You have a cylindrical piece of material 2.4 cm long and 2.0 mm in diameter. When you attach a

step 1 Okay, so what I've done here is we know resistance equals voltage divided by current, and we als

You have a cylindrical piece of material 2.4 cm long and...

You have a cylindrical piece of material $2.4 \mathrm{~cm}$ long and $2.0 \mathrm{~mm}$ in diameter. When you attach a 9-V battery to its ends, a 2.6-mA current flows. Which material from Table $24.1$ do you have?

Key Concepts

Material Identification via Resistivity

By measuring the resistance of a sample and knowing its dimensions, one can calculate the resistivity using the formula R = ?L/A. With the calculated resistivity value, it is possible to compare against standard resistivity values from reference tables for various materials. This process is a common method for identifying an unknown material based on how well it conducts electricity relative to known substances.

Conductor Geometry and Resistance

The geometry of a conductor, specifically its length and cross-sectional area, plays a critical role in determining its electrical resistance. A longer conductor will have a higher resistance, while a conductor with a larger cross-sectional area will have a lower resistance. The formula R = ?L/A encapsulates this relationship and is used to adjust for the physical dimensions when analyzing or comparing the electrical properties of different materials.

Resistivity

Resistivity is a material property that quantifies how strongly a material opposes the flow of electric current. It is intrinsic to the material and is independent of its shape or size. The relationship between resistance R, resistivity ?, the length L of the conductor, and its cross?sectional area A is given by the formula R = ?L/A. This concept allows one to compute the resistivity experimentally and thereby characterize the material.

Ohm’s Law

Ohm’s Law provides the fundamental relation between voltage, current, and resistance in an electrical circuit. It is expressed as V = IR, where V is the voltage applied across a component, I is the current flowing through it, and R is the resistance. This law is essential for determining how much current will flow for a given voltage or, conversely, what resistance a component must have to limit the current to a certain value.

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