How Do You Calculate the Radius of a Copper Cable Based on Current and Voltage?

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SUMMARY

The radius of a cylindrical copper cable carrying a current of 1060 A with a potential difference of 1.6 x 10^-2 V over a distance of 0.26 m is calculated to be 9.712 x 10^-3 m. The resistance (R) was determined using the formula R = V/I, resulting in 1.509 x 10^-5 ohms. This value was then used in the equation R = ρ(L/A), where ρ (resistivity of copper) is 1.72 x 10^-8 ohm-meters, L is 0.26 m, and A is the cross-sectional area calculated as π(r^2). The calculations confirm the radius is correct.

PREREQUISITES
  • Understanding of Ohm's Law (R = V/I)
  • Knowledge of resistivity and its application in electrical calculations
  • Familiarity with the formula for resistance in terms of resistivity (R = ρ(L/A))
  • Basic geometry for calculating the area of a circle (A = πr^2)
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  • Study the properties of copper and its resistivity in various conditions
  • Explore advanced applications of Ohm's Law in circuit analysis
  • Learn about the impact of temperature on the resistivity of materials
  • Investigate methods for measuring current and voltage in practical scenarios
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Electrical engineers, physics students, and anyone involved in electrical circuit design or analysis will benefit from this discussion.

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Electricity/Potential Difference

Homework Statement


A cylindrical copper cable carries a current of 1060 A. There is a potential difference of 1.6 x 10^-2 V between two points on the cable that are .26 m apart. What is the radius of the cable?

Homework Equations



R= V/I R= p(L/A) There may be more formulas needed.

p of Copper is 1.72 x 10^-8

The Attempt at a Solution


I divided the given V by the given current to get the resistance, which came out to be 1.509 x 10^-5. I plugged that into R= p(L/A) using 1.72 x 10^-8 for p, .26 for L, and (pi)(r^2) for A. I solved for r this way and got 9.712 x 10^-3 m. Is this right?
 
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Yes. It's right. What could be wrong?
 

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