Question

For a given circuit, it is observed that the current $I$ is independent of the value of the resistance $R_6$. Then, the resistance values must satisfy

• A. $R_2R_3 = R_1 R_4$
• B. $R_3 R_4R_6 = R_2R_1R_5$
• C. $\frac{1}{R_{3}+R_{4} } = \frac{1}{R_{5}}+\frac{1}{R_{6}} - \frac{1}{ R_{1}+R_{2}}$
• D. $R_3R_1 = R_2R_4 = R_5R_6$

Answer 1

Answer: (A)

$R_2R_3 = R_1 R_4$

Answer 2

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.