AS Daily A Level Physics question
A potential divider is used to sense temperature: a 6.0 kΩ fixed resistor is in series with an NTC thermistor. The supply is 9.0 V, and the output V_out is taken across the fixed resistor. The thermistor’s resistance falls from 8.0 kΩ at 20°C to 4.0 kΩ at 30°C. As the temperature rises from 20°C to 30°C, what happens to V_out?
Answer
The correct answer is D.
Correct: D — It increases by about 40%. Using the divider ratio across the fixed resistor: at 20°C, V_out = 9 × 6/(6+8) ≈ 3.86 V; at 30°C, V_out = 9 × 6/(6+4) = 5.40 V, which is a 40% increase. A uses the voltage across the thermistor instead of across the fixed resistor, which would indeed fall from about 5.14 V to 3.60 V (≈30% decrease). B calculates the percentage change relative to the final value (1.54/5.40 ≈ 28.6%) rather than relative to the initial value. C assumes an overly large change by treating the halving of the thermistor resistance as giving a much bigger rise in V_out, ignoring the series fixed resistor’s limiting effect.