The rod in Figure P 27.24 is made of two materials. The...

The rod in Figure $\mathrm{P} 27.24$ is made of two materials. The figure is not drawn to scale. Fach conductor has a square cross section $3.00 \mathrm{mm}$ on a side. The first material has a resistivity of $4.00 \times 10^{-3} \Omega \cdot \mathrm{m}$ and is $25.0 \mathrm{cm}$ long, while the second material has a resistivity of $6.00 \times 10^{-3} \Omega \cdot \mathrm{m}$ and is $40.0 \mathrm{cm}$ long. What is the resistance between the ends of the rod? (FIGURE CANNOT COPY)

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Key Concepts

Resistivity

Resistivity is a material property that quantifies how strongly a given material opposes the flow of electric current. It is defined as the resistance offered by a material per unit length and cross-sectional area, and its units are ohm-meters (?·m). A higher resistivity indicates that the material is less conductive.

Resistance of a Uniform Conductor

The resistance of a uniform conductor is determined by its resistivity, length, and cross-sectional area, using the formula R = ?L/A. This relationship shows that resistance increases with length and resistivity, but decreases with a larger cross-sectional area.

Series Connection of Resistive Elements

When resistive segments are connected end-to-end in a circuit, their total resistance is the sum of the individual resistances. This concept is crucial when dealing with composite materials or circuits where different materials or segments with distinct resistances are placed in series.

Cross-sectional Area Calculation

Calculating the cross-sectional area is essential for determining resistance since the formula R = ?L/A requires it. For conductors with regular shapes, like a square, the area is calculated using the appropriate geometric formula, which for a square is side length squared.

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