PHY112 Lab 5

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Northern Arizona University *

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112

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Electrical Engineering

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Jan 9, 2024

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Katya Milyard PHY112 3/31/23 Lab Title: The Effect of Ohm’s Law on Currents and Circuits Lab Purpose/Question: The purpose of this lab is to examine the relationship between voltage, current, and resistance through a circuit containing a series of batteries and a resistor. By creating a circuit with the batteries, resistor, and a voltmeter, we can change the voltage of the circuit by adding more batteries that will affect the current. Materials: * Multimeter * 5 batteries (1.5 V) * Insulated wires with alligator clips * 1 resistor * Battery holders Procedures: To begin the experiment, we will need to properly set up the voltmeter similar to the last experiment. In order to do this, you will need to plug the black lead into the COM slot, plug the read lead into the fused slot, and turn the dial to 20 DCV. Create a circuit by forming a loop with one of the batteries and the resistor while the voltmeter creates a loop of its own making sure that the voltmeter is properly connected in parallel to the rest of the circuit. For this particular experiment, we will also need to change the multimeter into an ammeter which is a device that measures current or the flow rate of charge. To do this, we will have to plug the red lead into the unfused slot, turn the dial to 20 DCA, and plug the black lead into the COM slot. In this experiment, the ammeter must be connected within the circuit in the same loop at the battery and the resistor. When you are not collecting data during the experiment, make sure you disconnect the batteries. Be very careful of the resistor, because the resistor may get very hot to the touch during experimentation. To start collecting data, create a circuit with batteries and resistors. Start off by connecting one battery to a resistor and measure the voltage. Take the black voltmeter lead and place it on the side of the resistor that is connected to the negative side of the battery while placing the red voltmeter lead on the other side of the resistor that is connected to the positive side of the battery. Record the measurements. Change the voltage acting on the circuit by gradually adding more batteries to the circuit causing the current to change. Change the settings on the multimeter to the proper setting to measure current. Disconnect one wire that is connected to the resistor and insert the ammeter into the circuit while recording the current. Insert another battery properly into the circuit and repeat the process again until all five batteries have been inserted into the circuit. For each battery, measure both voltage and current resulting in a total of five data points for each trial. Run a second trial to reduce error and average the data. In this experiment, we are only adding batteries to the circuit and keeping everything else constant. Create a scatter plot on excel with current on the x-axis and voltage on the y-axis including the line of best fit with the best fit equation. Using your data and graph, determine the resistance in the circuit you created comparing the experimental resistance results to the actual value. Photograph(s) of Experiment: Data: Data should be recorded in a properly labeled data table format. Units should be included with the column or row heading and not with the numbers. Evidence of repetitions in measurement should be present if appropriate. Measured values should be recorded with appropriate significant figures. Trial #1

Number of Batteries Voltmeter (V) Ammeter (A) 1 1.55 0.08 2 2.91 0.16 3 4.48 0.23 4 5.87 0.29 5 6.93 0.36 Trial #2 Number of Batteries Voltmeter (V) Ammeter (A) 1 1.57 0.08 2 2.95 0.16 3 4.49 0.23 4 5.83 0.29 5 6.99 0.36 Calculations and Graphs: Do not confuse data with calculations. Calculations are manipulations of the data you collected. For each type of calculation, show one example. Show the equation used, appropriate number substitutions, and the final answer for each sample calculation. The calculation results should be summarized in table format. This may be part of the original data table or may be a separate table. Be sure to use proper headings and units. Data Averages: Number of Batteries Voltmeter (V) Ammeter (A) 1 1.56 0.08 2 2.93

0.16 3 4.485 0.23 4 5.85 0.29 5 6.96 0.36 Calculation of Data Average Trial 2: Voltage: (2.91+2.95)/2 =2.93 V Currency: (0.16 + 0.16)/2= 0.16 A Results: This graph portrays the relationship between voltage and current. Based on the trendline, we can see that there is a positive linear relationship between voltage and current. Conclusion: * Theory / Background: This lab discusses the relationship between voltage, current, and resistance with the integration of Ohm’s law. Last lab, we discussed voltage as the difference in charge between points, in this case, two different points in a circuit. When a battery is connected to a closer circuit, an electric field is formed within the circuit due to the voltage difference across the positive and negative ends of the battery causing charge to move within the field. This particular rate of flow of charge is called current. While voltage allows for charge to flow within a circuit, resistors can limit the flow of charge, therefore, hindering current. Current is calculated by the equation I= delta Q/ delta t, where delta Q is the amount of charge flowing through a specific point, delta t is the time it takes for charge to flow through this specific point, and I is the current. Current has units of Coulombs/ second (C/s) which is also known as amperes or amps (A). In order for charge to flow through a battery generator, wire, or other things, it has to be attached to a circuit, While the battery doesn’t supply the charge, it does give the electric pressure that is necessary to cause the charge to flow that is in the circuit. Through this, we can see that as voltage increases, current increases. Since resistors hinder the flow rate of charge, we can see that flow and resistance are inversely proportional to each other. When we combine all these relationships of current, voltage, and resistance, we get Ohm’s law with an equation of V=IR. * Interpretation of Results: The graph analyzed the relationship between voltage and current with an equation of y= 19.854x-0.0902. This graph portrays a positive relationship between voltage and current due to the positive slope. Based on the graph, one can see that there is a positive linear relationship between voltage and current due to the trendline and the equation of the trendline. The trendline equation shows that the slope is 19.854. Since the slope of the trendline is positive, we can conclude that there is a positive relationship between voltage and current. For example, the point on the graph that is furthest to the left has coordinates of (0.08, 1.56) with current (A) on the x-axis and voltage (V) on the y-axis. The next data point to the right has the coordinates of (0.16, 2.93). This shows that as the voltage increases, the current also increases. Typically we are supposed to plot independent variables on the x-axis and the dependent, changing variable on the y-axis; however, for the purpose of this lab and analysis, we plotted the graph this particular way. Based on these two data points, we can see that as the voltage increased by an increment of 1.37 V, the current also increased by an increment of 0.08 A. Since current increased as voltage increased, we can see

