A) \[25.2\,\Omega \]
B) \[0.6\,\Omega \]
C) \[26.7\,\Omega \]
D) \[0.8\,\Omega \]
Correct Answer: A
Solution :
\[R=\rho \frac{l}{A}\] Given,\[{{R}_{1}}=4.2\,\Omega ,{{l}_{1}}=1m,{{A}_{1}}=\pi r_{1}^{2}=\pi {{\left( \frac{0.31}{2} \right)}^{2}}\] \[{{R}_{2}}=?,{{l}_{2}}=1.5,{{A}_{2}}=\pi r_{2}^{2}=\pi {{\left( \frac{0.155}{2} \right)}^{2}}\] \[\therefore \] \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{l}_{1}}}{{{A}_{1}}}\times \frac{{{A}_{2}}}{{{l}_{2}}}\] \[=\frac{4.2}{R}=\frac{1}{\pi {{(0.31)}^{2}}}\times \frac{\pi {{(0.155)}^{2}}}{1.5}\] \[\Rightarrow \] \[R=\frac{4.2\times 0.31\times 0.31\times 1.5}{0.155\times 0.155}=25.2\,\Omega \]
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