Balanced potential difference in the circuit

Steps:

• Galvanometer current of zero means the emf X equals the potential difference across one resistor.
• Total resistance is 6 Ω + 12 Ω = 18 Ω; current I = 18 V / 18 Ω = 1 A.
• Potential difference across 6 Ω resistor = 1 A × 6 Ω = 6 V.
• Therefore, X = 6 V.

Why A is correct:

• By Kirchhoff's voltage law, balance occurs when X matches the divided potential from the 18 V battery across the resistor ratio.

Why the others are wrong:

• B: 8.0 V assumes incorrect current or misapplied resistor values.
• C: 16 V results from subtracting resistances wrongly instead of using voltage division.
• D: 18 V takes the full battery emf without accounting for the partial drop.

Final answer: A