What diameter wire should be used for particular resistance?

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SUMMARY

The discussion centers on calculating the diameter of nichrome wire needed to achieve a resistance of 16.0 ohms over a length of 49 meters at 20 degrees Celsius. The relevant equations include R = ρ x L / A and A = πd² / 4. The diameter can be derived using the formula d = √(4ρL/πR). The resistivity (ρ) of nichrome at room temperature is essential for this calculation, and users are directed to a Wikipedia page for its value.

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  • Understanding of electrical resistance and Ohm's Law
  • Familiarity with the concept of resistivity in materials
  • Basic knowledge of geometry, specifically area calculations
  • Ability to manipulate algebraic equations
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  • Research the resistivity of nichrome at various temperatures
  • Learn how to calculate the cross-sectional area of a wire
  • Explore the impact of temperature on the resistance of conductors
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Kastner86
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Homework Statement



If 49 m of nichrome wire is to have a resistance of 16.0 ohms at 20 degrees celsius, what diameter wire should be used?

Homework Equations



R = [tex]\rho[/tex] x L / A

A = [tex]\Pi[/tex] d^2 / 4

The Attempt at a Solution



well i know what I'm looking for, that is d (diameter)

and d = [tex]\sqrt{}[/tex](4[tex]\rho[/tex]L/[tex]\Pi[/tex]R)

I don't know what the value of [tex]\rho[/tex] is.

I know it is supposed to be the resistivity of the material, at a certain temperature, but I have no idea how to include it in the equation.

Please Help!
 
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