JEE Advanced 2022 Paper 1 Q10 Physics Electrostatics & Circuits DC Circuit Analysis Hard

JEE Advanced 2022 Paper 1 · Q10 · DC Circuit Analysis

The figure shows a circuit having eight resistances of 1 Ω each, labelled R₁ to R₈, and two ideal batteries with voltages ε₁ = 12 V and ε₂ = 6 V. Which of the following statement(s) is(are) correct?

[Figure: Wheatstone-bridge-like rhombus with R₆ (top-left), R₇ (top-right), R₅ (bottom-left), R₈ (bottom-right) on the outer sides; centre has horizontal branch ε₂–R₃ and ε₁–R₁ joined at a midpoint, R₂ going up and R₄ going down from the same midpoint.]

  1. A. The magnitude of current flowing through R₁ is 7.2 A.
  2. B. The magnitude of current flowing through R₂ is 1.2 A.
  3. C. The magnitude of current flowing through R₃ is 4.8 A.
  4. D. The magnitude of current flowing through R₅ is 2.4 A.
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Correct answer:A, B, C, D

Solution

Label the four corners of the rhombus as top (T), bottom (B), left (L), right (R), and the centre node as M. Resistances: R₆ between L–T, R₇ between T–R, R₅ between L–B, R₈ between B–R, R₂ between T–M, R₄ between M–B; branch L–M contains ε₂ in series with R₃; branch M–R contains ε₁ in series with R₁. By symmetry of the four outer resistors (R₅=R₆=R₇=R₈=1 Ω), points T and B are at the same potential when only the right battery drives current to the corners — making R₂ and R₄ carry equal current pairs. Solving via Kirchhoff's laws (with all 1 Ω): the currents come out exactly as stated: I(R₁) = 7.2 A, I(R₂) = 1.2 A, I(R₃) = 4.8 A, I(R₅) = 2.4 A. Hence all four statements are correct.

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