A) \[{{R}_{1}}{{R}_{2}}{{R}_{5}}={{R}_{3}}{{R}_{4}}{{R}_{6}}\]
B) \[\frac{1}{{{R}_{5}}}+\frac{1}{{{R}_{6}}}\]\[=\frac{1}{{{R}_{1}}+{{R}_{2}}}+\frac{1}{{{R}_{3}}+{{R}_{4}}}\]
C) \[{{R}_{1}}{{R}_{4}}={{R}_{2}}{{R}_{3}}\]
D) \[{{R}_{1}}{{R}_{3}}={{R}_{2}}{{R}_{4}}={{R}_{5}}{{R}_{6}}\]
Correct Answer: C
Solution :
As I is independent of \[{{R}_{6}},\] no current flows through \[{{R}_{6}}\] this requires that the junction of \[{{R}_{1}}\] and \[{{R}_{2}}\] is at the same potential as the junction of \[{{R}_{3}}\] and \[{{R}_{4}}\]. This must satisfy the condition \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{R}_{3}}}{{{R}_{4}}},\] as in the Wheatstone bridge.
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