Balance condition in potential divider circuit

Steps:

• Uniform wire XY of length L has total PD V applied, so potential at J (distance x from X) is (x/L)V.
• R1 and R2 in series across same V, with R2 from low-potential end (X) to junction, R1 from junction to high-potential end (Y).
• Lamp off at null point: junction potential equals potential at J, so V2 = (x/L)V.
• Then V1 = V - V2 = V(L - x)/L.

Why D is correct:

• V1/V = (L - x)/L by voltage division at balance, where V = V1 + V2.

Why the others are wrong:

• A. V1 / L: Combines voltage and length; dimensionally inconsistent for a ratio.
• B. V2 / L: Same dimensional inconsistency as A.
• C. x / L: Equals V2/V, the fraction across R2, not R1.

Final answer: D