Wire resistance vs. Wire lenght of Nichrome 2.5 2.0 LINEAR 1.5 X-range: 1.35 - 7.70 y = mx + b m: 0.3494 b: -0.03121 1.0 r:0.9944 RMSE: 0.09889 0. 2.0 3.0 4.0 5.0 6.0 7.0 Wire Length L (m) 9. Then use the formula for percent error to find out how close your calculated resistivity values are to the accepted values given below. Please include all your calculation work and solutions in your lab submission, with correct units and appropriate significant figures. Metal Resistivity (Q- m) Nichrome 105 x 10-8 Wire Resistance R fohm
Wire resistance vs. Wire lenght of Nichrome 2.5 2.0 LINEAR 1.5 X-range: 1.35 - 7.70 y = mx + b m: 0.3494 b: -0.03121 1.0 r:0.9944 RMSE: 0.09889 0. 2.0 3.0 4.0 5.0 6.0 7.0 Wire Length L (m) 9. Then use the formula for percent error to find out how close your calculated resistivity values are to the accepted values given below. Please include all your calculation work and solutions in your lab submission, with correct units and appropriate significant figures. Metal Resistivity (Q- m) Nichrome 105 x 10-8 Wire Resistance R fohm
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Question
having a hard time with the percent error
![### Analysis of Wire Resistance vs. Wire Length of Nichrome
#### Graph Overview
The provided graph illustrates the relationship between wire resistance (R) and wire length (L) for Nichrome wire. The title of the graph is "Wire resistance vs. Wire length of Nichrome," suggesting that the purpose of this graph is to analyze how resistance changes with alterations in wire length.
1. **Axes**:
- The **x-axis** represents the **Wire Length (L) in meters (m)**.
- The **y-axis** represents the **Wire Resistance (R) in ohms (Ω)**.
2. **Data Representation**:
- Data points are plotted at several lengths ranging from about 1.35 meters to 7.70 meters.
- A linear fit line, described by the equation \(y = mx + b\), is fitted to these points, suggesting a direct relationship between wire length and resistance.
3. **Linear Fit Parameters**:
- **Slope (m)**: 0.3494, which indicates the rate at which resistance increases with wire length.
- **Y-intercept (b)**: -0.03121, representing the resistance when the wire length approaches zero.
- **Correlation Coefficient (r)**: 0.9944, indicating a very strong positive linear relationship between the variables.
- **Root Mean Square Error (RMSE)**: 0.09889, quantifying the standard deviation of the residuals or prediction errors.
#### Instructions for Analysis
1. **Using Formula for Percent Error**:
To assess the accuracy of your calculated resistivity values, you will need to compare them to the accepted values provided in the table below. The formula for percent error is:
\[
\text{Percent Error} = \left(\frac{\left| \text{Experimental Value} - \text{Accepted Value} \right|}{\text{Accepted Value}}\right) \times 100\%
\]
This will help ascertain how close your experimental results are to the accepted resistivity values.
2. **Lab Submission Requirements**:
- Include all calculations and solutions, showing each step clearly.
- Ensure that all values are presented with correct units and significant figures.
#### Accepted Resistivity Values
| **Metal** | **Resistivity (Ω·m)** |
|------------|------------------------|
| Nichrome | \(105](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F23c38651-d5a3-4c38-ab9e-97c20b9d1405%2F87b4cb65-c049-487d-bab5-adfdec042e67%2Fxbkqb5e_processed.png&w=3840&q=75)
Transcribed Image Text:### Analysis of Wire Resistance vs. Wire Length of Nichrome
#### Graph Overview
The provided graph illustrates the relationship between wire resistance (R) and wire length (L) for Nichrome wire. The title of the graph is "Wire resistance vs. Wire length of Nichrome," suggesting that the purpose of this graph is to analyze how resistance changes with alterations in wire length.
1. **Axes**:
- The **x-axis** represents the **Wire Length (L) in meters (m)**.
- The **y-axis** represents the **Wire Resistance (R) in ohms (Ω)**.
