Resistance Problem Find Length of Wire

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SUMMARY

The problem involves calculating the length of a copper wire with a diameter of 0.44mm carrying a current of 0.76A under a potential difference of 15V. The resistance is calculated using Ohm's Law (V=IR) and the resistivity formula (R=row(L/A)). The correct length of the wire is determined to be 170m, highlighting a critical error in converting the diameter from millimeters to meters during the calculations. The resistivity of copper is noted as 1.72 x 10^-8 ohm-meters.

PREREQUISITES
  • Understanding of Ohm's Law (V=IR)
  • Knowledge of resistivity and its application in resistance calculations
  • Familiarity with the formula for cross-sectional area (A=πD²/4)
  • Ability to convert units between millimeters and meters
NEXT STEPS
  • Review the principles of electrical resistance and its dependence on material properties
  • Learn about the significance of resistivity in different materials, focusing on copper
  • Practice unit conversion techniques, especially for electrical engineering applications
  • Explore advanced applications of Ohm's Law in circuit analysis
USEFUL FOR

Electrical engineering students, physics learners, and professionals involved in circuit design or analysis will benefit from this discussion, particularly those working with wire specifications and electrical resistance calculations.

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1.Problem
A current of 0.76A flows through a copper wire 0.44mm in diameter when it is connected to a potential difference of 15V. How long is the wire?
2. Homework Equations (Missing any?)
V=IR
R=row(L/A)
A=pieD^2/4
row=resistivity=p
p of copper=1.72 x 10^-8
3.Attempt
Pretty sure conversion is wrong.
V=IR
15=(.76a)R
R=19.737

D=.44mm mm to m
4.4 x 10^-5m

A=pieD^2/4
A=(3.14)(4.4 x 10^-5)^2/4
A=1.512 x 10^-9

Plug back into the resistance equation for L

R=row(L/A)R=row
19.737=(1.72 x 10^-8)(L/1.512 x 10^-9)
2.999x10^-8=1.72 x 10^-8L
L=(2.999x10^-80)/(1.72 x 10^-8)
L=1.744m

Correct Answer: 170m
 
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You made an error in converting the diameter of the wire from millimeters to meters.
 

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