Heating coil wire resistance and length of wire required

[servin247365]

Homework Statement

A portion of Nichrome wire of radius 2.50 mm is to be used
in winding a heating coil. If the coil must draw a current of
9.25 A when a voltage of 120 V is applied across its ends,
find (a) the required resistance of the coil and (b) the
length of wire you must use to wind the coil.

Homework Equations

RI = V
R = I/oA

The Attempt at a Solution

(a) RI = V
R = V/I = 120V/9.25A = 12.973Ohms

(b)
R = l/oA
l = RoA = (12.973Ohms)(.000001ohms*m)(.0025m*3.14*2) = 2.036761e-7m

The answer to the second part of the equation is 255m and I can't figure out what I did wrong...

Thanks!

 

[lewando]

Your units aren't working out well--equation for resistance seems odd.

Try R=ρl/A

ρ, resistivity in Ωm
l, length in m
A, cross-sectional area in m².

 

[TSny]

Did you use the correct formula for area? Did you use a value for resistivity or conductivity for the symbol "o"?

 

[servin247365]

Ah OK, that worked. I am not sure why the other formula from the book didn't show that but maybe I missed something... Thanks!

 

[Nickie]

I would first double check your calculations to make sure they are accurate. Then, I would consider the practicality of using a length of wire that is 255 meters long for a heating coil. This seems like a very long length and may not be feasible or efficient for the intended purpose. It may be worth exploring other options or materials that could achieve the desired resistance and current with a more manageable length of wire. Additionally, I would consider the potential safety hazards of using such a long length of wire for a heating coil and make sure proper precautions are taken.