SUMMARY
A cylindrical copper rod, originally with resistance R, is re-formed to twice its length while maintaining constant volume, resulting in a new resistance of 4R. This occurs because the cross-sectional area is halved when the length is doubled, according to the resistance formula R = ρ(L/A). The reduction in area leads to an increase in resistance, demonstrating the direct relationship between resistance and length, and the inverse relationship with cross-sectional area.
PREREQUISITES
- Understanding of electrical resistance and Ohm's Law
- Familiarity with the formula R = ρ(L/A)
- Knowledge of the properties of materials, specifically copper
- Basic concepts of volume conservation in geometric transformations
NEXT STEPS
- Study the effects of material properties on resistance, focusing on resistivity (ρ) of different materials
- Explore the relationship between resistance, length, and cross-sectional area in more complex geometries
- Learn about practical applications of resistance in electrical circuits and components
- Investigate the impact of temperature on the resistance of conductors like copper
USEFUL FOR
Students studying physics or electrical engineering, particularly those focusing on circuit analysis and material properties. This discussion is beneficial for anyone preparing for exams related to electrical resistance and material behavior.