Question

One 2-wire section of a 24-volt watchman clock signal system is operated through a 450-foot length of lead-covered cable. Th e size of the conductor is number 18, and the diameter is 40.3 mils. What is the resistance of one conductor? Express the answer to the nearest thousandth.

Answer 1

To find the resistance of one conductor, you can use the formula for resistance:

Resistance (R) = (ρ * L) / A

Where:

R is the resistance in ohms.

ρ (rho) is the resistivity of the material (copper, in this case).

L is the length of the conductor in feet.

A is the cross-sectional area of the conductor in square mils.

First, we need to calculate the cross-sectional area (A) using the diameter (d) provided:

A = π * (d/2)^2

A = π * (40.3/2)^2

A ≈ π * (20.15^2)

A ≈ π * 405.0225

A ≈ 1273.24 square mils

Now, you need to look up the resistivity (ρ) of copper. For copper, the resistivity is approximately 10.37 ohm-mil/foot.

Next, you can calculate the resistance (R) of one conductor:

R = (ρ * L) / A

R = (10.37 ohm-mil/foot * 450 feet) / 1273.24 square mils

Now, let's calculate it:

R ≈ (4666.5 ohm-mil) / 1273.24 square mils

R ≈ 3.665 ohms (rounded to three decimal places)

So, the resistance of one conductor is approximately 3.665 ohms.

Step-by-step explanation:

Have great day!