Physics

Physics

Problem

An aluminum busbar inside a small power-distribution unit is fabricated as a flat rectangular strip of constant cross-section. The strip has a length of 25 cm, a width of 1.5 cm, and a uniform thickness of 0.20 mm. At operating temperature, the resistivity of aluminum is 2.8×10−8 Ω ⁣⋅ ⁣m2.8\times10^{-8}\,\Omega\!\cdot\!\text{m}. Engineers consider replacing the strip with a round aluminum wire of the same length that offers the same electrical resistance. (a) Calculate the electrical resistance of the original rectangular aluminum strip. (b) Determine the diameter of a circular wire, made of the same aluminum and having the same length, that would have identical resistance to the strip. (c) Give one practical reason, unrelated to mass or cost, why the flat strip might be preferred over the round wire in this power-distribution application, and explain your reasoning.
Intuitive explanation

This problem is about using the resistance formula R=ρL/AR = \rho L / A to connect geometry to electrical properties. The key insight is that even though you're changing the shape from a flat strip to a round wire, the resistance stays the same—so you need to find what cross-sectional area the wire must have, then work backward to find its diameter. The resistivity and length don't change, only the geometry does.

Intuitive explanation

This problem is about using the resistance formula R=ρL/AR = \rho L / A to connect geometry to electrical properties. The key insight is that even though you're changing the shape from a flat strip to a round wire, the resistance stays the same—so you need to find what cross-sectional area the wire must have, then work backward to find its diameter. The resistivity and length don't change, only the geometry does.

Browse the problem library