determination of ohm’s law from physical data - … classes (generally grades 11 ... • students...

This work is supported by the National Science Foundation under NSF grant CNS-1138461. However, any opinions, findings, conclusions, and/or recommendations are those of the investigators and do not necessarily reflect the views of the Foundation.

© 2012 Northwestern University CT-STEM

Determination of Ohm’s Law

from Physical Data Time This activity should take one period for students to complete data collection, create graphs, and find best-fit functions using Excel. Level Physics classes (generally grades 11 and 12) that are studying electric circuits for the first time. Purpose Using measurements of electrical resistance, voltage and electric current, students will determine the mathematical relationship between electric currents, voltage and resistance by finding best-fit functions to those data. Overview You or your students will set up a basic electric circuit, consisting of a power supply, ammeter, resistors, and wiring. Using this circuit, students will follow a hand-out to conduct two sets of measurements and plot those data. • First, while keeping the resistance constant, students will vary the voltage and observe

its effect on electric current measured with an ammeter. Students should collect enough different voltages so they can produce a graph. This graph of electric current as a function of voltage should be linear.

• Second, students will vary the resistance while keeping voltage constant, and measure the effect of resistance on electric current. Again, enough different resistances should be used to get points for a graph of current as a function of resistance. With a power law fit, this should be current ~ 1/resistance.

Students will make two separate plots of current vs. voltage and current vs. resistance and determine the best-fits. The plots will suggest the relationship between current, voltage and resistance, and can be used to justify Ohm’s law, I = V/R. Student Outcomes Learner Objectives: Students in many science classes do not get many opportunities to use raw data to make plots, fit data, and extract laws or equations from those data. This activity is meant for students to do just that, much as experimentalists do at the professional level. • Students will learn how to make simple circuits, as well as measure the basic

quantities associated with electronics. • Students will also learn a useful relationship in Ohm’s law, and be aware of why it

is setup the way it is through direct observation and measurement.



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Computational Thinking in STEM Skills: • 1a Collecting Data • 1d Manipulating Data • 1e Analyzing Data • 1f Visualizing Data • 3a Using Computational Models to Understand a Concept • 3c Assessing Computational Models Next Generation Science Standards: HS.PS-SPM Structure and Properties of Matter c. Develop explanations about how the patterns of electrons in the outer level of atoms, as represented in the periodic table, reflect and can predict properties of elements. d. Construct arguments for which type of atomic and molecular representation best explains a given property of matter HS.PS-E Energy d. Design a solution to minimize or slow a system’s inclination to degrade to identify the effects on the flow of the energy in the system f. Construct models to represent and explain that all forms of energy can be viewed as either the movement of particles or energy stored in fields. g. Construct representations that show that some forms of energy may be best understood at the molecular or atomic scale. h. Design, build, and evaluate devices that convert one form of energy into another form of energy HS.PS-FE Forces and Energy a. Plan and carry out investigations in which a force field is mapped to provide evidence that forces can transmit energy across a distance b. Evaluate natural and designed systems where there is an exchange of energy between objects and fields and characterize how the energy is exchanged HS.PS-IF Interactions and Forces b. Use models to demonstrate that electric forces at the atomic scale affect and determine the structure, properties (including contact forces), and transformations of matter Illinois State Science Standards: • 11.A.5a – 11.A.5e: Know and apply concepts, principles, and processes of science

inquiry • 11.B.5a – 11.A.5g: Know and apply concepts, principles, and process of tech. design

12.C.5b: Know and apply concepts describing matter and energy – properties of materials 12.D.5a, 12.D.5b: Know and apply concepts describing forces (EM) and motion (electrons)

Common Core Standards for Literacy in History/Social Studies, Science, and Technical Subjects: Integration of Knowledge and Ideas



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• RST.11-12.7. Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem.

• RST.11-12.8. Evaluate the hypotheses, data, analysis, and conclusions in a science or technical text, verifying the data when possible and corroborating or challenging conclusions with other sources of information.

• RST.11-12.9. Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conflicting information when possible.

Prerequisites Students should be able to make graphs using Excel or other preferred software, and find best-fit equations to data (such as with Excel). Students should know what a basic circuit consists of, and should be familiar at least with the concepts of what resistance and currents are, so the understand what they are measuring. This activity can and should be done before students are exposed to basic circuitry principles; the goal is for students to ‘discover’ Ohm’s law. Background An electric circuit can be thought of as a racetrack for electrons. In order for the electrons to move through a material, it must get pushed in one direction. This is done with an electric field, which creates forces on electric charges such as electrons. But to have an electric field present either in space or between two points of a wire, there must be a voltage difference, ∆V, between those two points (which has a distance ∆r. The strength of the electric field is given by E = ∆V/∆r. How do we set up a voltage difference for a circuit? This is what the battery or power supply does. It is commonly called V in textbooks, but in reality this voltage represents the voltage difference between the two terminals of the battery or power supply. When the electric field goes through the wires and components of an electric circuit, the free electrons present in conducting materials feel a force, F = qE. This force pushes all the free electrons in the same general direction. The problem is, those electrons move short distances before they run into atoms and molecules of the material, and bounce around as if they are in a pinball machine. With all those collisions, energy is lost by the electrons and transferred to the lattice of the material. The vibrational energy of the atoms and molecules is felt by us as heat, and those collisions make it tougher for current to flow – this is electrical resistance, measured in ohms (Ω). Ohm’s law is the relationship between the voltage difference of the battery, V, and the resulting current. The bigger the voltage difference, the stronger the electric field and therefore the larger flow of electrons per unit time, which is electric current, I. Resistance is the constant of proportionality, and therefore Ohm’s law is V = IR.



