A) \[{{R}_{1}}=3\Omega ,{{R}_{2}}=3\Omega \]
B) \[{{R}_{1}}=6\Omega ,{{R}_{2}}=1.5\Omega \]
C) \[{{R}_{1}}=1.5\Omega ,{{R}_{2}}=\text{any}\,\text{finite}\,\text{value}\]
D) \[{{R}_{1}}=3\Omega ,{{R}_{2}}=\text{any}\,\text{finite}\,\text{value}\]
Correct Answer: D
Solution :
Key Idea: Given circuit is a balanced Wheatstone's bridge. The ratio of resistances in the opposite arms of the circuit is equal i.e., \[\frac{10}{30}=\frac{{{R}_{1}}}{9}\] \[\Rightarrow \] \[{{R}_{1}}=3\Omega \] and resistance \[{{R}_{2}}\]may have any finite value.
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