he 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 s 638 ohms, what is the resistance of 3700 ft of the same type of wire with a diameter of 0.25 inches? (Leave k in fraction form or round to at least 3 decimal places.
Round off your final answer to the nearest hundredth.)
We can set up the equation based on the given information:
R = k * (L / (d^2))
where R is the resistance, L is the length of the wire, d is the diameter of the wire, and k is a constant.
To find k, we can substitute the given values into the equation and solve for k:
638 = k * (3500 / (0.03^2))
Simplifying, we get:
638 = k * (3500 / 0.0009)
638 = k * 3,888,889.223
Dividing both sides by 3,888,889.223, we get:
k = 0.0001639 (rounded to at least 3 decimal places)
Now that we have found the value of k, we can use it to find the resistance of the wire with the new length and diameter.
R = 0.0001639 * (3700 / (0.25^2))
Simplifying, we get:
R = 0.0001639 * (3700 / 0.0625)
R = 0.0001639 * 59,200
R = 9.70528 (rounded to at least 3 decimal places)
Therefore, the resistance of 3700 ft of the same type of wire with a diameter of 0.25 inches is approximately 9.71 ohms.