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Teaching Notes Some students may be hesitant and overly cautious when using electrical circuits and power supplies for the first time. Teachers should be prepared to demonstrate proper use of equipment, how to make measurements of current and voltage, and ensure circuits are hooked up properly. Note that when students are changing the resistance of the circuit to measure the effect on current, they should also re-measure the total voltage for the circuit, and adjust it to a constant value they decide on. Overall this experiment has clean data that will lead to an accurate extraction of Ohm’s law. Pre-class Preparation Materials should be out prior to students coming into class. This activity can be set as a mini-lab, which is meant to take less than one period if students are properly prepared to use the equipment. If students have no prior experience setting up electric circuits, the teacher should demonstrate how to do this, or have lab stations setup prior to student arrival. The teacher should demonstrate safety tips with using electric circuits, such as the heat being produced and possible shocks using power supplies. Materials and Tools For this experiment, you will need: 1) Power supply, 2) wiring resistors, 3) ammeter, 4) voltmeter, 5) access to Excel or another graphing program, or graphing calculators that fit data. Assessment If your class typically uses lab reports, that would be appropriate for this lesson. Students should derive a direct relationship between current and voltage and an inverse relationship between current and resistance. Because students can find these relationships in a textbook, the assessment for this lab is more on the thought process and lab procedure than on the final result. Additional Information Your textbook will have chapters on circuitry/resistors and Ohm’s Law sample problems. • A useful video on drift velocity:

http://www.youtube.com/watch?feature=endscreen&NR=1&v=KgbqPKZU5IA. • A useful video on the Drude model:

http://www.youtube.com/watch?feature=endscreen&NR=1&v=dyX5I_io7bg. Handouts begin on following page.



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Mini-Lab: Ohm’s Law and Simple Circuits Purpose: Using measurements taken in class, you will derive Ohm’s law. Background: You don’t get any this time since it might “spoil the surprise.” Materials: Power supply Resistors Graph paper Multimeter/Ammeter Wires Breadboard Research Question: What does the electric current in a simple resistor circuit depend on? Procedures:

(A) The data you want consist of measurements of resistance, voltage and current, the “Big 3” of electricity. Set up a data table where you will have a single and constant resistance value. Select a voltage value and then measure the current. Do this for 5 different voltage values, and don’t go over 4 volts. Remember that resistors get hot after a while!

(B) Change the resistance value. Select a single and constant value of voltage. Record the current. After turning down the voltage, select another resistance value. Set the power supply back to the same voltage (bus-to-bus) you just had, and record the new current. Do this for at least 3 more resistance values, and use the same voltage value each time. Try predicting what current you will measure as you change resistance values.



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Analysis: 1. Make a graph of your data in part (A) above. The graph should be one of Voltage (y)

versus Current (x). Also make a graph of your data in part (B) above. This graph should be one of Current (y) versus Resistance (x). Make your graphs using a computer program such as Excel or Graphical Analysis, and find the best-fit functions for each graph.

2. What ‘shape’ are your graphs? What type of relationship (direct or inverse, linear or

nonlinear, etc.) exists between voltage and current for a constant resistance? Between current and resistance for a constant voltage? Use your best-fit functions to the data in your answer.

3. Based on your data and your graphs, combine the two results (best-fit functions) and

write down a single equation that shows a relationship between voltage, current and resistance. This is known as Ohm’s law. Put it in terms of I = _____.

4. For the following arrangements of resistors below, calculate the total resistance.

a. b. Let R1 = 10Ω, R2 = 8Ω, R3 = 4Ω, and R4 = 12Ω.



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5. Why do electronic devices get hot? Where does the energy come from that you eventually feel as heat? Explain in terms of what happens to electrons as they are moving through wires and resistors.

6. Based on your observations, what role might resistors have in electronic circuits?

After all, resistors waste energy and increase your power bill…why use them? 7. From a chemistry perspective, why are conductors and insulators so vastly different?

What is it about these various materials that make their electrical properties different? Also, from chemistry, what are semiconductors, and why are they important to electronics?

8. In your own words, why is the relationship E = -dV/dr (or think of it as E = -∆V/∆r)

the key to understanding how an electric circuit works? Be thorough, and write in terms of potential and electric fields, and what they do to free charges inside the wires of the circuit.



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9. How constant is the current in your circuit? Hook up the circuit to the LabPro voltage meter, and check the time dependence of the voltage across the resistor as current flows through the resistor using LoggerPro. Check over a few minutes.

10. Is it possible to have zero resistance in a circuit? If so, how, and are there any

applications of this in the real world?



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Post-Lab Run the following PhET computer simulations, in order to get some good visuals related to what you directly observed and measured in this experiment. The simulations are:

Ohm’s law - http://phet.colorado.edu/en/simulation/ohms-law Resistance - http://phet.colorado.edu/en/simulation/resistance-in-a-wire Basic Circuit - http://phet.colorado.edu/en/simulation/battery-resistor-circuit 11. Do these simulations agree with your observations and data measurements? That is,

does the mathematical model being used with the simulation mesh with reality (i.e. your experiment)? Justify your answer with examples or numbers from the simulation and lab.

12. On what physical properties of materials does electrical resistance depend?

Summary In your own words, summarize what you discovered in this lab. That is, what is your answer to the research question?



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Above and Beyond For a theoretical approach to Ohm’s law and conduction of electrons in materials, study the Drude model.

determination of ohm’s law from physical data - … classes (generally grades 11 ... • students...

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