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 4**: If you change the resistivity of the resistor, is the effect like changing the length or changing the area? (answer, explain, evidence)
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**Explanation**:
When you change the resistivity (\( \rho \)) of a resistor, it affects the resistance (\( R \)) similarly to how changing the length (\( L \)) or the cross-sectional area (\( A \)) does. This relationship is described by the formula:
\[ R = \rho \frac{L}{A} \]
**Effects**:
1. **Changing Resistivity** (\( \rho \)):
- Increasing resistivity increases resistance.
- Decreasing resistivity decreases resistance.
2. **Changing Length** (\( L \)):
- Increasing length increases resistance similarly to increasing resistivity.
- Decreasing length decreases resistance.
3. **Changing Cross-Sectional Area** (\( A \)):
- Increasing area decreases resistance.
- Decreasing area increases resistance.
**Conclusion**:
Changing resistivity has a similar effect on resistance as changing the length of the resistor. Both factors have a direct relationship: as one increases, so does the resistance. In contrast, the cross-sectional area has an inverse relationship with resistance.
**Evidence**:
To understand this, consider a copper wire. If the resistivity is increased (such as by using a different material or due to temperature changes), the resistance increases similarly to if the wire were made longer, keeping the same cross-sectional area. Conversely, increasing the cross-sectional area reduces the resistance, unlike increasing resistivity or length.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf5aa2e5-f0b0-4839-a4ef-6f98d6dc8551%2Fd3bd5ed2-4e35-45af-879a-d838909bd117%2Fv0ofnh_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 4**: If you change the resistivity of the resistor, is the effect like changing the length or changing the area? (answer, explain, evidence)
---
**Explanation**:
When you change the resistivity (\( \rho \)) of a resistor, it affects the resistance (\( R \)) similarly to how changing the length (\( L \)) or the cross-sectional area (\( A \)) does. This relationship is described by the formula:
\[ R = \rho \frac{L}{A} \]
**Effects**:
1. **Changing Resistivity** (\( \rho \)):
- Increasing resistivity increases resistance.
- Decreasing resistivity decreases resistance.
2. **Changing Length** (\( L \)):
- Increasing length increases resistance similarly to increasing resistivity.
- Decreasing length decreases resistance.
3. **Changing Cross-Sectional Area** (\( A \)):
- Increasing area decreases resistance.
- Decreasing area increases resistance.
**Conclusion**:
Changing resistivity has a similar effect on resistance as changing the length of the resistor. Both factors have a direct relationship: as one increases, so does the resistance. In contrast, the cross-sectional area has an inverse relationship with resistance.
**Evidence**:
To understand this, consider a copper wire. If the resistivity is increased (such as by using a different material or due to temperature changes), the resistance increases similarly to if the wire were made longer, keeping the same cross-sectional area. Conversely, increasing the cross-sectional area reduces the resistance, unlike increasing resistivity or length.
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