If the input to a full-wave rectifier has a frequency of 50 Hz, the ripple frequency of its output will be:

The correct answer is B, decreases. A semiconductor has a small forbidden energy gap, so heating supplies thermal energy that pushes more electrons from the valence band into the conduction band, creating more electron-hole pairs. More charge carriers mean higher conductivity, and therefore lower resistance, which is why a semiconductor is said to have a negative temperature coefficient of resistance. Option A is wrong because resistance rises with temperature in metals, where the carriers are already free and increased lattice vibration merely obstructs them; students apply the metallic rule here by mistake. Option C is wrong because the resistance change in a semiconductor is in fact large and is used in thermistors. Option D is wrong because the resistance never becomes zero; it falls steadily but a semiconductor does not become a superconductor on heating.

The correct answer is C, arsenic. An n-type semiconductor is made by doping with a pentavalent element, that is one with five valence electrons, such as phosphorus, arsenic, antimony or bismuth. Four of the five electrons form covalent bonds with neighbouring silicon atoms and the fifth is left almost free, so the impurity acts as a donor and electrons become the majority carriers. Option A is wrong because boron is trivalent and gives p-type material. Option B is wrong because indium is also trivalent and is a classic acceptor impurity. Option D is wrong for the same reason, as gallium has three valence electrons. The memory aid is that pentavalent means donor and n-type, while trivalent means acceptor and p-type, and the doped crystal stays electrically neutral in both cases.

The correct answer is B, holes. A p-type semiconductor is made by adding a trivalent impurity such as boron, aluminium, gallium or indium. Because the impurity atom has only three valence electrons, one covalent bond is left incomplete and a vacancy called a hole is created; the impurity therefore acts as an acceptor and holes are the majority carriers, while the few thermally generated electrons are the minority carriers. Option A is wrong because electrons are the majority carriers in n-type material, not p-type. Option C is wrong because protons are bound in the nuclei and never act as charge carriers in a solid. Option D is wrong because the acceptor ions are fixed in the crystal lattice and cannot move, so they carry no current even though they are negatively charged.

The correct answer is B, about 1.1 eV. Silicon is the most widely used semiconductor and its forbidden energy gap, the separation between the top of the valence band and the bottom of the conduction band, is about 1.1 electron volts at room temperature. Option A is wrong because 0.7 electron volts is the band gap of germanium, the other elemental semiconductor, and the two values are the pair most often swapped in examinations. Option C is wrong because a gap of that size belongs to a wide band gap material rather than to silicon. Option D is wrong because 5.5 electron volts is the band gap of diamond, which is quoted as the standard example of an insulator. Gallium arsenide, for comparison, has a gap of about 1.43 electron volts.

The correct answer is A, rectifier. A p-n junction conducts freely in forward bias, where the potential barrier is reduced, and blocks current in reverse bias, where only a tiny leakage current flows. This one-way conduction is exactly what is needed to turn alternating current into direct current, so the diode's main use is as a rectifier, in half-wave, full-wave or bridge arrangements. Option B is wrong because amplification needs a three-terminal device such as a transistor; a two-terminal diode cannot supply power gain. Option C is wrong because an oscillator requires an amplifier with positive feedback, although special diodes can support oscillation. Option D is wrong because a transformer works by mutual induction between coils, handles only alternating current, and contains no semiconductor at all.