The "third rail" that carries electric power to a subway...

The "third rail" that carries electric power to a subway train is an iron bar whose rectangular cross section measures $10 \mathrm{~cm}$ by $15 \mathrm{~cm}$. Find the resistance of a $5.0-\mathrm{km}$ length of this rail.

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Key Concepts

Unit Conversion

Ensuring that all quantities are expressed in consistent units is essential in electrical calculations. For instance, converting dimensions from centimeters to meters when calculating area ensures that the calculated resistance is in the correct unit (ohms).

Cross-sectional Area Determination

The cross-sectional area of a conductor plays a crucial role in its ability to conduct electricity, as a larger area typically allows more current to pass through. For a conductor with a rectangular shape, the area is calculated by multiplying its width by its height.

Resistance Calculation of a Conductor

The resistance of a conductor is determined by its geometry and material properties as expressed in the formula R = (?L)/A. Here, L is the length of the conductor and A is its cross-sectional area, making it essential for analyzing current flow in electrical circuits.

Electrical Resistivity

This is a material-specific property that quantifies how strongly a given material opposes the flow of electric current. It provides the basis for calculating resistance in a conductor using the formula R = (?L)/A, where ? is the resistivity.

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