Which of the following statements about resistance is true if the cross-sectional area is doubled?

• A. Resistance is reduced to zero
• B. Resistance is halved
• C. Resistance remains unchanged
• D. Resistance is doubled

Answer: (B)

When the cross-sectional area of a conductor is doubled, the resistance indeed becomes halved, which makes this the correct answer. The relationship between resistance, length, cross-sectional area, and resistivity is described by Ohm's Law and the formula for resistance ( R = \frac{\rho L}{A} ).

In this formula:

• ( R ) represents resistance,

• ( \rho ) is the resistivity of the material (a constant for a given material),

• ( L ) is the length of the conductor, and

• ( A ) is the cross-sectional area.

If you double the cross-sectional area ( A ), you effectively reduce the fraction ( \frac{L}{A} ). Since resistance is inversely proportional to the cross-sectional area, increasing the area decreases resistance. Hence, if ( A ) is doubled, ( R ) is halved, leading to the conclusion that the resistance is indeed reduced to half its original value.

This principle is crucial in electrical engineering and physics, particularly in understanding how conductors behave under various physical changes. Thus, recognizing how changes in dimensions affect electrical characteristics is essential for practical applications and designs in the field.