Voltage and Current Divider Circuits

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Objective

Students will continue to explore and discuss the ways in which energy is transferred in simple DC circuits.

Big Idea

The conservations of energy and charge can be leveraged to explain the behavior of circuits.

Overview

Over the past few day, my classes have suffered many absences due to weather, illnesses, and field trips. Today's lesson is heavy on notes and board work as I try to provide students with the right content background before proceeding. My goal is to help students understand the way that charges gain and lose energy in simple circuits in advance of an upcoming multi-day investigation of electric energy transformations. If successful, students will get a great opportunity to demonstrate the NGSS Performance Expectation HS-PS3-1.

Rubric for Energy Project

5 minutes

Students have been working on an assignment where they need to demonstrate a conceptual understanding of the conservation of energy. It has been a major theme of our year and resonates with several of the Physical Science Performance Expectations of the NGSS. Today, I take a few minutes to share the "higher-order thinking" rubric (HOT Scale) that will be used to assess their products.

I use this instrument as a way to focus my thinking - and my students' - about the essential elements of any product they might create. Whether it's a Prezi, a video, a poster, a pamphlet, an essay, or anything else, the final product needs to comprise three big components. First, it needs to illustrate the key ideas of the topic and anticipate an audience's needs. In other words, what information would a viewer need to make sense of the rest of the product? Second, there should be evidence or examples of the topic to help make the point. Without evidence, students might just simply be sharing an opinion. Finally, the flow of the product needs to be sensible. Ideas should build upon one another and there should be thoughtful transitions between sub-topics.

For me, this rubric keeps me from being "won over" by some beautiful illustration, for example, that is bereft of content. This is my effort to ensure that style does not win out over substance. The assessment should be based on the thinking, not the artistry.

I take five minutes in class to hand out this rubric, share my thoughts about each topic, and address any questions.

Warmup - Review of Voltage Divider Circuit

30 minutes

As we recover from a complicated week, I present a warmup problem that will allow me to meet multiple needs.

This "Voltage Divider" circuit is framed with references back to the self-paced electronics exploration (Activities A and B). My purpose here is to connect with previous learning and to prompt certain kinds of ideas to come forward. In addition, with absences due to field trips this week, I need to assess where my students are in terms of the basic relationships of voltage, current, and resistance. Finally, as the rest of this lesson depends upon a firm understanding of voltage and current, this warmup presents the opportunity to fill in any gaps that may exist.

Students take five minutes or so to address the questions in their notebooks. I circulate and attend to issues ranging from struggles with Ohm's Law, unclear ideas about the way series resistors are combined, and the nature of current in this circuit. After some time in this mode, I switch to a more global instructional mode and lead students through the solutions to these questions, amplifying on the "big picture" ideas of circuits: energy and charge conservation. The last question, in particular, allows me to highlight - once again - the explanatory power of the conservation of energy 

At the end of this time, I do a simple formative assessment: I ask students how confident they are with these ideas on a range of "fist to five." They raise their hands showing, with fingers on a 0 to 5 scale, their individual confidence level. Most students show at least 3 fingers with many showing 4 or 5 - a good sign that their confidence is growing.

Mechanical Analogy

15 minutes

In an effort to make the circuit activity more concrete, I use a mechanical analogy. I show a picture of a stick figure who has the "worst job in the world . . .  an absolutely futile one." I describe how he needs to haul bowling balls up to a shelf from which point they roll down, only to be hauled up again by the stick figure. This task is reminiscent of a Greek tragedy and, unless students mention it first, I ask which of the Greek mythological figures has such an impossible task. One way or another, we come up with the name of Sisyphus and, in his honor, we name our stick figure "Liftyphus."

I ask my students some key questions about this machine. How much potential energy do the balls have at the bottom? (Zero.) What can we say about the potential energy at the top shelf? (It's where it has its greatest amount.) How does it get that energy? (From the work of Liftyphus.) What will happen to Liftyphus as he continues to do this work? (He'll need to eat or be replaced.)

At some point, it becomes clear why we are talking about this machine. I ask my students to raise a hand if they can make one connection between the Liftyphus machine and a battery connected to a single light bulb. I wait for at least six hands to go in the air before selecting students to share their connections. Eventually, we have a complete map between the circuit and this mechanical analog - Liftyphus is a battery, the bowling balls are coulombs of charge, and the ramp is a circuit element (say, a light bulb or buzzer) to which the charges transfer their potential energy. 

In the next segment of class, we use this thinking to check for understanding.

 

Formative Assessment - Voltage Divider

15 minutes

Quickly, I ask my students to apply their "Liftyphus" thinking to the problem we dealt with in the warmup: the voltage divider circuit. I give my students just three minutes to draw and ask for a student response to be put up on the board for review. As we have agreed, in advance, that the battery part of the circuit is not different, I provide a Liftyphus template and the student adds in the ramps as she sees fit. In this case, given a circuit with a single loop and two resistors, she has correctly shown two ramps with a short ledge between them. The first ramp models the loss of energy in the first resistor while the second ramp shows that the rest of the energy is deposited into the second resistor. 

As a follow-up, I ask a similar question about a voltage divider circuit that features three resistors. I give students another five minutes or so to work on this problem, then show a solution for the three resistor problem. The problem is familiar but extends thinking just enough to serve as a formative assessment of student understanding.

Application - Current Divider Circuits

15 minutes

In the final segment of class, we turn our attention to another circuit featured in the self-paced exploration: the current divider circuit.

I begin by showing the current divider architecture. Students copy this down in their notebooks and follow along with a series of critical questions. We discuss the idea that any charge that reaches the junction of the two light bulbs has to go into one light bulb or the other, but certainly not both. This split leads us to the following statement:

Io = I1 + I2

Next, I ask "How much energy a coulomb of charge loses in the first light bulb?" and "Is this any different from the energy lost by a coulomb of charge passing through the second light bulb?" These questions force us to consider the idea that:

Vbattery = V1 = V2.

In response to the idea that this somehow violates the conservation of energy, I ask my students how many ways are there to get down from the Library (third floor in our building) to the Cafeteria (first floor). There are four ways - three separate staircases and an elevator. Comparing our loss of potential energy in any one of those cases to any other helps students to recognize the process of current division.

Before class ends, I ask my students to draw the Liftyphus analogy of the current divider circuit. Here's a sample response and a second sample.