(adsbygoogle = window.adsbygoogle || []).push({}); 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}=R_{1}^{-1}+R_{2}^{-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 m^{2}

Resistance of steel = (29e-8 * 1000) / 6.28e-4 = 0.46 ohm

Equivalent resistance = (R_{copper}^{-1}+ R_{steel}^{-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?

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# Homework Help: Resistance of a Composite Wire

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