A rod is $4.0 \mathrm {~m}$ long and has a square cross-section that is $1.5 \mathrm {~cm}$ on each side. An ohmmeter measures $0.040 \Omega$ across its ends. What is the resistivity of the material from which this rod is made?
A) $0.015 \Omega \cdot \mathrm { m }$
B) $2.3 \times 10 ^ { - 6 } \Omega \cdot \mathrm { m }$
C) $0.023 \Omega \cdot \mathrm { m }$
D) $1.5 \times 10 ^ { - 4 } \Omega \cdot \mathrm { m }$

Question

Quizplus · Accepted Answer

The resistivity ($\rho$) of the material can be calculated using the formula $\rho = R \cdot \frac{A}{L}$, where $R$ is the resistance, $A$ is the cross-sectional area, and $L$ is the length of the rod. Here, $R = 0.040 \Omega$, $A = (1.5 \times 10^{-2} \mathrm{m})^2 = 2.25 \times 10^{-4} \mathrm{m}^2$, and $L = 4.0 \mathrm{m}$. Plugging these values into the formula gives $\rho = 0.040 \Omega \cdot \frac{2.25 \times 10^{-4} \mathrm{m}^2}{4.0 \mathrm{m}} = 2.3 \times 10^{-6} \Omega \cdot \mathrm{m}$.

A Rod Is 4.0 m4.0 \mathrm {~m}4.0 m Long and Has a Square Cross-Section That Is

A Rod Is $4.0 \mathrm {~m}$ Long and Has a Square Cross-Section That Is