A 200 ft length of solid copper wire is measured to have a resistance of .500 Oh

Question

A 200 ft length of solid copper wire is measured to have a resistance of .500 Ohms.

a. Determine the cross sectional area of the wire in both square mils and in circular mils.

b. Determine the diameter of the wire in mils and in inches.


Here on Cramster it shows a step where

.500 ohms = [(10.36)(CM-oms/ft)(200ft) / A

Where is the 10.36 coming from? That should be Ohm Meters, but how do we know what that is? I don't see where or how its been stated in a wire table or in the problem itself. Where is the 10.36 coming from?

Explanation / Answer

Resistance is given as

R=l/A

where ------resistivity of copper = 1.7*10^-8 ohm-m

l=200ft =200*0.3048 =60.96 m

>>>>>> 0.5 = 1.7*10^-8 * 60.96 /A

>>>>>> 0.5 = 10.36 * 10^-7 / A

>>>>>>> A = 10.36 * 10^-7 /0.5 = 20.72*10^-7 m^2

Now 6.45*10^-10 m^2 = 1 square mil

>>>> 20.72*10^-7 m^2 = 1*20.72*10^-7 m^2/6.45*10^-10 m^2 = 3212.403 square mils

Circular mils = Square mils*4/ =3212.403*4/ = 4090.158 circular mils

b)Now area can be writen for circular wire as

  *(D/2)^2 = 3212.403 >>>>>>>D = 63.954 mils

Again *(D/2)^2  = 20.72*10^-7 m^2 >>>>>>>>>D = 0.00162 m = 0.00162*39.37 inch = 0.0639 inch

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