON 9: Electrostatics & Electricity Unit Review
- LESSON 10: Electrostatics & Electricity Unit Test