Potentiometer balancing lengths proportional to potential differences Steps: - Current I = ε / 30 Ω through series cell M (emf ε) and resistors 5 Ω + 10 Ω + 15 Ω. - p.d. M to Q across 5 Ω = (5/30)ε = ε/6, balances at l = 12.5 cm, so 1 part = 12.5 cm (proportionality constant). - p.d. P to R across 5 Ω + 10 Ω = 15/30 ε = ε/2 = 3 parts, l = 3 × 12.5 = 37.5 cm. - p.d. Q to S across 10 Ω + 15 Ω = 25/30 ε = 5ε/6 = 5 parts, l = 5 × 12.5 = 62.5 cm. Why B is correct: - Option B matches calculated lengths (e.g., 37.5 cm for P-R across 15 Ω, 62.5 cm for Q-S across 25 Ω) using resistance ratios in series circuit. Why the others are wrong: - A: Incorrect lengths (e.g., 50 cm for P-R) mismatch 3:1 ratio for 15 Ω section. - C: Swaps values (e.g., 75.0 cm for P-R) violating drop proportions. - D: Lists inconsistent …