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In this laboratory report, we conducted two experiments to investigate the relationship between the resistance of a wire and its length as well as its cross-sectional area. The first experiment focused on altering the wire's length while keeping the area constant, while the second experiment involved changing the wire's diameter while maintaining a constant length. We employed both direct and indirect methods to measure resistance, utilizing equipment such as a multimeter, ammeter, and voltmeter. Our predictions were based on the principles of metallic bonding and Ohm's law.
The objective of this experiment is to explore how changes in wire length and cross-sectional area affect its electrical resistance. Resistance, measured in ohms (Ω), is a fundamental property of materials that impacts the flow of electric current through a wire. It is governed by Ohm's law, which states that voltage (V) is directly proportional to current (I) and inversely proportional to resistance (R):
V = IR
Or
R = V/I
To measure resistance, we used an ammeter, which is connected in series with the wire, and a voltmeter, which is connected in parallel.
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The direct method involved altering the wire's length, while the indirect method focused on changing its diameter.
The specific aims of our experiments were as follows:
We made predictions based on our understanding of metallic bonding and the behavior of electrons within the wire.
Our experiments involved the following variables:
We controlled various factors to ensure the reliability of our results, including equipment consistency, voltage, the number of cells, wire thickness, room temperature, the time elapsed before readings, and zero errors.
Throughout the experiments, we prioritized safety precautions, including avoiding exposed conductors, refraining from working with electricity with wet hands, and handling potentially hot conductors with care.
Before conducting the main experiments, we performed a trial investigation to validate our predictions and ensure the experimental setup was functional.
For the first experiment, we followed these steps:
We employed a multimeter to measure resistance in this direct method.
For the second experiment, we followed these steps:
Our aim was to determine if resistance is inversely proportional to the area of the wire cross-section.
To further analyze our data, we used the formula for resistivity (ρ), a material property, defined as:
R = ρL/A
Where:
We aimed to calculate the resistivity of the nichrome wire and compare it to published resistivity values (e.g., 1.01 x 10-6 ohm meter).
1. Set up the apparatus as illustrated in Figure 1.
2. Begin with a 5cm length of the nichrome wire, ensuring that the wire's cross-sectional area remains constant throughout the experiment.
3. Measure and record the resistance using a multimeter. Repeat this process for wire lengths of 15cm, 25cm, 35cm, 45cm, and 55cm.
4. Conduct three trials for each wire length to obtain accurate and consistent results.
5. Calculate the average resistance for each wire length.
6. Plot a graph of resistance (Ω) against wire length (cm).
7. Account for any zero error in measurements.
1. Set up the apparatus as shown in Figure 2.
2. Begin with a wire diameter of 0.027 cm and a constant wire length of 20cm.
3. Measure and record both voltage (V) and current (I) for this diameter using an ammeter and voltmeter. Calculate resistance (R = V/I).
4. Repeat the measurements for wire diameters of 0.031 cm, 0.037 cm, 0.045 cm, and 0.055 cm.
5. Perform three trials for each wire diameter to ensure accuracy and consistency.
6. Calculate the average resistance for each diameter.
7. Create a table of results, including resistance and 1/area values.
8. Plot a graph of average resistance (Ω) against average 1/area (1/cm-1).
| Length of Wire (cm) | Resistance 1 (ohms) | Resistance 2 (ohms) | Resistance 3 (ohms) | Average Resistance (ohms) |
|---|---|---|---|---|
| 5.0 cm | 0.7 | 0.7 | 0.7 | 0.7 |
| 15.0 cm | 1.7 | 1.6 | 1.6 | 1.6 |
| 25.0 cm | 2.7 | 2.7 | 2.7 | 2.7 |
| 35.0 cm | 3.8 | 3.6 | 3.6 | 3.7 |
| 45.0 cm | 4.6 | 4.6 | 4.6 | 4.6 |
| 55.0 cm | 5.7 | 5.7 | 5.6 | 5.7 |
| Diameter (cm) | Area (cm2) | 1/Area (1/cm-1) | Resistance (ohms) |
|---|---|---|---|
| 0.027 | 0.000573 | 1747 | 4.3 |
| 0.031 | 0.000756 | 1325 | 3.0 |
| 0.037 | 0.00108 | 930 | 1.9 |
| 0.045 | 0.00159 | 629 | 1.5 |
| 0.055 | 0.00238 | 421 | 1 |
From Graph One, it is evident that as the wire length increases, the resistance also increases. This observation supports our prediction that increasing the length of the wire leads to an increase in resistance. The relationship between length and resistance is directly proportional, as demonstrated by the following example:
If the wire length is 5.0 cm, the resistance is 0.7 ohms.
If the wire length is doubled to 10.0 cm, the resistance also doubles to 1.4 ohms.
Thus, we can conclude that length is proportional to resistance.
From Graph Three, it is clear that as the area increases, the resistance decreases. However, this relationship is not linear; the graph shows a curved trend. To make it proportional, we plotted resistance against the inverse of the area (1/area), resulting in a straight-line graph.
This linear relationship between resistance and 1/area confirms our prediction that resistance is inversely proportional to the cross-sectional area of the wire. As the area of the wire increases, the resistance decreases proportionally.
Our experiments generally proceeded smoothly, and the results aligned with our predictions. However, some considerations should be noted:
1. Outlier Result: We encountered an outlier result in the experiment involving the shortest wire length (5.0 cm). This discrepancy may have been due to higher current resulting in increased wire temperature, leading to greater atomic vibration and resistance. In future experiments, we will avoid measuring at such a short length and keep the voltage low to minimize heating effects.
2. Repeatability: To enhance the reliability of our results, we conducted three repetitions for each data point. This approach helped identify and address anomalies and improved the accuracy of our average values.
3. Resistivity: We aimed to calculate the resistivity of the nichrome wire and compare it to published values. While most of our data aligned well with theoretical expectations, further refinements in the experimental setup and data analysis could provide more accurate resistivity values.
Our experiments successfully demonstrated the relationship between the electrical resistance of a nichrome wire and both its length and cross-sectional area. In Experiment One, we confirmed that resistance is directly proportional to wire length, as predicted. In Experiment Two, we observed that resistance is inversely proportional to the wire's cross-sectional area, supporting our hypothesis. These findings align with the principles of metallic bonding and Ohm's law.
By gaining a better understanding of how wire length and diameter affect resistance, we can make informed decisions in various electrical applications, such as designing circuits and selecting appropriate wire sizes.
Testing Wire Resistance with Varied Lengths: Experiment Report. (2020, Jun 02). Retrieved from https://studymoose.com/document/outline-plan-new
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