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When comparing the resistance of two wires, we can use the formula
R = (ρ * L) / A
where R is the resistance, ρ is the resistivity of the wire (which is constant for a given material such as copper), L is the length of the wire, and A is the cross-sectional area of the wire.
In this question, we are comparing two copper wires. The first wire has a radius of r and a length of l, and the second wire has a radius of 2r and a length of l/2.
To compare the resistance of the two wires, we need to calculate the cross-sectional area of each wire and then plug those values into the resistance formula.
The cross-sectional area of a wire is given by the formula A = π * r^2, where r is the radius of the wire.
For the first wire, the cross-sectional area is A1 = π * r^2.
For the second wire, the cross-sectional area is A2 = π * (2r)^2 = 4π * r^2.
Plugging these values into the resistance formula, we get:
R1 = (ρ * l) / A1
R2 = (ρ * (l/2))