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Wheatstone Bridge

In the given ...

Question

In the given circuit, it is observed that the current $I$ is independent of the value of resistance $R_{6}$ . Then the resistance values must satisfy the condition

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

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

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

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

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Solution

The correct option is C
$R_{1} R_{4} = R_{2} R_{3}$

We are given that the current is independent of the value of middle resistance $R_{6}$ means the Wheatstone bridge condition is satisfied.
Wheatstone bridge condition $\frac{R_{1}}{R_{2}} = \frac{R_{3}}{R_{4}}$
Therefore , $R_{1} R_{4} = R_{2} R_{3}$
So, the correct option is (C) $R_{1} R_{4} = R_{2} R_{3}$ .

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