If a wire's length is doubled, what happens to its resistance?

• A. The resistance halves
• B. The resistance quadruples
• C. The resistance remains the same
• D. The resistance doubles

Answer: (D)

When the length of a wire is doubled, its resistance also doubles. This relationship is explained by Ohm's Law and the formula for resistance, which is given by ( R = \frac{\rho L}{A} ), where ( R ) is the resistance, ( \rho ) is the resistivity of the material, ( L ) is the length of the wire, and ( A ) is the cross-sectional area.

As the length ( L ) increases, the resistance ( R ) increases proportionally, provided the resistivity and the cross-sectional area remain constant. Therefore, if the length is doubled, the resistance effectively becomes twice as much as the original value.

This principle reflects the fact that a longer wire presents more material for the electrons to pass through, which inherently increases the chances of collisions and resistance encountered by the electrons moving through the conductor.