A) 3 \[\Omega \]
B) 1.5 \[\Omega \]
C) 4.5 \[\Omega \]
D) 6.0 \[\Omega \]
Correct Answer: D
Solution :
Resistance of a conductor is directly proportional to ifs length and inversely proportional to its area. \[R\propto \frac{1}{A}\] \[\therefore \] \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{A}_{2}}}{{{A}_{1}}}\] \[\frac{{{R}_{A}}}{{{R}_{B}}}=\frac{\pi r_{B}^{2}}{\pi r_{A}^{2}}=\frac{r_{B}^{2}}{r_{A}^{2}}=\frac{{{(2{{r}_{B}})}^{2}}}{{{(2{{\pi }_{A}})}^{2}}}\] \[\frac{{{R}_{A}}}{{{R}_{B}}}=\frac{{{(2{{r}_{B}})}^{2}}}{\left( \frac{2{{\pi }_{B}}^{2}}{2} \right)}=\frac{4r_{B}^{2}}{r_{B}^{2}}\] \[\frac{24}{{{R}_{B}}}=\frac{4}{1}\] \[{{R}_{B}}=6\,\,\Omega \]
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