A2 Daily A Level Physics question
Which statement must be true when an NTC thermistor in a potential divider warms up? A 9.0 V supply feeds a series pair: a fixed 4.0 kΩ resistor R and an NTC thermistor T that is 4.0 kΩ at 25 °C. The output V_out is measured across R. As T warms, its resistance halves. Decide what happens to V_out and justify using fraction reasoning and the hot-limit check (T ≪ R).
Answer
The correct answer is B.
Correct: B — B. V_out increases from 4.5 V to about 6.0 V, because with T halved the fraction R/(R+T) rises from 1/2 to 2/3. Starting from 4.5 V (9 × 4.0k/(4.0k+4.0k)), halving T to 2.0 kΩ gives V_out = 9 × 4.0k/(4.0k+2.0k) = 6.0 V; the hot-limit T ≪ R would push V_out toward 9 V, confirming the increase. A confuses which element is measured: lowering T reduces its own drop and increases the share across R, so V_out should not decrease; the hot-limit T ≪ R would make V_out approach 9 V, not 3.0 V. B is correct for both ratio arithmetic and the limiting-case check. C assumes equal splitting in series regardless of resistance; equal halves only occur when R = T (4.0 kΩ each), so once T halves the split changes. D overestimates the effect by assuming the current nearly doubles; in fact I rises from 9/8.0k to 9/6.0k (a factor 1.33), so V_R increases to about 6.0 V, not to ~7.5 V or near 9 V.