SUMMARY
The discussion focuses on calculating the diameter of a copper wire given its resistance, mass, resistivity, and density. The relevant equations include Ohm's Law (V=IR) and the resistance formula R=ρL/A, where ρ is resistivity, L is length, and A is cross-sectional area. To find the diameter, one must first derive the length from the mass and density, then use the area formula A=4πr² to solve for the radius, which is subsequently doubled to obtain the diameter. The specific values provided include a resistance of 17.00 Ω, a mass of 37.0 g, a resistivity of 1.68×10-8 Ω·m, and a density of 8.90×103 kg/m³.
PREREQUISITES
- Understanding of Ohm's Law (V=IR)
- Familiarity with the resistance formula R=ρL/A
- Knowledge of mass density and its application in calculations
- Basic geometry for calculating the area of a circle (A=πr²)
NEXT STEPS
- Learn how to derive length from mass and density using the formula L = mass/density
- Study the relationship between resistance, resistivity, and dimensions of conductors
- Explore the implications of resistivity in different materials, particularly copper
- Practice solving similar problems involving electrical resistance and wire dimensions
USEFUL FOR
Students in physics or electrical engineering, educators teaching circuit theory, and anyone involved in materials science or electrical design who needs to calculate wire dimensions based on electrical properties.