Final answer:
To find the ratio of radii for iron and gold wires with equal resistance and length, use the square root of the inverse ratio of their resistivities.
Step-by-step explanation:
The resistance R of a cylindrical wire is given by the formula R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area. For wires with the same resistance and length, the resistivity ratio is inversely proportional to the area ratio. Since area A is πr^2, where r is the radius, the ratio of the radii of the wires can be found by taking the square root of the inverse ratio of the two resistivities. Considering the question where iron and gold wires have the same length and resistance, the ratio of their radii will be determined by the square root of the inverse ratio of their resistivities.
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