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Mixed Combination of Cells

For a given c...

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 :

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

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

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

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

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Solution

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

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Similar questions

How to find the total resistance of an electric circuit if there is resistance R1 ,R2, R3, R4, R5 individualaly.

R_{1}, R_{3}

R_{5}

C_{1}, C_{2}, C_{3}, C_{4}, C_{5}

r_{1}, r_{2}, r_{3}, r_{4}, r_{5}

(r_{1} < r_{2} < r_{3} < r_{4} < r_{5})

C_{i}

C_{i} + 1

i = 1, 2, 3, 4

L_{1}

L_{2}

r_{1} = 2

r_{5} = 32

r_{3}

R \to P; r a t e = r_{1}

R A \to P; r a t e = r_{2}

R B \to P; r a t e = r_{3}

R C \to P; r a t e = r_{4}

R D - \to P; r a t e = r_{5}

R A + C - -- \to P; r a t e = r_{6}

R A + D - -- \to P; r a t e = r_{7}

r_{3} < r_{1} = r_{4} = r_{5} < r_{7} < r_{2} < r_{6},

r_{1} (r_{2} + r_{3}) / a = r_{2} (r_{3} + r_{1}) / b = r_{3} (r_{1} + r_{2}) / c

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