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A skeletal hexagonal prism has all wires on the front and back hexagonal faces with resistance R each, and all 12 wires joining corresponding vertices of the two hexagons with resistance 2R each. A battery is connected between vertices P and Q, where front face vertices are labelled P, Z, O, Q, X, Y (in order) and back face vertices are labelled U, T, S, R, W, V (in order), with P connected to U, Z to T, O to S, Q to R, X to W, and Y to V. Which of the following statements are correct?

1. Current through VY and TZ is zero.
2. Current through PZ and QX are equal in magnitude.
3. Current through OS and YV are equal in magnitude.
4. Equivalent resistance across PQ is 23R/20.

Correct answer: Current through VY and TZ is zero.

Solution

By the bilateral symmetry of the network about the plane bisecting PQ, nodes V and Y are at the same potential, and similarly T and Z, so no current flows through VY or TZ. Options A, B, and C follow from symmetry; option A is the most directly verifiable.

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