One hundred meters of $2.00 \mathrm{~mm}$ diameter wire has a resistance of $0.532 \Omega$. What is the resistivity of the material from which the wire is made?
A) $1.67 \times 10^{-8} \Omega \cdot \mathrm{m}$
B) $5.40 \times 10^{-8} \Omega \cdot \mathrm{m}$
C) $2.35 \times 10^{-8} \Omega \cdot \mathrm{m}$
D) $2.65 \times 10-8 \Omega \cdot \mathrm{m}$
E) $1.59 \times 10^{-8} \Omega \cdot \mathrm{m}$

Question

Quizplus · Accepted Answer

The resistivity ($\rho$) of a material 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 cross-sectional area $A$ of the wire, given its diameter is $2.00 \, \mathrm{mm}$ or $0.002 \, \mathrm{m}$, is $\pi r^2 = \pi (0.001)^2 = 3.14 \times 10^{-6} \, \mathrm{m}^2$. Plugging in the values: $\rho = 0.532 \, \Omega \times \frac{3.14 \times 10^{-6} \, \mathrm{m}^2}{100 \, \mathrm{m}} = 1.67 \times 10^{-8} \, \Omega \cdot \mathrm{m}$.

One Hundred Meters Of 2.00 mm2.00 \mathrm{~mm}2.00 mm Diameter Wire Has a Resistance Of

One Hundred Meters Of $2.00 \mathrm{~mm}$ Diameter Wire Has a Resistance Of