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that there is a directly proportional relationship between these two variables. This is in accordance with Ohm’s law stating that the current through a circuit is directly proportional to the voltage but inversely proportional to resistance. The slope of this voltage vs. current graph is actually the resistance of the circuit, because resistance can also be stated as the amount of voltage needed to increase current by 1 A. This means that if a system has a lot of resistance, then it will take a large amount of voltage to cause a small increase in current. On the other hand, if a system has only a little amount of resistance, then a big increase in voltage will cause a big increase in current. Since this graph has a general linear constant slope, we can see that there is a constant resistance within the circuit. We also see the trendline has a y-intercept of (0, -0.0902) showing that when there is 0 A of current flowing through the circuit, then the voltage is -0.0902 which is very close to 0. This makes sense because if there is a 0 V difference between the two points, there will be no electrical field that will allow for the flow of charge, and therefore, be no current. I thought the quality of the results were fairly accurate and on point. We expected there to be a linear relationship between voltage and current based on Ohm’s law. My graph as well as the linear trendline proved that relationship indicating that my data was accurate and of high quality. Both trials also produced very similar results indicating that my data was relatively accurate. I thought my data was fairly precise as well. For example, I calculated the percent difference of current and voltage between trials 1 and 2 using 1 battery. The percent difference between the voltages of trials 1 and 2 was roughly 1.2%, but the percent difference between the current of trials 1 and 2 was 0% indicating that my data had high precision and internally consistent. There could have been several sources of error. For example, switching between the voltmeter settings and the ammeter settings was very difficult. We could have used the wrong settings for the experiment or possibly not set up the voltmeter or ammeter incorrectly. If you do not set these up correctly, this could potentially greatly affect the results of the experiment. I had a hard time properly adding the batteries to the circuit. If you did not add them correctly to the circuit, it would have affected that data as well. It was extremely important to remember that the voltmeter had to be connected in parallel to the circuit having its own loop from the loop containing the resistor and the battery. The ammeter on the other hard, was integrated within the circuit. If you did not connect things properly, it would have produced inaccurate results. Analysis Questions Response: Answer the following analysis questions: 1. How would you expect your results to change if the resistor in your circuit had a larger resistance value? Be specific. Resistance hinders the flow of charge within a system. It can be explained as the amount of voltage needed to increase the current by 1 A. Through this lesson, we learned that if a circuit had a large resistance value, then a big increase in voltage would cause only a small increase in current. This makes sense, because based on Ohm’s law, we know that voltage and resistance are inversely proportional. Since these two values are inversely proportional, it would expect a high resistance value to decrease the current values or only increase the current values by small increments compared to smaller resistance values. Since resistance prevents the flow of charge; therefore, a higher resistance value will cause a decrease of current in the data. The slope of the voltage vs. current graph is the resistance. If you had a larger resistance value as well, the slope of the graph would be much steeper compared to a graph with a smaller resistance value. 2. What effect would using a 12V car battery have on the operation of your circuit? (Do not try this.) What would happen to the current? What would happen to the resistance? Be specific and include appropriate calculations to support your answers. Based on Ohm’s law, we can see the voltage and current are directly proportional. Ohm’s law has an equation of V= IR where V is voltage, I is current, and R is resistance. Based on the equation we can see that I is directly proportional to V

but inversely proportional to R. If you increase the voltage to 12V then the current will also increase significantly. Voltage causes an electrical field which allows for the flow of charge, increasing current. If there is an increase in current due to the increase in voltage, there will be a decrease in resistance since charge flows more freely. In this case though, if the voltage is too high for the circuit to handle, the circuit would get destroyed and blow out completely. Different circuits can hold different amounts of voltage. When the circuit draws too much power from the battery, it causes the circuit to overload and blow out. References: All About Circuits. (2018). Ohm’s Law - How Voltage, Current, and Resistance Relate | Ohm’s Law | Electronics Textbook. All about Circuits. https://www.allaboutcircuits.com/textbook/direct-current/chpt-2/voltage-current- resistance-relate/ Ohm’s Law: Resistance and Simple Circuits - College Physics - OpenStax. (2012). Openstax.org. https://openstax.org/books/college-physics/pages/20-2-ohms-law- resistance-and-simple-circuits