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A cylindrical copper rod has length $\mathrm{L}$ and resistance $\mathrm{R}$. If it is melted and formed into another rod of length $2 \mathrm{~L}$, the resistance will be
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Verified Answer
The correct answer is:
$4 \mathrm{R}$
Applying volume conservation
$\begin{array}{l}
\mathrm{A} \times \mathrm{L}=\mathrm{A}^{\prime} \times 2 \mathrm{~L} \\
\mathrm{~A}^{\prime}=\frac{\mathrm{A}}{2} \\
\mathrm{R}=\frac{\rho \mathrm{L}}{\mathrm{A}} \\
\mathrm{R}^{\prime}=\frac{\rho \times 2 \mathrm{~L}}{\mathrm{~A}^{\prime}}=\frac{\rho \times 4 \mathrm{~L}}{\mathrm{~A}} \\
\mathrm{R}^{\prime}=4 \mathrm{R}
\end{array}$
$\begin{array}{l}
\mathrm{A} \times \mathrm{L}=\mathrm{A}^{\prime} \times 2 \mathrm{~L} \\
\mathrm{~A}^{\prime}=\frac{\mathrm{A}}{2} \\
\mathrm{R}=\frac{\rho \mathrm{L}}{\mathrm{A}} \\
\mathrm{R}^{\prime}=\frac{\rho \times 2 \mathrm{~L}}{\mathrm{~A}^{\prime}}=\frac{\rho \times 4 \mathrm{~L}}{\mathrm{~A}} \\
\mathrm{R}^{\prime}=4 \mathrm{R}
\end{array}$
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