Find the ratio of the resistances of 2 copper conductors if both the length and the cross-sectional

Find the ratio of the resistances of 2 copper conductors if both the length and the cross-sectional area of the first conductor are 2 times larger than the second.

Let’s write an expression to determine the resistivity of the wire:
ρsp = R * Ssech / l, where R is the resistance of the wire, l is the length of the wire, Ssech is the cross-sectional area.
Let us express R from here:
R = ρsp * l / Ssection
For the second conductor:
R1 = ρsp * l / Ssection
For the first conductor:
R2 = ρsp * 2 * l / 2 * Ssection
Find the ratio R2 / R1:
R2 / R1 = (ρsp * 2 * l / 2 * Ssection) / (ρsp * l / Ssection) = ρsp * 2 * l * Ssection / 2 * Ssection * ρsp * l = 1
Answer: the resistance of both conductors is the same.



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