Resistivity: A 2.0 mm diameter wire of length 20 m has a resistance of 0.25 Ω. What is the resistivity of the wire?

Question

Quizplus · Accepted Answer

The resistivity ($\rho$) can be calculated using the formula $\rho = R\frac{A}{L}$, where $R$ is the resistance, $A$ is the cross-sectional area of the wire, and $L$ is the length of the wire. The area $A$ of a wire with a diameter of 2.0 mm (or 0.002 m) is $\pi r^2 = \pi (0.001)^2 = 3.14 \times 10^{-6} m^2$. Plugging in the values: $\rho = 0.25 \frac{3.14 \times 10^{-6} m^2}{20 m} = 3.925 \times 10^{-8} \Omega \cdot m$, which rounds to $3.9 \times 10^{-8} \Omega \cdot m$.

Resistivity: a 2