30: Problem 30.66

INTRO:
Household wiring often uses 2.0-mm-diameter copper wires. The wires can get rather long as they snake through the walls from the fuse box to the farthest corners of your house.
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PART A:
What is the potential difference across a 16-m-long, 2.0-mm-diameter copper wire carrying an 7.8 A current?
Express your answer to two significant figures and include the appropriate units.

SOLUTION:
Using eq. (30. 21)... I = A⋅ΔV/ρL

→ ΔV = IρL/A
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using table (30.2) → ρ_copper = 1.7×10^-8 Ωm
& A = π/4⋅d²

→ ΔV = (7.8 A)(1.7×10^-8 Ωm)(16 m)/(π/4⋅d²)
⇒ ΔV = 0.675 V = 0.68 V​