A) \[\frac{3}{5}\,\Omega \]
B) \[2\,\Omega \]
C) \[\frac{6}{5}\,\Omega \]
D) \[3\,\Omega \]
Correct Answer: D
Solution :
Let\[{{R}_{1}}\]and\[{{R}_{2}}\]be the resistances of two wires. In parallel combination, \[\frac{{{R}_{1}}{{R}_{2}}}{{{R}_{1}}+{{R}_{2}}}=\frac{6}{5}\] ? (i) If one of the wires breaks, then effective resistance becomes\[2\Omega \], that is,\[{{R}_{1}}=2\Omega \] Substituting in Eq. (i), we have \[\frac{2{{R}_{2}}}{2+{{R}_{2}}}=\frac{6}{5}\] or \[10{{R}_{2}}=12+{{R}_{2}}\] or \[4{{R}_{2}}=12\] \[\therefore \] \[{{R}_{2}}=\frac{12}{4}=3\Omega \]
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