In household wiring, copper wire 2.05 mm in diameter is often used. Find the resistance of a 24

step 1 All right, so in this problem, we have a copper wire whose lens is, let me see, 24 meters, and d

In household wiring, copper wire 2.05 mm in diameter is...

Key Concepts

Cross-Sectional Area Calculation

For a wire with a circular cross-section, the area is calculated using the formula A = ?(d/2)². This calculation is crucial because the resistance is inversely proportional to the cross-sectional area. A larger area means a lower resistance for a given material and length.

Electrical Resistance

This concept refers to the opposition offered by a material to the flow of electric current. It is quantified by the resistance (R) of the conductor, which depends not only on the material's properties but also on its dimensions. The relationship is often expressed by the formula R = ?L/A, where ? is the material's resistivity, L is the length, and A is the cross-sectional area.

Resistivity of Materials

Resistivity is an intrinsic property of a material that indicates how strongly the material opposes the flow of electric current. Copper, for example, has a low resistivity, which means it is highly conductive and commonly used in household wiring. The resistivity value is used in the resistance calculation and is typically provided at a given temperature.

Unit Conversion and Geometric Considerations

When working with dimensions provided in different units (such as millimeters for diameter and meters for length), proper unit conversion is essential to ensure consistency in calculations. In this type of problem, converting the diameter from millimeters to meters is required before applying it in the cross-sectional area formula, thereby ensuring accurate computation of the resistance.

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