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

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Quizplus · Accepted Answer

The resistivity ($\rho$) of a material is given by the formula $\rho = R \frac{A}{L}$, where $R$ is the resistance, $A$ is the cross-sectional area, and $L$ is the length of the material. Here, $R = 0.040 \Omega$, $A = (1.5 \times 10^{-2} m)^2 = 2.25 \times 10^{-4} m^2$, and $L = 4.0 m$. Plugging these values into the formula gives $\rho = 0.040 \Omega \times \frac{2.25 \times 10^{-4} m^2}{4.0 m} = 2.25 \times 10^{-6} \Omega \cdot m$, which is closest to option D, $2.3 \times 10^{-6} \Omega \cdot m$.

A Rod Is 4