Copper wire #1 has a length $L$ and a radius $b$. Copper wire #2 has a length $2 L$ and a radius $2 b$. Which statement about the resistance across the ends of the wires is true?

Question

Quizplus · Accepted Answer

The resistance $R$ of a wire is given by $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity (constant for the same material), $L$ is the length, and $A$ is the cross-sectional area. For wire #2, the length is doubled ($2L$) and the radius is doubled ($2b$), so the area ($\pi r^2$) is quadrupled ($4\pi b^2$). Thus, the resistance of wire #2 is $R_2 = \rho \frac{2L}{4\pi b^2} = \frac{1}{2} \rho \frac{L}{\pi b^2}$, which is half the resistance of wire #1, making wire #1's resistance twice as high as wire #2's.

Copper Wire #1 Has a Length LLL And a Radius bbb Copper Wire #2 Has a Length

Copper Wire #1 Has a Length $L$ And a Radius $b$ Copper Wire #2 Has a Length