In the given circuit, it is observed that the current I is independent of the value of the resistance R₆. Then the resistance values must satisfy

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$\frac{1}{R_{5}} + \frac{1}{R_{6}} = \frac{1}{R_{1} + R_{2}} + \frac{1}{R_{3} + R_{4}}$

$R_{1} R_{4} = R_{2} R_{3}$

$R_{1} R_{3} = R_{2} R_{4} = R_{5} R_{6}$

$R_{1} R_{2} R_{5} = R_{3} R_{4} R_{6}$

answer is C.

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Detailed Solution

As I is independent of R₆ , that is, no current flows through R₆ . This means that the junction of R₁ and R₂ is at the same potential as the junction of R₃ and R₄ . This must satisfy the condition $\frac{R_{1}}{R_{2}} = \frac{R_{3}}{R_{4}}$ as in the balanced condition of Wheatstone bridge.