Testing Wire Resistance with Varied Lengths: Experiment Report

Categories: Physics

Abstract

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.

Introduction

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.

Aim

The specific aims of our experiments were as follows:

  1. Experiment One: To investigate the relationship between the length of a nichrome wire (measured in SWG/mm) and its resistance while keeping the wire's cross-sectional area constant.
  2. Experiment Two: To examine how changes in the cross-sectional area (diameter) of a nichrome wire affect its resistance while maintaining a constant wire length.

We made predictions based on our understanding of metallic bonding and the behavior of electrons within the wire.

Variables

Our experiments involved the following variables:

  • Independent Variables: The length and diameter of the wire.
  • Dependent Variable: Resistance (R).

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.

Safety

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.

Trial Investigation

Before conducting the main experiments, we performed a trial investigation to validate our predictions and ensure the experimental setup was functional.

Materials and Methods

Experiment One

For the first experiment, we followed these steps:

  1. Set up the apparatus as shown in the diagram.
  2. Vary the lengths of the nichrome wire from 5cm to 55cm in 10cm increments while keeping the wire's cross-sectional area constant.
  3. Repeat the experiment three times to ensure accuracy and consistency of results.
  4. Record the resistance values for each length and calculate the average resistance.
  5. Plot a graph of resistance against wire length.
  6. Account for any zero error in measurements.

We employed a multimeter to measure resistance in this direct method.

Experiment Two

For the second experiment, we followed these steps:

  1. Set up the apparatus as shown.
  2. Vary the diameter of five wires while keeping the length constant at 20cm.
  3. Use an ammeter and voltmeter to measure current (I) and voltage (V) according to Ohm's Law (R = V/I).
  4. Repeat the experiment three times for each wire diameter to ensure accuracy.
  5. Record the voltage and current values for each diameter and calculate the resistance using Ohm's Law.
  6. Calculate the average resistance for each diameter.
  7. Create a table of results and plot a graph of average resistance versus average area.

Our aim was to determine if resistance is inversely proportional to the area of the wire cross-section.

Resistivity

To further analyze our data, we used the formula for resistivity (ρ), a material property, defined as:

R = ρL/A

Where:

  • R: Resistance (Ω)
  • ρ: Resistivity (ohm meter)
  • L: Length of the wire (meters)
  • A: Cross-sectional area of the wire (meters squared)

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).

Experimental Procedure

Experiment One - Altering Wire Length

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.

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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.

Experiment Two - Altering Wire Diameter

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).

Results

Experiment One - Resistance vs. Wire Length

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

Experiment Two - Resistance vs. 1/Area

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

Analysis

Experiment One - Resistance vs. Wire Length (Graph One)

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.

Experiment Two - Resistance vs. 1/Area (Graph Three)

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.

Evaluation

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.

Conclusion

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.

Updated: Dec 29, 2023

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Testing Wire Resistance with Varied Lengths: Experiment Report. (2020, Jun 02). Retrieved from https://studymoose.com/document/outline-plan-new

Testing Wire Resistance with Varied Lengths: Experiment Report essay
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