Potentiometer balancing length inversely proportional to driving cell's emf Steps:

• In this setup, each cell drives the potentiometer; balance is found using a standard emf E_s across length l.
• Potential gradient k = E_cell / total wire length L; at balance, E_s = k × l, so E_cell = E_s × (L / l).
• Thus, E_cell ∝ 1/l; smaller l means larger E_cell.
• For cell X (l=44 cm), E_X > E_Y (l=70 cm); emfs depend on E_s and L, unknown here.

Why C is correct:

• No information on E_s, L, or driving setup; emfs could exceed 6V if E_s >6V or L small (E_cell = E_s L / l).

Why the others are wrong:

• A: Correct—at balance, main circuit current flows through R and wire but nulls galvanometer (no current).
• B: Correct—shorter l for X (44 cm vs. 70 cm) means larger E_X than E_Y per E ∝ 1/l.
• D: Correct—when investigating X, current flows through X-R-wire circuit; Y is uninvolved (no current through Y).

Final answer: C