Solve the problem. Round to the nearest tenth unless indicated otherwise.
-The resistance of a wire varies directly as the length of the wire and inversely as the square of the diameter of the wire. A 20 foot length of wire with a diameter of 0.1 inch has a resistance of
3 ohms. What would the resistance be for a 48 foot length, with diameter 0.01 inch, of the same
Kind of wire ?
A) 720 ohms
B) 717.5 ohms
C) 713 ohms
D) 732 ohms

Question

Quizplus · Accepted Answer

The resistance $R$ of a wire can be expressed as $R = k \cdot \frac{L}{d^2}$, where $L$ is the length, $d$ is the diameter, and $k$ is a constant. Given $R = 3$ ohms for $L = 20$ feet and $d = 0.1$ inch, we can find $k$ and then use it to find the resistance of the wire when $L = 48$ feet and $d = 0.01$ inch. The resistance increases with length and decreases with the square of the diameter. Calculating for the new conditions, the resistance is $720$ ohms.

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