Circuit Configuration Determines Potential Difference Steps:

• Identify the setup: three identical cells (emf E, negligible internal resistance) each connected in series with one identical resistor (resistance R), forming three parallel branches.
• In each branch, the cell drives current through its resistor alone.
• Apply Kirchhoff's voltage law: the potential difference across the resistor equals the emf E, as no other voltage drops occur.
• Thus, the potential difference across any one resistor is E.

Why B is correct:

• The emf E is the open-circuit voltage of the cell, which equals the potential difference across the resistor in a simple series connection with negligible internal resistance (Ohm's law: V = IR, but V = E total).

Why the others are wrong:

• A: 0 implies no voltage source or complete short circuit, not the case here.
• C: 2E/3 suggests voltage division across multiple cells, but each resistor sees one cell.
• D: Duplicate of B (both E), but B is specified as correct.

Final answer: B