Voltage Division in Series Thermistor Circuit

Steps:

• Assume initial resistance of each thermistor is R.
• After change, X has resistance R/2, Y has 2R; total resistance = R/2 + 2R = 2.5R.
• Total emf E = 20 mV across series combination.
• V across X = [(R/2) / 2.5R] × 20 mV = (0.5R / 2.5R) × 20 = (1/5) × 20 = 4 mV.

Why A is correct:

• Potential divider rule: V_out = [R1 / (R1 + R2)] × E, where R1 = R/2 (X), R2 = 2R (Y), yielding exactly 4 mV.

Why the others are wrong:

• B: 5 mV misapplies fraction, e.g., using (R/2 + R) total incorrectly.
• C: 15 mV confuses with initial 10 mV plus wrong change.
• D: 16 mV is voltage across Y, not X.

Final answer: A