First slide

combination of resistance

Question

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

Moderate

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

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

Solution

As I is independent of R₆, no current flows through R₆. This requires 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 Wheatstone bridge.

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