How long is a wire made from 100 cm³ of copper if its resistance is 4.0 ohms? The resistivity of copper is 1.7 × 10^-5 Ω·m. A)4.9 m B)1.7 × 10² m C)2.6 × 10² m D)1.5 × 10³ m E)24 m

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Quizplus · Accepted Answer

The resistance $R$ of a wire is given by $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity, $L$ is the length, and $A$ is the cross-sectional area. Rearranging for $L$, we get $L = \frac{RA}{\rho}$. Given $R = 4.0 \, \Omega$, $\rho = 1.7 \times 10^{-5} \, \Omega \cdot m$, and $A = 100 \, cm^2 = 100 \times 10^{-4} \, m^2 = 10^{-2} \, m^2$, we find $L = \frac{4.0 \times 10^{-2}}{1.7 \times 10^{-5}} \, m \approx 4.9 \, m$.

How Long Is a Wire Made from 100 Cm3 of Copper

How Long Is a Wire Made from 100 Cm³ of Copper