Potentiometer balancing lengths proportional to potential differences across resistors in series

Steps:

• In the potentiometer setup, the balancing length for the potential difference across R1 is 60 cm from one end.
• The balancing length for the total potential difference across R1 + R2 is 80 cm from the same end.
• The balancing length for R2 is the difference: 80 cm - 60 cm = 20 cm.
• Since potential difference V ∝ balancing length l (uniform wire), R1 / R2 = V1 / V2 = 60 / 20 = 3 / 1.

Why A is correct:

• The ratio follows from V = IR and V ∝ l in potentiometer, so R1 / R2 = l1 / l2 = 60 / 20 = 3 / 1.

Why the others are wrong:

• B: 4/3 assumes direct 80/60 ratio, ignoring the total length interpretation.
• C: 1/3 reverses the 3/1 ratio without basis.
• D: 3/4 assumes direct 60/80 ratio for R1/R2, missing the subtractive step for series resistors.

Final answer: A