Voltage, Current, and Resistance II Lab Report

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Apr 3, 2024

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Anika Chugh (with Sofi Sintes) Section 12 Ajaykumaar Sivacoumare February 29, 2024 Voltage, Current, and Resistance II Lab Report Objective : As a continuation of the previous lab, the series of experiments in this lab allows the experimenters to observe how voltage and current are generated through the 850 interface and how they are related via Ohm’s law. Another component of Ohm’s law is resistance, which is also applied to the apparatus via a circuit board. As resistance is changed, the corresponding changes in the relationship between voltage and current based on Ohm’s law are also observed. Resistance is applied to the circuit both in series and in parallel, allowing the experimenter to observe the effects of how resistance is applied as well. Description/Procedure : The Capstone interface is the primary apparatus through which voltage and current are applied and observed — the interface is connected to the RLC circuit board via banana leads. Due to the unreliability of the analog ammeter, specifically when trying to observe Ohm’s law, the analog ammeter was only used to generate internal resistance in the last experiment. The voltage sensor was also used in the last experiment in order to be compared to the voltage displayed on the interface. Upon the recommendation of the instructor, section 6.1.1 was skipped. Theory : Once again, Ohm’s law is observed and analyzed in this experiment, which is outlined by the following equation,

Where V =voltage in V, I =current in A, and R =resistance in Ω. A voltmeter is typically connected to a resistor in parallel, while an ammeter is connected to a resistor in series — in this lab, the resistors themselves were placed in parallel and in series to each other and while. When in parallel, the total resistance can be defined as While the total resistance in series can be defined by Data/Calculations : Section 3 Section 6.1: In Series Voltage (V) Current (A) Calculated Resistance (Ω) Average Resistance (Ω) 1 0.007 142.9 137.6 2 0.014 142.9

3 0.022 136.4 4 0.029 137.9 5 0.037 135.1 6 0.045 133.3 7 0.052 134.6 Section 6.2: In Parallel Voltage (V) Current (A) Calculated Resistance (Ω) Average Resistance (Ω) 0.5 0.019 26.3 25.4 1 0.039 25.6 1.5 0.059 25.4 2 0.079 25.3 2.5 0.099 25.3 3 0.119 25.2 3.5 0.139 25.2 4 0.159 25.2 Section 7: Voltage Sensor and Analog Current Meter Analog Current Meter Sensitivity (mA) Interface Output Voltage (V) Interface Output Current (A) Voltage Sensor Voltage (V) Analog Current Meter (A) 30 0.999 0.024 0.821 0.024 100 0.999 0.027 0.930 0.027 300 0.999 0.028 0.967 0.030 Questions : 3: Count the peaks. Do the graphs match the applied frequency?

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The applied frequency is 0.2 Hz and the graph displays 2 peaks within 10 seconds, which amounts to 0.2 s -1 ; therefore, the graphs do match the applied frequency. 3: Is Ohm’s law being obeyed? How? Ohm’s law dictates that as voltage increases, current must increase accordingly. Considering both voltage and current increase and decrease at the same time and they have a perfectly directly proportional linear relationship, it can be concluded that Ohm’s law is being obeyed. 3: What are the values of the slope and intercept of the fitted line? What does it represent? Are they what you expect? The slope is 98.2 while the y-intercept is 0.0822, which means that when the current is 0 A, the voltage is 0.0822 V. This is unexpected — according to Ohm’s law, if the value for current is 0, the value for voltage must automatically be 0 as well since voltage is a product of current and resistance. However, some internal error could be contributing to the reading being slightly above 0 instead. 4: Polarity doesn’t matter. Why? Since the lightbulb essentially acts as a resistor, the positive and negative ends do not matter when connecting the leads, as long as the current can still run through. 4: Keep an eye on the bulb. Discuss your results. As the voltage approaches its highest magnitude (7V or -7V), the bulb is at its brightest. As the graph approaches the x-axis where the voltage is 0V, the bulb dims almost completely. 4: What would occur if the voltage were swept very quickly? If the voltage were swept very quickly, the bulb would dim and brighten much more quickly to keep in concert with the speed of the changes in voltage. 4: Is the graph of the filament an Ohmic function? Explain this result. The graph of the filament does not necessarily follow Ohm’s law — though there is surely a proportional relationship between voltage and current, where if one increases, the other does the

same, the graph depicted is a logarithmic function rather than a perfectly linear function as depicted prior. This is likely due to the fact that the current is not passing through a true resistor, but rather a lightbulb. Since resistance is not being kept constant, there is no reason for voltage and current to display an Ohmic function. 5: Which part of the curve was obtained by sweeping the voltage up and which part by sweeping the voltage down? A rough depiction of the graph is drawn above. The part of the curve outlined in black was obtained by decreasing the voltage, while the part of the curve in red was obtained by increasing the voltage. The bulb shone the brightest at the peaks (-7V and 7V) and dimmed/turned off as it approached 0V. 6.2: Compare the average resistance to the theoretical resistance of the resistors in parallel. When the resistors are in parallel, the average resistance obtained is 25.4 Ω. Based on the equation for calculating resistance in parallel, the theoretical resistance is 25.0 Ω, which is very close to the average resistance, allowing us to conclude that there must be little internal error within the interface.

7: Does the analog current meter affect the current in the circuit? What is the resistance of the analog current meter on the three different scales? Is there a drop in voltage due to the analog current meter? How does turning the sensitivity knob change the sensitivity of the current meter? The analog current meter generates some resistance in the circuit, causing the voltage detected by the voltage sensor to be lower than the reading from the interface, which occurs before the current reaches the analog current meter. The resistance on the 30 mA scale is 34.2 Ω, on the 100 mA scale it’s 34.4 Ω, and on the 300 mA scale it’s 32.2 Ω. There is no consistent drop in voltage due to the analog current meter; however, it is observed that as the sensitivity of the analog current meter increases, the difference in voltage between the interface reading and the voltage sensor reading decreases. Turning up the sensitivity of the analog current meter makes the meter more sensitive to the current passing through, so it creates less resistance. Error Analysis : Section 6.1 (In Series) Avg Resistance (Ω) Theoretical Resistance (Ω) Percent Difference 137.6 133 3.46% Section 6.2 (In Parallel) Avg Resistance (Ω) Theoretical Resistance (Ω) Percent Difference 25.4 25.0 1.60% There are very low percent difference values between the average and theoretical resistance in series and parallel — this can likely be attributed to the little internal error within the interface, which makes it ideal for such experiments since the interface voltmeter draws little current. A possible source of error could arise from internal errors within the circuit: when connecting the leads to the bulb, issues with the circuit itself prevented the lightbulb from turning on. Although we replaced the defective circuit board with a new one, there are possible flaws within the circuit from repeated use that could cause mistakes in readings but we, as the experimenters, have no

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standard to compare our values to, which makes it difficult to truly tell if the readings we obtained are accurate. Conclusion : Overall, the experiment was surely effective in depicting the relationship between voltage, current, and resistance, especially when displaying the linear Ohmic relationship between voltage and current. The experimentation with the non-Ohmic resistor in the form of the lightbulb allowed the experimenters to actually see the current pass through the circuit and view it while in function. Whether resistance is applied in series or in parallel, voltage and current still display a linear Ohmic relationship. The last part of the lab also allowed the experimenters to see exactly why analog meters are not always reliable — the fact that the analog voltage sensor reported lower voltages than the interface after passing through the analog current meter makes it clear that there must be some internal resistance within the apparatus that impedes the current.