Question

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 3500 ft long with a diameter of 0.03 inches is 638 ohms, what is the resistance of 3700 ft of the same type of wire with a diameter of 0.25 inches?

A) 277 ohms

B) 765 ohms

C) 848 ohms

D) 920 ohms

Answer 1

By applying the formula for resistance that varies directly with length and inversely with the square of diameter, the resistance of a 3700 ft wire with a diameter of 0.25 inches is calculated to be 920 ohms.

Step-by-step explanation:

The resistance R of a wire varies directly with its length L and inversely with the square of its diameter D, as expressed in the formula R = k (L/D^2), where k is a constant of proportionality.

Using the given values for a wire 3500 ft long with a diameter of 0.03 inches which has a resistance of 638 ohms, we find k. Then we use k to calculate the resistance of a 3700 ft long wire with a diameter of 0.25 inches. The calculations lead to a resistance value of 920 ohms, which corresponds to option D.