In this scenario, we have two conducting wires A and B made of the same material. We are given that the length of wire B is twice that of wire A. Additionally, the radius of the circular cross-section of wire A is twice that of wire B.

Resistance is directly proportional to the length of the wire and inversely proportional to the cross-sectional area. Therefore, we can use the formula for resistance (R = ρ * L / A) to compare the resistances of wires A and B.

Let`s consider the length and radius of wire A as L and R respectively. So, the length of wire B will be 2L and the radius will be R/2.

Plugging the values into the formula, we get the resistance of wire A as RA = ρ * L / (π * R²) and the resistance of wire B as RB = ρ * 2L / (π * (R/2)²).

Simplifying the equations, we get RA = 8 * ρ * L / (π * R²) and RB = ρ * 4L / (π * R²).

Now, we can observe that the ratio of RA to RB is 8:4, which simplifies