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Mnenie [13.5K]
4 years ago
14

Electrical Resistance The electrical resistance R of a wire varies inversely with the square of its diameter d. If a 25-foot wir

e with a diameter of 2 millimeters has a resistance of 0.5 ohm, find the resistance of a wire having the same length and a diameter of 3 millimeters.
Mathematics
1 answer:
kati45 [8]4 years ago
8 0

Answer:

The answer is below

Step-by-step explanation:

The electrical resistance R of a wire varies inversely with the square of its diameter d:

R ∝ 1 / d

Let k represent the constant of proportionality, hence we can represent the statement as an equation:

R=\frac{k}{d^2}\\ \\when\ R=0.5 \Omega,d=2\ mm\\\\0.5=\frac{k}{2^2} \\\\k=2\\\\The\ equation\ becomes :\\\\R=\frac{2}{d^2}\\ \\When\ d=3, we\ find\ R\\\\R=\frac{2}{3^2} \\\\R=0.22\ \Omega

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