Question
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.)
Round off your final answer to the nearest hundredth.)
Answers
GPT 3.5
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.
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.
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