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JEE Main 2024 (4 Apr, Shift 1) · Combination of Resistors

Combination of Resistors question from JEE Main 2024 (4 Apr, Shift 1)

Q27JEE Main 2024 · 4 APR · SHIFT 1Difficult

Combination of Resistors

Twelve wires each having resistance $2\ \Omega$ are joined to form a cube. A battery of $6\text{ V}$ emf is joined across point $a$ and $c$ . The voltage difference between $e$ and $f$ is ________ V.

Numerical answer type. Work it out, then open the answer.

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Answer: 1

Battery across face diagonal a–c: take $V_a = 6$ , $V_c = 0$ . By symmetry b, d, e, g are all at $3$ V; let $V_h = y$ and $V_f = 6 - y$ .
KCL at h (neighbours a, e, g; equal resistances): $(y - 6) + (y - 3) + (y - 3) = 0 \Rightarrow y = 4$ V, so $V_f = 2$ V.
$V_e - V_f = 3 - 2 = 1$ V

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