9.2 Resistivity

9.2 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:

1. Graph Setup:

   • Vertical Axis:

   • Horizontal Axis:

2. 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:

1. Equipment Needed:

   • Multimeter (or ammeter & voltmeter)

   • Conductive dough

   • Tools to alter temperature (e.g., ice bath, hot plate, or Bunsen burner)

2. 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.

3. 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.