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
![**Problem: Calculating Resistance of Aluminum Wire**
Find the resistance of a 78.0-meter length of No. 20 aluminum wire at a temperature of 20°C. The resistivity (\( \rho \)) of the wire is \( 2.83 \times 10^{-6} \, \Omega \cdot \text{cm} \), and the cross-sectional area (A) is \( 2.07 \times 10^{-2} \, \text{cm}^2 \).
**Solution Approach:**
To calculate the resistance (R) of the wire, use the formula:
\[ R = \frac{\rho \cdot L}{A} \]
where:
- \( R \) is the resistance in ohms (\( \Omega \)),
- \( \rho \) is the resistivity in ohm-centimeters (\( \Omega \cdot \text{cm} \)),
- \( L \) is the length of the wire in centimeters (cm),
- \( A \) is the cross-sectional area in square centimeters (\(\text{cm}^2\)).
**Calculate the Resistance:**
1. **Convert Length to Centimeters:**
\[ L = 78.0 \, \text{m} = 7800 \, \text{cm} \]
2. **Substitute the Known Values:**
\[ R = \frac{2.83 \times 10^{-6} \, \Omega \cdot \text{cm} \times 7800 \, \text{cm}}{2.07 \times 10^{-2} \, \text{cm}^2} \]
3. **Solve for R:**
Complete the multiplication and division to find the resistance.
This step-by-step approach will guide students in calculating the resistance of a wire, considering the material properties and dimensions provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc463f08e-ec7e-4810-a9a2-5563bca4d00b%2F9f485938-75e1-4a2f-9479-83bb4eb3364e%2F01o7nu6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem: Calculating Resistance of Aluminum Wire**
Find the resistance of a 78.0-meter length of No. 20 aluminum wire at a temperature of 20°C. The resistivity (\( \rho \)) of the wire is \( 2.83 \times 10^{-6} \, \Omega \cdot \text{cm} \), and the cross-sectional area (A) is \( 2.07 \times 10^{-2} \, \text{cm}^2 \).
**Solution Approach:**
To calculate the resistance (R) of the wire, use the formula:
\[ R = \frac{\rho \cdot L}{A} \]
where:
- \( R \) is the resistance in ohms (\( \Omega \)),
- \( \rho \) is the resistivity in ohm-centimeters (\( \Omega \cdot \text{cm} \)),
- \( L \) is the length of the wire in centimeters (cm),
- \( A \) is the cross-sectional area in square centimeters (\(\text{cm}^2\)).
**Calculate the Resistance:**
1. **Convert Length to Centimeters:**
\[ L = 78.0 \, \text{m} = 7800 \, \text{cm} \]
2. **Substitute the Known Values:**
\[ R = \frac{2.83 \times 10^{-6} \, \Omega \cdot \text{cm} \times 7800 \, \text{cm}}{2.07 \times 10^{-2} \, \text{cm}^2} \]
3. **Solve for R:**
Complete the multiplication and division to find the resistance.
This step-by-step approach will guide students in calculating the resistance of a wire, considering the material properties and dimensions provided.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
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