Worked solution
(a) The fan must switch on (F=1) only when BOTH T=1 and D=1; in every other combination it must stay off (F=0). Completed table: T=0,D=0 -> F=0; T=0,D=1 -> F=0; T=1,D=0 -> F=0; T=1,D=1 -> F=1. (b) This truth table (output is 1 only when both inputs are 1) is the definition of the AND function, so the required gate is an AND gate, with Boolean expression F = T · D (equivalently written F = T AND D). (c) A single npn transistor has a current gain (hFE) typically in the range of perhaps 50-300, meaning the maximum collector current it can switch is hFE multiplied by the (small) base current the logic gate can supply — for a very small logic-level base current, this may still not be enough to fully switch on (saturate) a transistor driving a real motor's operating current. A Darlington pair consists of two transistors connected so that the emitter current of the first transistor becomes the base current of the second; its overall current gain is approximately the product of the two individual gains (hFE(total) ≈ hFE1 × hFE2), which can be several thousand. This means a very small logic-level base current into the first transistor can control a much larger collector current through the second transistor, making it far better suited to switching a motor's higher operating current from a low-current logic gate output than a single transistor would be. (d) Design description: the AND gate's output (5 V logic level, low current) connects through a base resistor (e.g. approximately 1 kΩ, its value chosen to limit the base current of the transistor to a safe level while still ensuring the transistor is driven into saturation) to the base of an npn transistor (or, given the current requirement discussed in part (c), the base of a Darlington pair). The transistor's emitter is connected to 0 V (common ground with the logic circuit), and its collector is connected to one terminal of the 12 V fan motor, with the motor's other terminal connected to the separate +12 V supply rail — this arrangement allows the low-voltage, low-current logic signal to switch the higher-voltage, higher-current motor circuit safely, since the transistor's collector-emitter path, not the logic gate, carries the motor current. A protection (flyback) diode is connected directly across the motor terminals, with its cathode toward the +12 V rail, so that it is reverse-biased and does not conduct during normal operation; when the transistor switches off and the motor's current suddenly stops, the diode provides a safe path for the back-EMF voltage spike generated by the motor's inductive coil, protecting the transistor from being damaged by this voltage spike. Answer: (a) F = 0,0,0,1; (b) AND gate, F = T·D; (c) a Darlington pair's much higher combined current gain (hFE1 x hFE2) lets a small logic current switch the motor's larger current; (d) base resistor limits base current into the transistor, the transistor's collector-emitter path switches the 12V motor circuit, and a flyback diode across the motor protects the transistor from back-EMF.
Marking scheme
(a) [4]: 1 mark per correct output row, to a maximum of 4. (b) [3]: [1] AND gate correctly named; [2] correct Boolean expression F = T·D (or F = T AND D; accept F = TD). (c) [4]: [1-2] correct explanation that hFE is the current gain, and a single transistor's available current may be insufficient for the motor; [1-2] correct explanation that a Darlington pair's gain is approximately the product of its two transistors' gains (hFE1 x hFE2), giving much greater amplification suited to driving the motor from a small logic current. (d) [9], 3-tier Level-of-Response: Level 1 (1-3 marks) — basic circuit idea (e.g. 'a transistor switches the motor') with components missing or unexplained, minimal technical vocabulary. Level 2 (4-6 marks) — most required components present (base resistor, transistor, protection diode) with a reasonable explanation of function, though possibly with an omission or minor inaccuracy (e.g. diode orientation not stated). Level 3 (7-9 marks) — all required components present and correctly explained: base resistor (limiting/setting base current), transistor correctly connected to switch the motor's higher-current circuit, and a flyback/protection diode correctly placed across the motor in reverse bias to protect the transistor from back-EMF; clear, fluent, well-organised technical description throughout.