A) \[4\,\Omega \] when the resistance of wire \[A\] is \[4.25\,\Omega \]
B) \[5\,\Omega \] when the resistance of wire \[A\] is \[4.25\,\Omega \]
C) \[4\,\Omega \] when the resistance of wire \[B\] is \[4.25\,\Omega \]
D) \[4\,\Omega \] when the resistance of wire \[B\] is \[4.25\,\Omega \]
Correct Answer: A
Solution :
\[\frac{{{R}_{A}}}{{{R}_{B}}}={{\left( \frac{{{r}_{B}}}{{{r}_{A}}} \right)}^{4}}\] Þ \[\frac{{{R}_{A}}}{{{R}_{B}}}={{\left( \frac{1}{2} \right)}^{4}}=\frac{1}{16}\] Þ \[{{R}_{B}}=16{{R}_{A}}\] When RA and RB are connected in parallel then equivalent resistance \[{{R}_{eq}}=\frac{{{R}_{A}}{{R}_{B}}}{({{R}_{A}}+{{R}_{B}})}=\frac{16}{17}{{R}_{A}}\] If \[{{R}_{A}}=4.25\Omega \] then \[{{R}_{eq}}=4\Omega \] i.e. option is correct.
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