What is the Optimal Diameter for a 12.0 Ω Nichrome Wire at 20°C?

AI Thread Summary
To achieve a resistance of 12.0 Ω with 46 m of nichrome wire at 20°C, the optimal diameter calculated is approximately 2.3 mm. The resistance formula used is R = ρ(L/A), where ρ for nichrome is 108e-8. The area (A) was determined first, leading to the diameter calculation using A = (1/4)π(d²). The discussion emphasizes the importance of unit consistency throughout the calculations. The final diameter ensures the wire meets the specified resistance requirement.
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Homework Statement



If 46 m of nichrome wire is to have a resistance of 12.0 Ω at 20°C, what diameter wire should be used?

Homework Equations



R=\rho(L/A)

The Attempt at a Solution



I tried and I got 2.1. The \rho of nichrome is 108e-8
 
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First solve for the variable you are looking for and put it on one side. Keep your knowns on the other side. Remember that A stands for area, and area is related to wire diameter.

I am online for a bit, so give it a go. DON'T FORGET YOU UNITS!
 
ok yeah i got 2.3 mm. after i figured out A. I figured out diameter doing A=1/4pi(dsquared)
 
ok i got it right. thanks!
 
Good for you!
 
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