Resistivity: What must be the diameter of a cylindrical 120-m long metal wire if its resistance is to be 6.0 Ω? The resistivity of this metal is 1.68 × 10^-8 Ω ∙ m.

Question

Quizplus · Accepted Answer

The resistance (R) of a wire is given by the formula $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity, $L$ is the length, and $A$ is the cross-sectional area. For a cylindrical wire, $A = \pi r^2$, where $r$ is the radius. Rearranging the formula to solve for $r$, we get $r = \sqrt{\frac{R}{\rho \frac{L}{\pi}}}$. Substituting the given values ($R = 6.0 \Omega$, $\rho = 1.68 \times 10^{-8} \Omega \cdot m$, $L = 120 m$), we find $r$ and then double it to get the diameter. The correct calculation leads to a diameter close to 0.65 mm.

Resistivity: What Must Be the Diameter of a Cylindrical 120-M