A) \[6.67\,\Omega \]
B) \[60\,\Omega \]
C) \[120\,\Omega \]
D) \[180\,\Omega \]
Correct Answer: D
Solution :
Wire is stretched, therefore its volume remains unchanged \[\begin{align} & {{A}_{1}}{{l}_{1}}={{A}_{2}}{{l}_{2}} \\ & {{A}_{1}}l={{A}_{2}}\times 3l \\ & {{A}_{2}}=\frac{{{A}_{1}}}{3} \\ \end{align}\] Ratio of resistance\[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{l}_{1}}}{{{l}_{2}}}\times \frac{{{A}_{2}}}{{{A}_{1}}}\] \[=\frac{l}{3l}\times \frac{1}{3}=\frac{1}{9}\] \[\Rightarrow \] \[\begin{align} & \frac{20}{{{R}_{2}}}=\frac{1}{9} \\ & {{R}_{2}}=180\,\Omega \\ \end{align}\]
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