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Resistance of a Composite Wire

1. The problem statement, all variables and given/known data
A transmission wire is made of a cylindrical core of copper surrounded by a sheath of steel. The copper core is 1 cm in diameter, and the sheath has an outer diameter of 2 cm. What is the resistance of 1 km of wire?


2. Relevant equations
R=ρl/A


3. The attempt at a solution
I tried treating the two layers of wire as resistors in parallel, so I found the resistance of each one and added them that way (R-1=R1-1+R2-1). For the area of the outer sheath, I used the area of the total wire minus the area of the inner copper part.

Resistance of copper = (1.72e-8 * 1000) / 7.85e-5 = 0.219 ohm
Area of steel part: 7.07e-4 - 7.85e-5 = 6.28e-4 m2
Resistance of steel = (29e-8 * 1000) / 6.28e-4 = 0.46 ohm

Equivalent resistance = (Rcopper-1 + Rsteel-1)-1 = 0.15. But the answer key says it's 0.19. I tried to keep as many decimal places all the way through, and used values for resistivity straight out of the textbook. Any help please?
 
1,506
17
I think you have mis-calculated the cross sectional area of the steel.
The outside diameter of the steel is 2cm and the inside diameter is 1cm
I got the area to be 3.142 x 10^-4 - 7.86 x 10^-5
This gave a total resistance of 0.186 (0.19)
 
Alright, I see how you did that. but how come you used 1 (half of 2) instead of 1.5 (half of 3, total diameter of the wire) for the first radius?
 
1,506
17
The wire has a central core of diameter 1cm. The steel coating has a diameter of 2cm.....it is not 3cm.
Imagine a Doughnut.... the hole in the middle is the copper (1cm diameter) the best bit of the doughnut is the steel.... diameter 2cm
 
Oh ok silly mistake on my part. Thank you very much.
 
1,506
17
glad you got it.... enjoy the doughnut
 

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