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4. If you change the resistivity of the resistor, is the effect like changing the length or changing the area? (answer, explain, evidence)

4. If you change the resistivity of the resistor, is the effect like changing the length or changing the area? (answer, explain, evidence)

College Physics
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) --- **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.
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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