You have a piece of copper wire and a piece of carbon rod, each (1.5 mathrm{~m}) long

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You have a piece of copper wire and a piece of carbon rod, each \(1.5 \mathrm{~m}\) long and each having a cross-sectional area of \(8.0 \times 10^{-6} \mathrm{~m}^{2}\). When you connect the copper wire to the terminals of a \(9.0-\mathrm{V}\) battery, the current in the wire is \(I\). If you want to connect the carbon rod to another battery and have the same current \(I\) in the wire, what must the potential difference of the battery be \(\left[\sigma_{\text {copper }}=5.9 \times 10^{7} \mathrm{~A} /(\mathrm{V} \cdot \mathrm{m})\right.\), \(\left.\sigma_{\text {carbon }}=7.3 \times 10^{4} \mathrm{~A} /(\mathrm{V} \cdot \mathrm{m})\right]\) ?

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