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)...
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Question
![**Title: Understanding Resistance in Pencil Leads**
**Introduction:**
Pencil "lead" is actually made of carbon, a material known for its remarkable electrical properties. In this exercise, we will explore how to calculate the electrical resistance of a mechanical pencil lead.
**Problem Statement:**
**Part A:**
What is the resistance of a 0.660 mm-diameter, 5.10 cm-long lead from a mechanical pencil?
**Solution:**
To find the resistance, we need to use the formula for the resistance of a cylindrical conductor:
\[ R = \frac{\rho L}{A} \]
Where:
- \( R \) is the resistance.
- \( \rho \) is the resistivity of the material (in this case, carbon).
- \( L \) is the length of the conductor.
- \( A \) is the cross-sectional area of the conductor.
Ensure each value is correctly converted to consistent units, i.e., convert diameter and length to meters and calculate the area using the formula for a circle \((A = \pi (d/2)^2)\).
**Interactive Tools:**
- An image editing icon for calculations and annotations.
- Various text and formatting options for entering and organizing solutions.
- Submission button to finalize your answer.
- Option to request an answer if needed.
This activity promotes critical thinking and understanding of key concepts in physics and material science.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F31a7d002-7306-48cb-8411-4964e654c6a5%2Fcb1a3f54-4e20-43db-b2a9-d5424e69a3f8%2Fqmj9rh_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Resistance in Pencil Leads**
**Introduction:**
Pencil "lead" is actually made of carbon, a material known for its remarkable electrical properties. In this exercise, we will explore how to calculate the electrical resistance of a mechanical pencil lead.
**Problem Statement:**
**Part A:**
What is the resistance of a 0.660 mm-diameter, 5.10 cm-long lead from a mechanical pencil?
**Solution:**
To find the resistance, we need to use the formula for the resistance of a cylindrical conductor:
\[ R = \frac{\rho L}{A} \]
Where:
- \( R \) is the resistance.
- \( \rho \) is the resistivity of the material (in this case, carbon).
- \( L \) is the length of the conductor.
- \( A \) is the cross-sectional area of the conductor.
Ensure each value is correctly converted to consistent units, i.e., convert diameter and length to meters and calculate the area using the formula for a circle \((A = \pi (d/2)^2)\).
**Interactive Tools:**
- An image editing icon for calculations and annotations.
- Various text and formatting options for entering and organizing solutions.
- Submission button to finalize your answer.
- Option to request an answer if needed.
This activity promotes critical thinking and understanding of key concepts in physics and material science.
Expert Solution
Step 1
Given data:
A carbon pencil
Diameter (d) = 0.660 mm
Length (L) = 5.10 cm
Required:
The resistance (R)
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