Symmetric cell configuration balances potentials at X and Y

Steps:

• Examine the circuit paths connecting X and Y through the identical cells.
• Apply Kirchhoff's current law at junction points to find branch currents.
• Use Kirchhoff's voltage law on loops: net emf equals IR drops, revealing balanced voltages.
• Conclude V_X equals V_Y due to identical emfs and resistances canceling differences.

Why A is correct:

• Kirchhoff's voltage law requires the algebraic sum of voltages in any closed loop to be zero, so the symmetric setup of identical cells ensures no net potential difference between X and Y.

Why the others are wrong:

• B: E applies to a single cell's emf, but X and Y span a balanced network, not one cell.
• C: 2E applies to two cells in aiding series, but the configuration opposes or parallels them.
• D: 3E applies to all three in aiding series, but the setup forms loops with zero net emf.

Final answer: A