Math Problem Statement
As part of a class project, you need to create a bun- dle of aluminum wiring. Aluminum has a resistivity of ρ = 2.65 × 10−8 Ω · m. The bundle will be L = 15 m long, and will be composed of N individual strands that each have a radius of r = 0.22 mm. In order to be certain that the wiring will not overheat, you need to ensure that the current remains below i = 12 A when it is connected to a V = 3.0 V battery. What is the maximum number of strands N you can use while ensuring that the current re- mains below 12 A? The symbolic answer should be stated in terms of ρ, L, r, i, and V , though not all of these quan- tities may be needed.
Solution
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Math Problem Analysis
Mathematical Concepts
Electric Resistance
Ohm's Law
Parallel Circuits
Resistivity
Formulas
R = ρ (L / A)
A = π r^2
V = i R
1 / R_total = N / R
Theorems
Ohm's Law
Suitable Grade Level
Grades 11-12
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