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 25 foot length, with diameter 0.01 inch, of the same kind of wire ?
A) 368 ohms
B) 372.5 ohms
C) 375 ohms
D) 387 ohms

Question

Quizplus · Accepted Answer

The resistance $R$ of a wire varies directly as the length $L$ of the wire and inversely as the square of the diameter $d$ of the wire, which can be represented by the formula $R = k \cdot \frac{L}{d^2}$, where $k$ is a constant. Given a 20-foot length of wire with a diameter of 0.1 inch has a resistance of 3 ohms, we can find $k$ by substituting these values into the formula: $3 = k \cdot \frac{20}{(0.1)^2}$. Solving for $k$ gives $k = 0.15$. For a 25-foot length of wire with a diameter of 0.01 inch, the resistance $R$ can be found by substituting these values and the found $k$ into the formula: $R = 0.15 \cdot \frac{25}{(0.01)^2}$, which calculates to 375 ohms.

Round to the Nearest Tenth Unless Indicated Otherwise