Question

An old house is wired with copper wire with a diameter of 0.2 cm and resistivity rho=1.72×10⁸Ωm. One circuit consists of only one wire behind walls and has a resistance of 1.22Ω. How long is this wire, in meters?

Answer 1

The length of the wire is approximately 69.2 meters.

Step-by-step explanation:

To find the length of the wire, we can use the formula for resistance:

R = (ρ * L) / A

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

Given that the resistance is 1.22Ω, and the diameter of the wire is 0.2 cm, we can calculate the radius (r) using the formula r = d/2 = 0.1 cm. The cross-sectional area (A) is then π * r^2.

Plugging in the values, we get:

1.22Ω = (1.72×10^8 Ωm * L) / (π * (0.1 cm)^2)

Solving for L, we find that the length of the wire is approximately 69.2 meters.