Students use a simulator to determine the mathematical relationships between voltage, current and resistance for a simple circuit.

Ohm's Law, V=IR, is the mathematical relationship between voltage, current and resistance.

In this lesson, students us a computer simulation laboratory to determine the mathematical relationship between voltage, current and resistance in a circuit. Students plan their investigation, collect data and analyze them to "discover" Ohm's Law. This builds off the previous lesson where students learned the definitions for voltage, current and resistance.

An engineering NGSS is applied here, HS-ETS1-4: Use a computer simulation to model the impact of proposed solutions to a complex real-world problem with numerous criteria. Science Practice 3: Planning and carrying out investigations, Science Practice 4: Analyzing and interpreting data, Science Practice 5: Using mathematics and computational thinking and Science Practice 8: Obtaining, evaluating, and communicating information are all used in this activity. Since voltage is an electric potential due to electric fields, the performance standards HS-PS3-5: Develop and use a model of two objects interacting through electric or magnetic fields to illustrate the forces between objects and the changes in energy of the objects due to the interaction. Also, students build virtual circuits which applies HS-PS3-3: Design, build, and refine a device that works within given constraints to convert one form of energy into another form of energy.

CCSS Math Practice 2: Reason abstractly and quantitatively and Math Practice 4: Model with mathematics are also applicable as students graph data and determine the mathematical relationship between variables.

Students need access to computers and the internet to perform this activity. They use a simulator called PhET: Circuit Construction Kit (DC Only) which is provided by the University of Colorado.

40 minutes

Today, students determine the mathematical relationship between: voltage and current, then resistance and current. From Turning On Simple Circuits, students know the definitions of voltage, current and resistance and the water analogy that goes along with each concept (pressure, flow and narrow pipe). Before I hand out the Determine Ohms Law activity sheets, I project a sample simple circuit from the PhET simulator Circuit Construction Kit (DC Only) on the board. I demonstrate the basics of how to construct a circuit and change the variables such as voltage and resistance.

Students work cooperatively in groups of 2-3, which gives them a chance to talk through the assignment and to help each other. I don't like to have groups bigger than 3 as the smaller group makes it more likely that all students make significant contributions to the assignment. Each group needs one laptop which I provide. There are some students who have their own which I allow them to use. I tell the students that they should spend about 15 minutes on each experiment so that both are completed 5 minutes before the end of the period.

The handout has students identify the independent, dependent and variables held constant throughout the experiment. Then students build their circuit and collect the data which is recorded on the handout. They graph the data so they can see the mathematical relationships that exist between the independent and dependent variables.

While students work on the sheet, I circulate the classroom and give support where needed. In order to better serve the students who need my help, I have devised a **three cup **system that alerts me to who needs help. My students sit at tables in groups of four. At each table are three cups, a red one, a yellow one and a red one (pictured right). Depending on how students are doing in the assignment, they will put one of the colored cups on top.

**Green Cup**: Default cup: Everything is going well, we don't need help.

**Yellow Cup**: We are struggling with a concept: We need you to affirm that we are heading in the right direction.

**Red Cup**: Help! We are totally stuck and can't move forward.

Half-way through the period, I tell the class that they should be done or close to finishing the first experiment (Circuit Basics 1: Determine the mathematical relationship between current and voltage) and move onto the second experiment (Circuit Basics 2: Determine the mathematical relationship between current and resistance). We spend 5 minutes in review of the experiements the students do, so all groups must finish before then.

5 minutes

To close the activity, I project two student work samples to share with the rest. I use my document camera and show Student Work - Circuit Basis Exemplar from one of the groups. I then call on random students to provide their observations either from their own sheets or from the one being shown. I get responses such as:

- There is a linear relationship between voltage and current.
- Even though I have different values for voltage and current, my relationship is the same.
- The slope of a line is y=mx+b.
- The Y-axis is the current and X-axis is the voltage.
- The slope of the line is the inverse of the resistor.
- The result matches Ohm's Law.

I repeat the same exercise for Student Work - Circuit Basics 2 Exemplar.

- It is an inverse relationship between resistance and voltage.
- Even though I have different values for resistance and current, my relationship is the same.
- The Y-axis is the current and X-axis is the resistance.
- The result matches Ohm's Law and works for any value of the resistance or voltage.

I collect the students worksheet and finish the lesson with the application of Ohm's Law and why fuses were invented.

5 minutes

I display the Ohms Law and Fuses Power Point. This mini-lecture summarizes that the current in a circuit is determined by the voltage and resistance. If there is a situation where the resistance is too low, or if a "short-circuit" happens (the positive end of the power supply is connected directly to the negative end), then the current becomes so large it can start a fire.

I show images of the different types of fuses that exist and give a brief history of household fuses and how easy it was for people to bypass the old style fuses by putting in the wrong value fuse or jamming a penny in the fuses place. The new style breaker boxes are fool proof. Only a trained and knowledgeable professional can bypass the safety features, but they don't because they understand the dangers.

To conclude, I write Ohm's Law, V=IR, on the board and inform students that today they determined the mathematical relationships between voltage, current and resistance. With their new-found knowledge they can predict and control the current of any simple circuit. I handout a homework sheet that has several Ohm's Law practice problems and ask students to complete it for tomorrow. (This sheet is copied from another source and for copy right reasons is not included here.)