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University of Colorado, Denver *

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2341

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Electrical Engineering

Date

Feb 20, 2024

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Lab Notebook: <Lightbulb II > P a g e 1 | 7 Name P uurich Yip Station # 1 Lab Group Members Ivan Fatima Jane Instructions: Please increase space as necessary. Make sure your notebook is legible, clear, and well organized. Objective The objective of this lab is to find a better understanding of the data we found last week. We found from our data last week, there are 2 parts to our data. One part looks exponential, the other part looks linear. We will analyze that in this lab. Method The methods for this lab include taking our data from last week’s lab and analyzing the data using semi-logs and log-log plots. Using these plots will help us determine trends for non-linear data, which our graph from last week was non-linear.

Lab Notebook: <Lightbulb II > P a g e 2 | 7 With these methods, we used the laws of semi-log and log-log plots to determine which equation to use based on our linearized data.

Lab Notebook: <Lightbulb II > P a g e 3 | 7 Data This is our data from last week ’ s lab, and we decided that our cutoff boundary would be at 0.29 amps. This was decided because it is the point in which the data splits and stops following the exponential trend, and instead starts to follow a linear trend. This is the plot, cutting off at 0.29. this part of the graph is non-linear, and we can see that this data follows an exponential relationship. 0 1 2 3 4 5 6 7 8 9 0 0.1 0.2 0.3 0.4 0.5 0.6 Voltage Current (A) Voltage vs Current 0 0.5 1 1.5 2 2.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 V vs A

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Lab Notebook: <Lightbulb II > P a g e 4 | 7 y = 15.37x - 3.833 -5 -4 -3 -2 -1 0 1 0 0.05 0.1 0.15 0.2 0.25 0.3 ln V A ln(V) vs A 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 -5 -4 -3 -2 -1 0 V ln A V vs ln(A) -5 -4 -3 -2 -1 0 1 -5 -4 -3 -2 -1 0 ln V ln A ln(V) vs ln(A)

Lab Notebook: <Lightbulb II > P a g e 5 | 7 Plot / Data Analysis Within these log-log and semi-log plots, the plot of V vs ln(A) is very clearly non-linear. The log- log plot looks like it could potentially be linear, but towards the end of the plot, it looks like it starts to move exponentially. The closest one to being perfectly linear is the plot of ln(V) vs A. It is still not perfectly linear, because it is stemmed from an exponential or a power graph. The semi-log plots are used to better and more easily analyze the data. The R^2 squared value does help in determining the “ better ” fit in the plots closest to being fully linear. Changing the boundary point would help, if you chose the wrong one from the beginning. The original graph should have a clear split in the points, and the boundary should be right between the exponential part of the graph and the linear part. We chose the ln(V) vs A graph, it looked the most linear, and the R^2 value is the closest to 1.00, telling us that it is the most linear. o What happens to the resistance of the lightbulb as current increases? The resistance has a direct relationship to current, because as temperature increases in the lightbulb, the movement of electrons increases, resulting in an increase in both. o As current flows through the resistor, the temperature generally increases. What does this suggest about the relationship between resistance and temperature? More current leads to an increase in resistance, so the relationship between resistance and temperature is a direct one, as one increases, so does the other. o What does your model equation suggest about the resistance at very cold temperatures (e.g. zero Kelvin)? This model equation suggests that in cold temperatures, it would result in very low resistance, following the direct relationship. o Do you feel comfortable using your model to predict a value at zero Kelvin?

Lab Notebook: <Lightbulb II > P a g e 6 | 7 I would not feel comfortable using my model to predict the value at zero Kelvin. Because we took our measurements at room temperature, we can base a general trend at zero kelvin, but I would not be able to place a comfortable value at that low of a temperature.

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Lab Notebook: <Lightbulb II > P a g e 7 | 7 Conclusion This lab was conducted to better understand the non-linear relationship between voltage and current. We used semi-log and log-log plots to linearize our data. Linearizing this data helped us analyze our data more easily, based on the quadratic plot we found from our data last week. This linearized data helped us understand the relationship between voltage and current, which in turn helps us understand the relationships those have with temperature as well as resistance.