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Two ideal cells of emf V1 and V2 together with three resistors R1, R2 and R3 are wired as in the figure (V1 with R1 in one branch, V2 with R3 in another, and R2 in the middle branch). For what condition is the current through R2 exactly zero? [JEE Advanced 2014]

1. V1 = V2 and R1 = R2 = R3
2. V1 = V2 and R1 = 2R2 = R3
3. V1 = 2V2 and 2R1 = 2R2 = R3
4. 2V1 = V2 and 2R1 = R2 = R3

Correct answer: V1 = V2 and R1 = 2R2 = R3

Solution

With I2 = 0, the junction potentials at both ends of R2 must be equal; balancing the bridge-like network gives V1 = V2 with the symmetric resistance condition.

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