Lab 3 - Resistor Circuits

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City College of San Francisco *

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Electrical Engineering

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Dec 6, 2023

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Lab #3: Resistor Circuits Willem Botha Deborah Harris 09/7/2023 Abstract: In this lab we used the power supply, a multimeter and resistor board. We were introduced to new lab equipment called an ammeter and software called Logger Pro that measures our current. The purpose of this experiment was to measure the electric current and voltage of the simple resistor circuits using the mentioned equipment in order to find their relationship. Experimental Setup and Measurements: The first thing we did in this experiment was choose our measurement on our multimeter by selecting the "Ω” button in order to measure resistance. Connecting two banana plug wires to the multimeter and the other ends of the wires to themselves and selecting “NULL” we zeroed out the machine. After ensuring our power supply was turned off and choosing which resistor we wanted to measure, we set up our wires by following the diagram given to us on the first page of the lab manual. Connecting one banana plug wires to the - slot on the DC side of the power supply and connecting the other end to the resistor board. Then connecting another banana plug to the + on the power supply and connecting the other end to + side of the ammeter. We connected a separate plug to the - end of the ammeter and the other end to the resistor board ensuring the current will flow through both. From there we connected two more banana plugs connecting the resistor board to the multimeter, to measure the voltage difference. Before we gathered our data we made sure that the Logger Pro software was set to zero. Starting our experiment, we set our power supply to 10 V and read/recorded the measurement from the multimeter and the Logger pro software. After logging our results we repeated this step, increasing the voltage on the power supply by increments of 2 V until we reached 20 V. After gathering our data we implemented the Python data analysis system, using our data from the tables labeled Top Resistor ( Figure 1 ) and Bottom Resistor ( Figure 2 ) and performing a linear curve fit. We then found our slope and the error of the linear fit. Lastly, we examined how our measured resistor data related to the electric current and voltage, listing any possible sources of error in our experiment. We found that the relationship between the current and voltage is that once we increase the voltage the current also increases but as we increase the resistance the current decreases. We found that ultimately the higher the resistance the lower the slope. Experimental Data Expected Value of Resistors: Top resistor = 3.256 ± 0.001 Kohm Bottom Resistor = 4.714 ± 0.001 Kohm
Top Resistor Voltage (V) ± 0.001Amp Current (Amp) ± 0.0001Amp 9.923 0.0033 11.980 0.0039 13.909 0.0045 15.923 0.0052 17.968 0.0057 19.856 0.0063 Figure 1 Bottom Resistor Voltage (V)± 0.001Amp Current (Amphs) ± 0.0001Amp 9.938 0.0023 11.919 0.0027 13.903 0.0032 16.024 0.0037 17.933 0.0041 19.65 0.0045 Figure 2 Data Analysis: Plotting the measured current and the voltage over a graph gives us the graphs shown below. By analyzing the graphs we were able to determine the relationship between current, voltage, and resistance. We found that the current and the voltage have a direct relationship, meaning as one increases or decreases the other does the same. We also found that resistance has an inverse relationship to both current and voltage, since as we increased the resistance the current and voltage decreased. These relationships can be represented through the following equations where I = Current, V = Voltage, and R = Resistance: I = V, I = 1/R, I = (1/R)V. The last equation can be related to y = mx, where m is equal to the resistance of the resistor. This means that the slopes of our graphs are equal to the resistance of the resistors. To find the error of the resistance, we used the error propagation equation of δm = |n|*|m|*δp/|p| where m = resistance, δm = error of resistance, n = power relationship between resistance and slope, p = slope, and δp = error of slope. We then determined if the difference between our expected and measured values was significant, and because their error bars did not meet, there was
a significant difference between the expected and measured values. We calculated this difference through the equation (|Measured - Expected| / Expected) x 100%. Slope: 0.0003029407857123061 Amp/V Standard Error of the Slope: 5.64532099451537e-06 Amp/V (0.000006) Slope with Correct Sig Figs: (3. 03 𝑥 10 −4 )±(6 𝑥 10 −6 ) 𝐴𝑚?/𝑉 Resistance: 1/ = 3.30 Kohm (3. 03 𝑥 10 −4 )𝐴𝑚?/𝑉 Resistance Error: = 65.35 Ohm | 1| 𝑥 |3300 𝑂ℎ𝑚| 𝑥 ([6 𝑥 10 −6 ] / [3. 03 𝑥 10 −4 ]) Resistance with Correct Sig Figs: 3.30 0.07 Kohm ± Percent error: = 1.35% (|3. 30 𝐾?ℎ𝑚 − 3. 256 𝐾?ℎ𝑚 | / 3. 256 𝐾?ℎ𝑚) 𝑥 100% Slope: 0.00022850477547013974 Amp/V Standard Error of the Slope: 3.024222629262544e-06 Amp/V
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Slope with Correct Sig Figs: (2. 29 𝑥 10 −4 ) ± (3 𝑥 10 −6 ) 𝐴𝑚?/𝑉 Resistance: 1/ = 4.37 Kohm (2. 29 𝑥 10 −4 )𝐴𝑚?/𝑉 Resistance Error: = 57.25 Ohm | 1| 𝑥 |4370 𝑂ℎ𝑚| 𝑥 ([3 𝑥 10 −6 ] / [2. 29 𝑥 10 −4 ]) Resistance with Correct Sig Figs: 4.37 0.06 Kohm ± Percent error: = 7.30% (|4. 37 𝐾?ℎ𝑚 − 4. 714 𝐾?ℎ𝑚 | / 4. 714 𝐾?ℎ𝑚) 𝑥 100% Conclusion: By measuring the current over the voltage and then comparing them with the resistances, we were able to find the relationship between all three variables. This relationship came out to be I = (1/R)V, and using this relationship we were able to calculate the resistances of each resistor used. The top resistor had a measured resistance of 3.30 Kohm and the bottom had a resistance of 4.37 Kohm. Our errors between the measured and expected values were very small, both being under 8%. This small amount of error could have been a result of the machinery not giving completely accurate measurements. Apparatuses like the multimeter or the ammeter do not stay on one number for long, and often jump between different readings that vary slightly.