An NTC thermistor has (temperature in °C, resistance in kΩ) values (10, 8.1), (20, 5.4), (30, 3.7), (40, 2.6), (50, 1.9), (60, 1.4). It is series with 3.3 kΩ across 6.0 V; output is across the fixed resistor. (a) Find output at 20 °C and 50 °C. (b) Explain sensitivity direction. (c) Estimate trigger temperature for 3.5 V. (d) Explain voltmeter loading and a comparator improvement.

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Outputs 2.28 V and 3.81 V; output rises with temperature; 3.5 V corresponds to about 43.4 °C. Vout = VsRfixed/(Rfixed + Rthermistor). At 20 °C, Vout = 6.0 × 3.3/(3.3 + 5.4) = 2.28 V. At 50 °C, Vout = 6.0 × 3.3/(3.3 + 1.9) = 3.81 V. NTC resistance falls as temperature rises, increasing fixed-resistor voltage share. At 3.5 V, solve 3.5/6.0 = 3.3/(3.3 + R), giving R = 2.36 kΩ. Interpolate between 2.6 kΩ at 40 °C and 1.9 kΩ at 50 °C: T ≈40 + (2.6 − 2.36)/(2.6 − 1.9) × 10 = 43.4 °C. A finite voltmeter lies parallel with 3.3 kΩ and changes the divider. A high-input-resistance comparator with adjustable reference and hysteresis produces a sharper, stable switch.

Thermistor divider alarm

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NTC calibration

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NTC calibration — supplied values
Temperature / °C	Resistance / kΩ
10	8.1
20	5.4
30	3.7
40	2.6
50	1.9
60	1.4