The electrical resistance, r ohms, of 1,000 ft of solid copper wire at 77¡ãF can be approximated by the model r = 10,770 / d^2 - 0.37 for any wire diameter, d mils (1 mil = 0.001 inch), such that 5 ¡Ü d ¡Ü 100. What is the approximate resistance, in ohms, for such with a diameter of 50 mils?
F. 1
G. 4
H. 17
J. 215
K. 430
Such that 5 is less than or equal to d is less than or equal to 100. It wouldn't show the sign.
430
To find the approximate resistance, we can substitute the given diameter into the equation r = 10,770 / d^2 - 0.37.
Given diameter, d = 50 mils.
Substituting d = 50 into the equation:
r = 10,770 / (50)^2 - 0.37
r = 10,770 / 2,500 - 0.37
r = 4.308 - 0.37
r ≈ 3.938 ohms
Therefore, the approximate resistance for a wire with a diameter of 50 mils is approximately 3.938 ohms.
Since none of the answer choices exactly match 3.938 ohms, we can round it to the nearest whole number, which is 4.
Therefore, the correct answer is G. 4.
To find the approximate resistance in ohms for a wire with a diameter of 50 mils, we can substitute the value of d in the resistance model equation r = 10,770 / d^2 - 0.37.
Substituting d = 50 mils into the equation, we get:
r = 10,770 / (50^2) - 0.37
r = 10,770 / 2500 - 0.37
r = 4.308 - 0.37
r ≈ 3.938
Therefore, the approximate resistance for a wire with a diameter of 50 mils is approximately 3.938 ohms.
Since none of the given answer choices match exactly, we can round our result to the nearest whole number. In this case, the rounded answer is 4.
Hence, the correct answer is G. 4.