Physics- Lab 2

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University of Guelph *

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1010

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Electrical Engineering

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Dec 6, 2023

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Lab 2 – Ohm’s Law and Kirchhoff’s rules PHYS*1010 – W21 Lab 2 Page 2 - 1 Learning Objectives: 1. Become familiar with making simple circuits with the IOLab and the E+M kit. 2. Show using a simple circuit that the rules you’ve learned in class for solving circuits apply in an actual circuit situation. 3. Practice using Kirchhoff’s rules and confirming that they apply in a real-world circuit. You’ve learned a couple of simple rules in Week 6 of your class lectures. One is Ohm’s Law, which told you that for simple circuit components, the potential difference across those components (V, in Volts) scaled linearly with the current across those elements (I, in Amperes), and that we could call that linear coefficient the resistance of the component (R, in Ohms). In other words, the classic statement of Ohm’s Law: 𝑉 = 𝐼𝑅 (1) Also in Week 6, you learned a couple of different rules about how potential difference, current, and resistance interact in a simple circuit – these are Kirchhoff’s rules, and they may be stated as: 1. The sum of all currents entering a junction must equal the sum of all currents leaving the junction. (The “junction rule”, “node rule”, or “current rule”) 2. The algebraic sum of changes in potential around any closed circuit path (loop) must be zero. (The “loop rule” or “voltage rule”). To prepare for this lab, you should review your Week 6 notes, review Hawkes 23-3 through 23-5, and make sure you’re comfortable with solving circuits using Kirchhoff’s rules. You should also review the document posted in the “Labs” section on Courselink, titled “What’s in my IOLab E+M kit”. In particular, pay close attention to how to identify the various resistors (there’s a code using bands of colour that you will want to be familiar with).

Lab 1 – Ohm’s Law and Kirchhoff’s rules Lab 2 Page 2 - 2 Experiment 1 – Ohm’s law in a simple series circuit In this lab, you’ll build a simple circuit with two resistors in series, use Ohm’s Law to determine the current through them, and, use your IOLab to measure that current. The purpose of this experiment is to make sure you’re familiar with these things in a simple circuit, before moving on to a more complicated one in Experiment 2. Materials IOLab device Breadboard Two 1000 Ω resistors Two alligator-clip leads Procedure 1. Your first step will be to show your expected, or theoretical, values for the current in your series circuit. To the left is shown a circuit diagram, showing two 1000 Ω resistors and a 3.3 V power source. Use your knowledge of series circuits to determine what the expected current will be through each resistor. Note that the resistors have a built-in uncertainty of 5% - you should include that in your calculations. You may assume that the IOLab power source has a built-in uncertainty of 3%. 2. Now, you will set up the circuit shown in the diagram using your IOLab. Begin by placing the two 1000 Ω resistors in the breadboard. Pause here for a moment, go and look again at the “What’s in my IOLab E+M kit” document, and look to see how the breadboard is set up. The holes in the breadboard are arranged in rows of five, and each row of five is connected electrically . So, if two wires are plugged into two holes in the same row of five, they are connected to each other. This is illustrated in the document. 3. Place the two 1000 Ω resistors in the breadboard, so that they are connected at one end (in other words, put one end of each resistor into the same row of five. It doesn’t matter where the other end of each one goes, as long as they’re not in the same row of five). This is an example of how that could look: These are connected (same row of five)

Lab 1 – Ohm’s Law and Kirchhoff’s rules Lab 2 Page 2 - 3 4. Plug two leads into your IOLab, one in one of the 3.3V power sources, and one in a ground port (GND): 5. Connect the alligator clip from the 3.3 V source to one end of your two resistors, and connect the ground to the other end. It should look something like this:

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Lab 1 – Ohm’s Law and Kirchhoff’s rules Lab 2 Page 2 - 4 6. Finally, select a wire to use as a voltage probe – this is identical to what you did in Lab 1. That wire should be plugged into the A7 port:

