A 200 m long aluminum wire has the same resistance and cross-sectional areaas a carbon wire. What is the length of the carbon wire

To solve this problem, we need to use the formula for resistance in a wire, which is:

R = ρL/A

where R is the resistance, ρ is the resistivity, L is the length, and A is the cross-sectional area.

Given that the resistance and cross-sectional area of the aluminum wire and the carbon wire are the same, we can set up the following equation:

ρ_Al * L_Al = ρ_C * L_C

where ρ_Al and ρ_C are the resistivities of aluminum and carbon, respectively, and L_Al and L_C are the lengths of the aluminum and carbon wires, respectively.

We are given that L_Al = 200 m, and we want to find L_C. We can rearrange the equation to solve for L_C:

L_C = (ρ_Al / ρ_C) * L_Al

The resistivity of aluminum is approximately 2.82 x 10^-8 ohm meters, and the resistivity of carbon is approximately 3.5 x 10^-5 ohm meters. Plugging these values into the equation gives:

L_C = (2.82 x 10^-8 / 3.5 x 10^-5) * 200 m

Solving this equation gives the length of the carbon wire.