The resistance, R (ohms) of a copper wire of fixed length is inversely proportional to the square of its diameter, d mm. Given the resistance of a wire 2.5 mm in diameter of a wire is 20 ohms. Find the diameter of a wire with a resistance of 31.25ohms.
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Step-by-step explanation:
Resistace is inversely proportional to the area of conductor ,so with the increasing of the diameter the value of resistance will be decrease. Resistance is inversely proportional to the square of the diameter of a wire. If diameter is doubled then resistance is reduced by 4 times.
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Answer:
R ∝ 1/d²
20=k/(2.5)²
20=k/6.25
k=20x6.25
k=125.
The diameter of a wire with resistance 31.25:
R ∝ 1/d²
31.25x100 = 3125
d²= 3125x125
d= √390625
d= ±625
(we add ± sign when we perform square root.)
(always turn decimal into whole numbers or else your answer is marked as incorrect.)
THIS ANSWER IS CORRECT, I GOT IT IN AN EXAM AND THE ANSWER WAS CORRECT.
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