What effect does doubling the diameter of a wire have on its resistance?

• A. Resistance doubles
• B. Resistance is halved
• C. Resistance is quartered
• D. Resistance remains the same

Answer: (C)

Doubling the diameter of a wire has a significant effect on its resistance due to the relationship defined by the formula for resistance in a conductor, given as:

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

where ( R ) is resistance, ( \rho ) is resistivity, ( L ) is the length of the wire, and ( A ) is the cross-sectional area.

When the diameter of a wire is doubled, its cross-sectional area increases. The area ( A ) of a wire with diameter ( d ) can be expressed as:

[ A = \pi \left(\frac{d}{2}\right)^2 = \frac{\pi d^2}{4} ]

Thus, when you double the diameter (let's represent the original diameter as ( d ) and the new diameter as ( 2d )), the new area becomes:

[ A' = \pi \left(\frac{2d}{2}\right)^2 = \pi \left(d\right)^2 = \pi d^2 ]

The area has quadrupled since:

[ A' = 4 \times A ]

Substituting this new area back into the resistance formula shows