Lab 1 – Ohm’s Law and Kirchhoff’s rules Lab 2 Page 2 - 5 7. Connect and turn on your IOlab device and open up the A7 reading (as you did in Lab 1). Begin taking readings. Using the tip of your voltage probe, read the voltage at three places on your circuit. In the picture below, the voltage probe wire is shown taking a reading in location 2: Notice a few things about these readings as you take them – these should be commented on in your writeup: I. Location 1 is clipped to the 3.3 V power source. What should you expect to read with the voltage probe when you touch that location? Do you get the reading you expect? II. Location 3 is connected to ground. What voltage should you expect to read there, and do you see what you expect? III. Explain why the following statement is true: “It doesn’t matter where along Location 2 you touch the voltage probe, the reading is always the same”. 2 1 3

Lab 1 – Ohm’s Law and Kirchhoff’s rules Lab 2 Page 2 - 6 This is an example of the readings that were seen for the three locations – your writeup should include a similar picture, showing the voltage readings at each location (you can hover the mouse over a specific location to see the value of the data at that location, as shown – here, the actual values have been blacked out here – you will have to find them on your own!): 8. Complete a version the following chart. You should be able to calculate the currents by using Ohm’s Law, Eq (1). Assume a 3% error in the IOLab’s potential readings: Your writeup for Experiment 1 should include:  A short Methods section consisting of pictures that clearly show your experimental setup including the fully assembled breadboard.  A Results section that includes: o The full derivation of the expected current through the theoretical circuit from Step 1, with calculated uncertainty in your expected currents. o Comments on Questions I – III from Step 7. o A completed chart from Step 8  A short Conclusions section that compares your theoretical currents through the two resistors (with uncertainty) to your experimentally determined currents (with uncertainty). Did you find the experimental results you expected?

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Lab 1 – Ohm’s Law and Kirchhoff’s rules Lab 2 Page 2 - 7 Experiment 2 – Kirchhoff’s rules In this experiment, you will use the same techniques that you used in Experiment 1 to try to verify Kirchhoff’s Rules. Note that you will be finding currents in your circuit in exactly the same way – a voltage probe to read potentials on either side of a resistor, and then Ohm’s Law to determine the current through that resistor. Remember, Kirchhoff’s rules are: 1. The sum of all currents entering a junction must equal the sum of all currents leaving the junction. (The “junction rule”, “node rule”, or “current rule”) 2. The algebraic sum of changes in potential around any closed circuit path (loop) must be zero. (The “loop rule” or “voltage rule”). Begin by analyzing the following circuit diagram fully, using Kirchhoff’s Rules. Clearly show the expected current through each branch of the circuit: Now, you will recreate this circuit and see if your experimental results match what you determined theoretically. Note that uncertainty analysis is not required in Experiment 2. Materials: IOLab device Breadboard Two 1000 Ω resistors Two 2000 Ω resistors One 4700 Ω resistor Five alligator-clip leads

Lab 1 – Ohm’s Law and Kirchhoff’s rules Lab 2 Page 2 - 8 Procedure: We will not be walking you through the setup step-by-step for this experiment – instead, we will offer you some tips and a photo gallery that you may use as a reference.  In all the photos, taking note of wire colours will aid you greatly in making sure that your circuit is set up correctly.  You will need to connect two 3.3 V power sources and two grounds into your circuit.  Remember to be deliberate about which ends of which connectors are placed in the same group of five holes, and so are electrically connected.  You can always determine the value of a resistor that you see in a picture using the colour-coded bands. Use the information on this page to set up your circuit, and use the voltage probe to determine the potential difference across each resistor. You can then use Ohm’s Law to determine the current through each resistor. 1000 Ω 1000 Ω 2000 Ω 2000 Ω 4700 Ω

Lab 1 – Ohm’s Law and Kirchhoff’s rules Lab 2 Page 2 - 9 Your writeup for Experiment 2 should include:  A short Methods section consisting of pictures that clearly show your experimental setup, including the fully assembled breadboard, and where the wires are connected into your IOLab. Screencaps showing your data collection should also be included.  A Results section that includes: o All calculations for your theoretical values for the currents in your circuit’s loops. o Potential readings and current calculations for each of your experimental circuit’s resistors.  A Conclusions section that compares you theoretical values with your experimentally-derived values and comments on whether they agree – and if not, what might be the cause? In total, the writeup for Lab 2 should not be more than 3 pages.

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