Eddie asked in Science & MathematicsMathematics · 2 months ago

# 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?

Relevance
• 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

• 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

• 2 months ago

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.

• 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

• 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