If the width of a wire is increased four times, what happens to its resistance?

• A. Resistance is doubled
• B. Resistance remains the same
• C. Resistance is halved
• D. Resistance is 1/4

Answer: (D)

When the width of a wire is increased, its resistance is affected by the geometry of the conductor. Resistance in a uniform wire is inversely proportional to its cross-sectional area. Specifically, the formula for the resistance ( R ) of a wire is given by:

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

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

If the width of the wire is increased four times, the cross-sectional area will increase by a factor proportional to the square of the increase in width (assuming a uniform shape). For a cylindrical wire, if the diameter (or equivalently the width) is increased four times, the area increases by a factor of ( 4^2 = 16 ).

As a result, if the area increases by a factor of 16, the resistance, which is inversely proportional to this area, will decrease by a factor of 16. This means that if the original resistance was ( R ), the new resistance would be:

[ R' = \frac{R}{16} ]

Thus, when the width of the wire