A) \[2\,\,\Omega \]
B) \[3\,\,\Omega \]
C) \[6\,\,\Omega \]
D) \[1\,\,\Omega \]
Correct Answer: B
Solution :
[b] Key Idea: The bridge formed with given resistances is a balanced Wheatstone's bridge. The situation can be depicted as shown in figure. |
As resistances S and \[6\,\,\Omega \] are in parallel their effective resistance is |
\[\frac{6S}{6+S}\,\Omega \] |
As the bridge is balanced, hence it is balanced Wheatstone's bridge. |
For balancing condition, |
\[\frac{P}{Q}=\frac{R}{\left( \frac{6S}{6+S} \right)}\] |
or \[\frac{2}{2}=\frac{2(6+S)}{6S}\] |
or \[3\,S=6+S\] |
or \[S=3\,\Omega \] |
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