Lab Report: Analysis of a Lightbulb as a Resistor

Abstract

In this lab report, we aimed to analyze whether a lightbulb behaves as an ohmic resistor. An ohmic resistor is a material that limits the flow of electrical charge in a circuit. We explored the relationship between voltage and current to determine if the lightbulb exhibited consistent resistance. The experiments involved measuring voltage and current at various points within a range of +6.0V to -6.0V in 1V increments. We plotted voltage against current and calculated the slopes for three different ranges of data points.

Our results showed that the lightbulb did not act as a constant resistor, but its resistance varied with voltage and temperature. We discuss the implications of these findings in the context of ohmic and non-ohmic behavior.

Introduction

The primary objective of this lab was to investigate whether a lightbulb could be considered an ohmic resistor. Ohmic resistors are materials that exhibit a consistent resistance () and follow Ohm's Law, which states that voltage () is equal to current () multiplied by resistance ().

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This relationship can be expressed as I = V/R. When plotted on a graph with voltage on the x-axis and current on the y-axis, ohmic resistors result in a linear relationship with a trend line equation of y = mx + b. The slope () of this trend line is equal to 1/Resistance. Linear regression analysis can be used to determine the goodness of fit of the trend line, represented by the R squared () value. In the case of ohmic resistors, the resistance remains constant, resulting in a consistent slope for the entire dataset.

Materials and Methods

Materials:

• Lightbulb
• Voltage source
• Ammeter
• Voltmeter

Procedure

1. We set up a circuit with a lightbulb, voltage source, ammeter, and voltmeter.
2. We measured the current and voltage across the lightbulb at twelve different data points, ranging from +6.0V to -6.0V in 1V increments.
3. We plotted the voltage (x-axis) against the current (y-axis) to visualize the relationship between the two variables.
4. We divided the data into three ranges: slope1 (+6.0V, +5.0V, and +4.0V), slope2 (+1V, 0V, and -1V), and slope3 (-6.0V, -5.0V, and -4.0V).
5. We calculated the slopes () of the trend lines for each range using linear regression analysis.
6. We determined the R squared () values for each range to assess how well the trend lines represented the data.

Results

The experiment aimed to determine whether a lightbulb could be considered an ohmic resistor. The analysis involved calculating the resistance () based on the slopes of three separate data ranges and assessing the goodness of fit using R squared () values.

Analysis of Slopes and Resistance

Three different data ranges were selected for analysis:

The analysis revealed significant variations in the slopes () and, consequently, the calculated resistances ().

Assessment of Linearity

To assess the linearity of the data within each range, we calculated the R squared () values:

The high R squared () values indicate a strong linear relationship within each data range.

Discussion

The results of this experiment suggest that a lightbulb does not behave as a constant ohmic resistor. Ohmic resistors maintain a consistent resistance () across a range of voltages, resulting in a uniform slope () when voltage is plotted against current. However, our analysis revealed varying slopes and resistances for different data ranges, indicating that the lightbulb's resistance changes with voltage and temperature.

The three analyzed data ranges (slope1, slope2, and slope3) exhibited significantly different slopes (), corresponding to different resistances (). For example, slope2 had a slope of 0.7241 A/V, resulting in a resistance of 1.38Ω, while slope3 had a slope of 0.1965 A/V, leading to a resistance of 5.09Ω. These variations demonstrate that the lightbulb's resistance is not constant and may depend on external factors.

Despite the variations in resistance, all three data ranges displayed high R squared () values close to 1, indicating strong linearity between voltage and current within each range. This suggests that the lightbulb exhibits linear behavior under specific conditions, particularly at higher voltages or temperatures.

The observed relationship between resistance and voltage/temperature resembles exponential growth, where the resistance initially increases rapidly and then levels out. This behavior suggests that the lightbulb may begin to behave more like a resistor at high voltages or temperatures, as indicated by the change in slope from 0.7241 A/V to 0.1965 A/V.

It's important to note that some groups attempted to use a single trend line to assess linearity. However, given the close-to-linear nature of the data, this approach may not provide accurate R squared () values and standard errors, making it less suitable for drawing conclusions.

Conclusion

In conclusion, the experiment revealed that a lightbulb does not act as a constant ohmic resistor. The analysis of different data ranges showed variations in resistance and slope, indicating that the lightbulb's resistance is not consistent across different voltage and temperature conditions. However, the strong linearity observed in the data suggests that the lightbulb exhibits linear behavior under specific circumstances, such as at higher voltages or temperatures.

Recommendations

For future experiments and investigations, it is advisable to explore the factors that influence the lightbulb's resistance under different conditions. This may involve varying voltage, temperature, or other external factors to better understand the non-ohmic behavior observed. Additionally, using more advanced equipment and techniques for resistance measurement may yield more precise results.

Overall, further research in this area can provide valuable insights into the behavior of electrical components and their resistance characteristics.

Peer Review Statement

The peer reviews provided valuable feedback for improving this lab report. While the initial reviews praised the report, some wording and details were refined to enhance clarity and flow. The collaborative peer review process contributed to the overall quality of the report.