Doubling the cross-sectional area of a wire affects its resistance how?

• A. The resistance doubles
• B. The resistance is halved
• C. The resistance remains unchanged
• D. The resistance increases significantly

Answer: (B)

When the cross-sectional area of a wire is doubled, its resistance is halved. This principle is derived from the relationship defined by the formula for resistance:

[ R = \frac{\rho L}{A} ]

where ( R ) is resistance, ( \rho ) is the resistivity of the material, ( L ) is the length of the wire, and ( A ) is the cross-sectional area. From this formula, it is clear that resistance is inversely proportional to the cross-sectional area.

As the area increases (in this case, doubled), the overall resistance decreases since the wire can now allow more current to pass through it with less opposition. Specifically, if the area is doubled, the resistance becomes half of its original value, assuming the resistivity and length of the wire remain constant. This is a fundamental concept in electrical engineering and helps to understand how wire dimensions affect electrical properties.