Equal ammeter currents require symmetric resistance paths

Steps:

• Identify setup: Battery supplies voltage across two terminals; ammeters measure currents in the other two output paths.
• Apply Kirchhoff's current law: Total current from battery splits into the two ammeter paths.
• For identical currents, resistance in each path must be equal, ensuring symmetric division.
• Test circuits: Only symmetric configuration yields equal splits.

Why D is correct:

• In D, resistors form a balanced Wheatstone bridge, where equal ratios (R1/R2 = R3/R4) make galvanometer current zero, splitting battery current equally per Kirchhoff's law.

Why the others are wrong:

• A: Series resistors create single path; one ammeter reads zero.
• B: Unbalanced parallel paths divide current unequally due to different resistances.
• C: Asymmetric bridge causes unequal current splits from imbalanced ratios.

Final answer: D