A-LevelPhysicsElectricity9702/42 · May/June 2019 · Q710 Marks

Use band theory to explain why the resistance of an intrinsic semiconductor decreases as its temperature rises.

(a)Use band theory to explain why the resistance of an intrinsic semiconductor decreases as its temperature rises.[5]
(b)The variation with temperature t of the resistance R of a thermistor is shown in Fig. 7.1. The thermistor is connected into the circuit shown in Fig. 7.2. The battery has electromotive force (e.m.f.) 9.00 V and negligible internal resistance. When the temperature of the thermistor is 25°C, the potential difference between the terminals A and B is 1.00 V. The temperature of the thermistor changes from 25°C to 10°C. Determine, to two significant figures, the change in potential difference between A and B. change = ................................................................ V[3]
(c)The temperature of the thermistor in (b) changes from 25°C to 10°C at a constant rate. State two reasons why the potential difference between A and B does not change at a constant rate. 1. 2.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

7(a) Any five from: B5 • (as temperature rises) energy of electrons increases • electrons (have enough energy to) cross forbidden band • electrons enter conduction band • leaving holes in valence band • both holes and electrons act as charge carriers • more charge carriers results in lower resistance • increased lattice vibrations outweighed by increase in (number of) charge carriers
7(b) (at 10 °C resistance is) 2.55 ΚΩ C1 new potential difference = 9.00 × 2.55 / (2.55 + 12.0) C1 = 1.58 V change in p.d. = 0.58 V A1
7(c) change of resistance with temperature is not linear B1 change in potential with resistance is not linear B1 or potential divider equation is non-linear

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