Resistivity
As of 2021, the College Board tests only Units 1-7 on the AP Physics 1 exam. While this content will not be directly tested, it serves as a valuable resource for understanding resistivity and its real-world applications.
Enduring Understanding 1.E
Materials possess macroscopic properties that arise from the arrangement and interactions of atoms and molecules.
What is Resistivity?
Resistivity is a fundamental property of materials that measures how strongly a material opposes the flow of electric current. Materials with low resistivity, such as copper, are excellent conductors, while those with high resistivity, such as rubber, are effective insulators.
Examples:
Copper:
Rubber:
Resistivity Formula:
Where:
= Resistivity
= Resistance
= Cross-sectional area
= Length
Temperature Dependency of Resistivity
Resistivity is influenced by temperature. Generally, higher temperatures increase the resistivity and resistance of a material. This phenomenon is crucial in understanding material behavior but is explored in greater detail in AP Physics 2. For AP Physics 1, it suffices to know:
Real-World Example: Conductive Dough Experiment
Students experimented with conductive dough molded into cylinders of varying lengths and cross-sectional areas. They applied a potential difference () and measured the resistance ().
Determining Resistivity from Experimental Data:
Graph Setup:
Vertical Axis:
Horizontal Axis:
Graph Interpretation:
Plot the given quantities to find a linear relationship.
The slope of the line corresponds to the resistivity.
Example Answer:
Resistivity of Dough: Using the graph, estimate the slope to determine .
Exploring Different Shapes: Does Shape Matter?
When another group shaped the dough into rectangles instead of cylinders, the question arose: Does the shape affect resistivity?
Answer: No. Resistivity is an intrinsic property of the material. As long as the material remains the same, the resistivity remains constant regardless of shape.
Justification:
The formula only depends on material properties and not its geometric configuration.
Experimental Procedure: Temperature’s Effect on Resistivity
To determine whether the resistivity of dough changes with temperature:
Equipment Needed:
Multimeter (or ammeter & voltmeter)
Conductive dough
Tools to alter temperature (e.g., ice bath, hot plate, or Bunsen burner)
Steps:
Mold the dough into a uniform shape (consistent and ).
Measure initial resistance at room temperature.
Incrementally change the temperature and record resistance after each change.
Calculate resistivity using for each temperature.
Data Representation:
Graph vs. Temperature.
Analyze the trend to confirm that resistivity increases with temperature.
Key Takeaways
Resistivity quantifies a material’s opposition to current flow and varies between conductors and insulators.
While resistivity depends on temperature, it remains independent of shape.
Understanding resistivity helps in designing efficient electrical systems and materials for various applications.
