Q.
In the given circuit shown in figure it is observed that the current$\ i$ is independent of the value of resistance $R_{6}.$ Then the resistance values must satisfy
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) $R_{1}R_{3} = R_{2}R_{4} = R_{5}R_{6}$
Explanation
(c) Since current $i$ is independent of the value of $R_{6}$, it is clear that the circuit is of a balanced Wheatstone bridge. As per condition of balance, we have
$\frac{R_{1}}{R_{3}} = \frac{R_{2}}{R_{4}}\ \Rightarrow \ R_{1}R_{4} = R_{2}R_{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.