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

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Homework Help Overview

The problem involves determining the optimal diameter for a nichrome wire with a specified resistance at a given temperature. The subject area includes electrical resistance and properties of materials.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between resistance, resistivity, length, and cross-sectional area, with emphasis on how area relates to diameter. There are attempts to calculate the diameter based on the given resistance and material properties.

Discussion Status

Some participants have shared their calculations and results, indicating progress in understanding the problem. There is a mix of responses regarding the calculations, with some confirming their results while others provide encouragement.

Contextual Notes

Participants are reminded to pay attention to units and the relationships between variables in the equations used. There is an emphasis on ensuring correct interpretation of the area in relation to diameter.

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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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