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
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Electricity and Magnetism
Resistivity
Ohm's Law
Parallel Circuits
Formulas
R = ρL / A
A = πr^2
R_total = R / N
i = V / R_total
N_max = (12 * ρ * L) / (π * r^2 * V)
Theorems
Ohm's Law
Resistors in Parallel
Suitable Grade Level
College-level Physics or Advanced High School Physics
Related Recommendation
Calculate Maximum Number of Strands in Aluminum Wiring Using Ohm's Law
Calculate Resistance of Aluminum Wire with Length 40m and Diameter 4.2mm
Find the Resistance of a Circuit with 480 Volts and 12 Amps
Calculate Electrical Resistance of Copper Conductor - Problem and Solution
Find Length and Volume of Stainless Steel Foil in a Parallel Circuit with 1.425Ω Resistance