- 84

- 0

**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?