The resistance, R. of a wire varies directly as its length and inversely as the square of its diameter. If the resistance of a wire 100 ft long with a diameter of 0. 14 inches is 14521 ohms, what is the resistance of 2700 ft of the same type of wire with a diameter of 0.43 inches?
Let R be the resistance of the wire, L be its length, and D be its diameter.
According to the problem, R varies directly with L and inversely with the square of D. This can be written as:
R = k * (L / D^2)
where k is a constant.
Given that the resistance of a wire 100 ft long with a diameter of 0.14 inches is 14521 ohms, we can substitute these values into the equation to find k:
14521 = k * (100 / 0.14^2)
14521 = k * (100 / 0.0196)
14521 = k * 5102.04
k = 14521 / 5102.04
k = 2.846
Now we can use this value of k to find the resistance of 2700 ft of the wire with a diameter of 0.43 inches:
R = 2.846 * (2700 / 0.43^2)
R = 2.846 * (2700 / 0.1849)
R = 2.846 * 14604.20
R ≈ 41595.62
Therefore, the resistance of 2700 ft of the same type of wire with a diameter of 0.43 inches is approximately 41595.62 ohms.