Calculating Resistance of a Conductor. The resistance of a nine inch length of copper that has a diameter of 0.005 in. is...?

I know that the Answer is 311 mOhms. But I dont know how. I have the formula but I get lost on the procedure. 

R= p x (L/A)p of copper = 10.37 CM-Ohm / ft

L = 9 in

A = must find given diameter = 0.005 in

A = Pi r^2

3.14 x 0.0025^2

= 1.96 x 10 ^ -5 inches

9 in / 1.96 x10^-5 in

= 459183.67 inches

divide by 12 to get feet = 38265.3 ft

10.37 CM-Ohm/ft x 38265.3 ft = 396811.2 CM-Ohm

How to I factor out CM to just get ohms?

5 Answers

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  • 2 months ago

    ρ = [rho] resistivity of copper = 1.68E-08 Ωm

    L = length of conductor = 9 in = 0.2286 m

    D = diameter of conductor = 0.005 in = 0.000127 m

    A = cross-sectional area of conductor = to be determined

    A = πD²/4

    A = (3.14)(0.000127 m)²/4

    A = 1.26677E-08 m²

    R = resistance of conductor = to be determined

    R = ρL/A

    R = [(1.68E-08 Ωm)(0.2286 m)] / 1.27E-08 m²

    R = 0.303171369 Ω

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  • 2 months ago

    Okay so I looked up how to calculate Resistance of a conductor and I found some PDF of a book explaining how to Calculate R if you are given a diameter of a conductor.

    The area of diameter of a conductor can be found by taking the diameter given and converting to Mils.

    1 Mil = 0.001 inch.

    The formula for Area CM = diameter in Mils ^2 

    0.005 in x (1 mil /0.001 in) = 5 mils

    so the formula becomes R = p x (L / A)

    A = 5 mils ^2 = 25 CM

    Convert 9 inches to ft 

     9 in x (1 ft / 12 in) = 0.75 ft

    R = 10.37 CM-Ohm/ft x (0.75 ft / 25 CM)

    CM and Ft Cancel out and you get 0.311 Ohms

    or for engineering notation 311 mOhms

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  • Your stuff is way off.

    p of copper = 10.37 CM-Ohm/ft

    https://en.wikipedia.org/wiki/Circular_mil

    The diameter of the wire is 0.005 inches

    The area of the cross-section is pi * (0.005/2)^2 square inches = pi * (5/2)^2 square mil-inches

    pi * (25/4) =>

    6.25 * pi CM

    R = p * (L/A)

    R = 10.37 CM-Ohm/ft  *  (9 inches / (6.25 * pi CM)

    R = 10.37 CM-Ohm/ft * (0.75 ft / (6.25 * pi CM))

    R = (10.37 * 0.75 / (6.25 * pi)) CM * Ohm * ft / (ft * CM)

    R = (10.37 * 75 / (625 * pi)) Ohms

    R = ‭0.39610482236710911166159791028151‬

    396 milli-Ohms.

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  • Anonymous
    2 months ago

    < = 1.96 x 10 ^ -5 inches >

    The units are in^2, not in.  That, with a conversion, will allow you to cancel the cm.  Your math still doesn't look right but you have the overall approach right.

    < 396811.2 CM-Ohm >

    So this is really 396811.2 CM-Ohm/in per the comment above.  Since there are 2.54 cm/in, you get 156225 ohm which is a LONG way from 311 mohm or 0.311 ohm.  It's more than just a factor of 10 issue.

    • Eddie2 months agoReport

      it CM vs cm, as in Circular Mils vs centimeters 

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  • alex
    Lv 7
    2 months ago

     What is 10.37 CM-Ohm / ft ?

    the resistivity of copper is generally given as: 1.72 x 10-8 Ωm

    • Eddie2 months agoReport

      my book uses circular mils ohm per foot not meters unfortunately 

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