Physics

Physics

Problem

A 2.0 m2.0\,\text{m} long copper wire is to be made into a 3 Ω3\,\Omega resistor. The resistivity of copper is 1.7×10−8 Ω m1.7\times10^{-8}\,\Omega\,\text{m}. Calculate the diameter of the wire that should be chosen. (Take π=3.14\pi = 3.14.)
Intuitive explanation

The key is using the resistance formula R=ρLAR = \rho \frac{L}{A} to connect what you know (length, resistivity, and target resistance) to what you need (cross-sectional area, which determines diameter). Rearrange to find the area, then use A=πr2A = \pi r^2 to back out the radius and diameter—it's just geometry once you have the area.

Intuitive explanation

The key is using the resistance formula R=ρLAR = \rho \frac{L}{A} to connect what you know (length, resistivity, and target resistance) to what you need (cross-sectional area, which determines diameter). Rearrange to find the area, then use A=πr2A = \pi r^2 to back out the radius and diameter—it's just geometry once you have the area.

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