ConceptThe main concept in this lab report was to analyze whether or not a lightbulb acted as a resistor. A resistor is any material that reduces or limits the amount of electrical charge that flows past a certain part of the circuit. How well a substance limits this flow is the object’s resistance (). Resistors follow Ohm’s LawV=IR where voltage is equal to current (A) multiplied by resistance (). This formula can be rewritten as I=V/R. When the voltage (x axis) and current (y axis) are plotted on a graph, it results in a linear relationship.
The linear relationship can be represented by a trend line with the equation y=mx+b. The slope of this trend line is equal to 1/Resistance. Linear regression can then be used to find an R squared value to show how close the data points are to the trend line. The resistance never changes with ohmic resistors just like the slope never changes in a straight line.
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With materials that are non-ohmic, the resistance often is not constant so the R squared value is not as accurate. ProcedureTo determine if a lightbulb is an ohmic resistor we decided to measure the current and voltage at twelve different data points. These data points ranged from +6.0V to -6.0V with 1V increments. The data was then plotted on a scatter plot as voltage vs current to determine if there was a linear trend. If the lightbulb was a resistor, the slope of the data should have been the same (or similar) throughout the entire graph. Three points were chosen from three separate ranges of the data. The slopes of these three ranges were calculated using linear regression then compared to each other to see if the slope was constant throughout the graph. The first three points were +6.0V, +5.0V, and +4.0V and was labelled slope1. The next range was +1V, 0V, -1V labelled slope2. The third range was -6.0V, -5.0V, and -4.0V and labelled slope3. The R squared values of these regression lines were then found to see how accurate the regression line portrayed the data. It was important to measure both positive and negative voltages to see if the lightbulb behaved differently with a different flow of electrons. The R squared value for these slopes were also found to show that the trend lines linearly fit the data ranges. To reduce error, the increments in which the voltage was changed was standardized to 1V. Argument and DataOur argument for this experiment is that a filament lightbulb did not act as a resistor. This was shown by the resistance data and by calculating the slopes of the three trend lines for three separate data ranges. The equation R=1/m was used to find resistance and SE/m2was used to find the uncertainty in the slope. The group slope1 had a slope of 0.1941 A/V with an R squared value of 0.99930.007. This translates to a resistance of 5.150.14 ohms and the R squared value tells us that the trend line almost perfectly fits the data points. The second group (slope2) had a drastically different slope of 0.7241 A/V but with a similarly perfect R squared value of 0.99990.007. The resistance for slope2 was found to be 1.40.01ohms. The group slope3 had a negative slope of 0.1965 A/V with an R squared value of 0.99920.008. This translates to a resistance of 5.10.14 ohms. The slopes calculated across the three data ranges were different. This means that the resistance of the lightbulb was not constant. To show how close the data points are to the trend lines the R squared values were found. All three R squared values were extremely close to 1. This tells us that the regression line of each groups fits the data well. High R squared values combined with differing slopes shows that the slope for the whole data set is not constant. While the lightbulb is not a resistor, there are certain circumstances that the bulb begins to behave like a resistor. As the bulb heats up with more voltage and current, the resistance seems to not only increase, but also become more linear when compared to data points between 0V and +3V. This is shown by the change in slope from 0.7241 A/V to 0.1965 A/V. This suggests that the lightbulb acts more like a resistor at high voltages/ temperatures. This relationship is similar to exponential growth as the slope starts large and levels out. Other groups decided to use a singular trend line to tell if the data was linear. This seemed slightly inaccurate as the data was close to being linear already. The R squared value and standard error for that value would not be accurate enough to draw a reasonable conclusion. Peer Review Statement The peer reviews were very helpful when finishing up my lab report. This was my first ECU physics lab report so I was not sure how to go about it. Both reviews said that the report was excellent and that nothing needed to be changed. Even though no negative comments were made on the lab report, I did edit it a bit. I changed some wording so the paper flowed better as well as added a few more details in the argument section.