2. **Data Representation**:
- Data points are plotted at several lengths ranging from about 1.35 meters to 7.70 meters.
- A linear fit line, described by the equation \(y = mx + b\), is fitted to these points, suggesting a direct relationship between wire length and resistance.
3. **Linear Fit Parameters**:
- **Slope (m)**: 0.3494, which indicates the rate at which resistance increases with wire length.
- **Y-intercept (b)**: -0.03121, representing the resistance when the wire length approaches zero.
- **Correlation Coefficient (r)**: 0.9944, indicating a very strong positive linear relationship between the variables.
- **Root Mean Square Error (RMSE)**: 0.09889, quantifying the standard deviation of the residuals or prediction errors.
#### Instructions for Analysis
1. **Using Formula for Percent Error**:
To assess the accuracy of your calculated resistivity values, you will need to compare them to the accepted values provided in the table below. The formula for percent error is:
\[
\text{Percent Error} = \left(\frac{\left| \text{Experimental Value} - \text{Accepted Value} \right|}{\text{Accepted Value}}\right) \times 100\%
\]
This will help ascertain how close your experimental results are to the accepted resistivity values.
2. **Lab Submission Requirements**:
- Include all calculations and solutions, showing each step clearly.
- Ensure that all values are presented with correct units and significant figures.
#### Accepted Resistivity Values
| **Metal** | **Resistivity (Ω·m)** |
|------------|------------------------|
| Nichrome | \(105
![### Example Data Table
**Wire Type:** Nichrome
**Wire Radius, r:** 0.10 mm = 0.0001 m = 0.1 * 10^-3 m
**Cross-sectional Area, A:**
\[ A = (\pi)(0.1 * 10^{-3})^2 = 3.14 * 10^{-8} \text{ m}^2 \]
#### Table
| **Run** | **Wire Length, L (m)** | **Wire Resistance, R (Ω)** |
|---------|------------------------|-----------------------------|
| 1 | 2.9 | 1.02 |
| 2 | 1.35 | 0.46 |
| 3 | 5.78 | 1.87 |
| 4 | 7.7 | 2.75 |
| 5 | 6.3 | 2.24 |
| 6 | 5.93 | 1.94 |
In this table, various lengths of Nichrome wire are compared with their corresponding resistances. The relationship between the wire length (in meters) and the resistance (in ohms) is shown for six separate runs. Special attention should be given to the calculated cross-sectional area, which is a crucial factor in determining the wire’s resistance. The area is derived using the formula:
\[ A = (\pi r^2) \]
where \( r \) is the radius of the wire. This example illustrates how a consistent wire type and diameter can help understand how resistance scales with length.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F23c38651-d5a3-4c38-ab9e-97c20b9d1405%2F87b4cb65-c049-487d-bab5-adfdec042e67%2Fplxp5nl_processed.png&w=3840&q=75)
Transcribed Image Text:### Example Data Table
**Wire Type:** Nichrome
**Wire Radius, r:** 0.10 mm = 0.0001 m = 0.1 * 10^-3 m
**Cross-sectional Area, A:**
\[ A = (\pi)(0.1 * 10^{-3})^2 = 3.14 * 10^{-8} \text{ m}^2 \]
#### Table
| **Run** | **Wire Length, L (m)** | **Wire Resistance, R (Ω)** |
|---------|------------------------|-----------------------------|
| 1 | 2.9 | 1.02 |
| 2 | 1.35 | 0.46 |
| 3 | 5.78 | 1.87 |
| 4 | 7.7 | 2.75 |
| 5 | 6.3 | 2.24 |
| 6 | 5.93 | 1.94 |
In this table, various lengths of Nichrome wire are compared with their corresponding resistances. The relationship between the wire length (in meters) and the resistance (in ohms) is shown for six separate runs. Special attention should be given to the calculated cross-sectional area, which is a crucial factor in determining the wire’s resistance. The area is derived using the formula:
\[ A = (\pi r^2) \]
where \( r \) is the radius of the wire. This example illustrates how a consistent wire type and diameter can help understand how resistance scales with length.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON