2026 paper questions

A diode passes current in one direction only, so it is commonly used as a rectifier, changing ac into one-way current. Option C is correct.

A resistor, a transformer and a capacitor each have a different job (limiting current, changing ac voltage and storing charge). None of them depends on the one-way action of a PN junction.

If the angle of incidence is zero, the ray travels along the normal. Snell's law gives $n_1\sin 0=n_2\sin {\theta }_r$, so $\sin {\theta }_r=0$ and ${\theta }_r=0$: the ray is not bent, whatever the refractive indices are.

Options B and C describe bending, which happens only when the angle of incidence is more than zero and the speed of light changes. Option D needs light going from a denser to a rarer medium at an angle greater than the critical angle.

An object is negatively charged when it has more electrons than protons. Since the protons stay in the nucleus, this happens only when the object gains electrons.

Option B is the tempting wrong choice: losing electrons leaves more protons than electrons, so the object becomes positive. Neutrons (A) are neutral, and protons (C) are positive and cannot be added by charging, so they could not make the object negative.

A NAND gate is an AND gate followed by a NOT gate, $X=\overline{A\cdot B}$. With both inputs $1$ (HIGH) the AND output is $1$, and the NOT gate turns it into $0$ (LOW). This is the only row of Table 18.5 where the NAND output is $0$, so option D is correct.

Option B (HIGH) is what an AND gate gives for these inputs. For a NAND gate the output is HIGH in the other three rows.

Thermal insulation (double glazing, foam in gaps, false ceilings, thick curtains) slows the flow of heat through the walls, windows and roof, so less heat is lost from a building in winter.

Open ventilation (A), large windows (B) and thin walls (D) all let heat pass more easily, so they increase heat loss.

The force is largest when the conductor cuts the field lines at right angles, that is, when it is perpendicular to the field (D). When the conductor lies parallel to the field (B) it cuts no field lines and the force is zero. Option A has no meaning, since the conductor itself carries the current, and the force is not the same at every angle (C).

Current is the rate of flow of charge: charge divided by time, $I=\frac{Q}{t}$ (coulomb per second, or ampere). Option D is the same equation turned upside down and wrongly written, since $Q=It$, not $I/t$.

From $\Delta V=\beta V_0\Delta T$ (book equation 11.3), dividing both sides by $V_0\Delta T$ gives

which is the fractional change in volume per kelvin (option B). Option A is the inverse of this. C and D put $\Delta T$ in the wrong place, so they do not have the unit ${\mathrm{K}}^{-1}$.

Amplitude is the maximum displacement of a vibrating particle from its mean (rest) position, that is, the height of a crest or the depth of a trough. Option D is wrong: wavelength is the distance between two successive crests (or troughs), a distance along the wave and not a displacement of a particle.

The speed of a wave is $v=f\lambda$ and depends on the medium (and the source frequency), not on the amplitude. Doubling the amplitude makes the wave carry more energy, but it is still $7\mathrm{m}{\mathrm{s}}^{-1}$. Option B is the tempting wrong choice: amplitude is not in the relation $v=f\lambda$.

Without the commutator the current in the coil cannot be reversed. The coil turns only until it reaches the vertical position, where the forces on its two sides are balanced, so it stops at the end of its first half-turn swing (a simple coil cannot turn more than $90^{\circ }$ on its own). Option D is the tempting wrong option: smooth rotation needs the current to be reversed every half-turn, which is the commutator's job. The motor still uses electrical energy, so A is wrong.

Sound is a mechanical wave, so it needs particles of a medium to pass the vibrations on. A vacuum has no particles, so sound cannot travel through it. This is why the bell in a bell jar cannot be heard when the air is pumped out.

Air (B), water (C) and steel (D) all have particles, so they carry sound. Steel is in fact the fastest of the three.

In Rutherford's experiment a beam of $\alpha$-particles was fired at a very thin gold foil and the scattered particles were detected on a zinc sulfide screen. The findings gave evidence for the following facts (any three):

These results disproved Thomson's plum pudding model and led to Rutherford's nuclear model of the atom.

Electric field (1 mark)

An electric field is the region around a charge in which it exerts a force on other charges. The charges do not have to touch: any charge brought into the region feels a force.

Its strength is measured by the electric field intensity $E$, the force per unit positive test charge, $E=\frac{F}{q_0}$, with SI unit $\mathrm{N}{\mathrm{C}}^{-1}$.

Two characteristics (2 marks)

1. It is a vector quantity. The electric field intensity $E=F/q_0$ has both magnitude and direction. Its direction at a point is the direction of the force on a positive test charge placed there, and its SI unit is $\mathrm{N}{\mathrm{C}}^{-1}$.
2. Its strength decreases with distance from the source charge, following an inverse square law for a point charge. If the strength is $E_0$ at distance $r_0$, it is $\frac{1}{4}{E}_0$ at $2r_0$.

(Other correct points: a positive charge in the field is pushed along the field and a negative charge against it, with force $F=qE$; and the field does not depend on the size of the test charge.)

Working under forward bias (1.5 marks)

A diode is forward biased when the positive terminal of a DC source is connected to its p-type side and the negative terminal to its n-type side.

1. The holes of the p-side are repelled by the positive terminal and driven towards the junction.
2. The electrons of the n-side are repelled by the negative terminal and driven towards the junction.
3. The depletion region becomes narrow and the potential barrier is reduced.
4. Once the applied voltage lowers the barrier enough (about $0.7\mathrm{V}$ for silicon, $0.3\mathrm{V}$ for germanium), electrons and holes combine at the junction and a current passes through the diode. This forward current is of the order of a few milliamperes, and the diode acts like a conductor.

Diagram (1.5 marks)

Diagram. The figure shows a transverse wave moving to the right (the direction of travel is the direction of energy transfer). The particles are marked with dots; the double arrow shows the direction of their vibration.

Explanation. When one end of a rope is moved up and down, each particle of the rope moves up and down about its rest position, along the vertical line shown by the double arrow. The wave itself, and with it the energy, moves horizontally along the rope. The vertical line of vibration and the horizontal line of travel are at $90^{\circ }$ to each other, so the vibration direction is perpendicular to the direction of energy transfer. The particles do not move along with the wave: they only pass the energy on to the next particle.

Series. The positive terminal of each cell is joined to the negative terminal of the next, so the emfs add: ${\epsilon }_{net}={\epsilon }_1+{\epsilon }_2+\cdots +{\epsilon }_n$.

Snell's law (2 marks). The laws of refraction are known as Snell's law:

• First law: the incident ray, the normal and the refracted ray all lie in the same plane.
• Second law: the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media. It relates the angles to the refractive indices of the two media.

Mathematical expression (1 mark).

For light entering a medium of index $n$ from air ($n_1=1$) this becomes $n=\frac{\sin {\theta }_i}{\sin {\theta }_r}$, which is the form on the paper's formula list.

Lenz's law: the direction of the induced current in a circuit is always such that it opposes the cause which produces it. (1 mark)

Conservation of energy with an example (2 marks)

Take a north pole of a magnet moved towards a coil. The induced current makes the near end of the coil a north pole, which repels the magnet, so the magnet must be pushed against a force. The work done in pushing it is the energy supplied, and it appears as the electrical energy of the induced current in the coil. When the magnet is pulled away, the near end becomes a south pole which attracts the magnet back, and again work must be done to pull it away.

If the law were opposite, the induced current would attract the approaching magnet and push away a receding one. The magnet would speed up by itself and the current would keep growing, so energy would be gained for nothing. Because the induced current opposes the motion, energy is only converted from the work done into electrical energy, none is created or lost, and the law of conservation of energy is obeyed.

Direct current (d.c.)

Current that flows steadily in a single direction. It may be steady or may vary in size, but it never reverses.

Alternating current (a.c.)

Current in which the charges keep switching direction, going forward half the time and backward the other half.

• Advantage of d.c.: it is steady and in one direction, so it is suited to electronic circuits and can be stored in batteries.
• Advantage of a.c.: its voltage can be changed easily, so it can be transmitted over long distances.

Convection in seawater is caused by differences in density due to temperature and salinity. Warm water is less dense and rises; cold or salty water is denser and sinks. These convection currents support marine life in three ways.

Any three of these differences carry full marks. Example: a bird has a high pitch and a lion a low pitch, while a shout is louder than a whisper.

Charge on an insulator cannot flow through it, because an insulator has no free electrons. Heating changes the insulator and the air around it so that the charge can escape (section 15.3.4).

• The heat excites the electrons and ionises the surrounding air, which makes the air conducting. Opposite ions in the air are attracted to the charged surface and neutralise it.
• The heat also increases the surface conductivity of the insulator for a short time, so the static charges can move and discharge.

Therefore holding a charged insulator over a flame discharges it.

Going from radio waves to gamma rays, the frequency and the energy increase while the wavelength decreases. The correct order is:

1. Radio waves
2. Microwaves
3. Infrared
4. Visible light
5. Ultraviolet
6. X-rays
7. Gamma rays

Radio waves have the lowest frequency and gamma rays the highest. Any six of the seven regions, in this order, earn the marks.

Ohm's law

The current through a conductor is directly proportional to the potential difference across its ends, as long as the temperature and physical state of the conductor stay constant. That is, $I\propto V$, or $V=IR$.

A magnifying glass is a convex lens. When the object is placed between the lens and its focal point ($p<f$), the image is:

• Virtual: it cannot be caught on a screen, and it is on the same side of the lens as the object.
• Erect: it has the same orientation as the object.
• Enlarged: it is larger than the object ($|M|>1$).

Both boiling and evaporation change a liquid into vapour, but they differ as follows (book Table 11.4).

Other differences that can be written instead: evaporation is slow and boiling is fast; evaporation uses energy from the surroundings and causes cooling, while boiling needs a continuous external source of heat; evaporation depends on the surface area, boiling does not.

Phenomenon (1 mark)

The change of colour is due to the scattering of light by the molecules of the atmosphere (shorter wavelengths are scattered more than longer ones).

Explanation (2 marks)

At sunset the Sun is low in the sky, so its light has to travel a much longer path through the atmosphere than at noon (Figure 20.16). On this long path it meets many more air molecules. The short wavelengths (blue and violet) are scattered more, so they are scattered out of the beam and do not reach the observer. The long wavelengths, red and orange, are scattered least, so they travel the long distance and reach the eyes. The Sun and the sky near it therefore look red or orange. The same happens at sunrise.

Nuclear fission (2 marks)

Nuclear fission is the process of splitting a heavy and unstable nucleus into comparatively smaller nuclei by absorbing a neutron, with the emission of more neutrons and a large amount of energy. A typical reaction is

The nucleon numbers balance (1+235=141+92+3) and so do the charges (92=56+36). The mass of the products is less than the mass of the reactants, and the difference appears as energy by E=mc^{2}: about 200\,\mathrm{MeV} per fission, with about 2.5 neutrons released on average.

Chain reaction (1 mark)

The neutrons released can cause further fissions in other uranium-235 nuclei. As long as the average number of neutrons causing new fissions is greater than 1, the number of fissions grows. Uncontrolled, this is the atomic bomb.

Controlled fission in reactors, with diagram (2 marks)

Each fission of uranium-235 releases about 2.5 neutrons. If every one of them caused a new fission, the number of fissions would grow in each generation and the energy would be released in an instant, as in an atomic bomb (uncontrolled chain reaction). In a nuclear reactor the chain reaction is kept controlled: on average only one neutron from each fission is allowed to cause a new fission, so the number of fissions per second, and the power, stays steady. The energy is then released slowly and can be put to use.

Main parts of the reactor

1. Fuel rods: uranium-235 (natural uranium has a little less than 1% of it, so the proportion is increased before it is used as fuel). The fissions take place here.
2. Moderator (for example graphite or heavy water): the neutrons from a fission are fast, but slow (thermal) neutrons are the ones that cause fission in uranium-235. The moderator slows them down by collisions.
3. Control rods (boron or cadmium): they absorb neutrons. Pushing them further in absorbs more neutrons and slows the reaction; pulling them out lets more neutrons cause fission and raises the power. Pushed fully in, they shut the reactor down.
4. Coolant (water or a gas): it flows through the core, takes away the heat released in fission and carries it to a heat exchanger, where steam is made. The steam turns a turbine and generator to produce electricity.

(a) Effect of changing amplitude and frequency

Amplitude (2 marks). The amplitude is the maximum displacement of the particles of the medium and it shows the energy carried by the wave. A larger amplitude gives a louder sound (loudness \propto A^{2}), and the pitch stays the same.

Frequency (1 mark). The frequency is the number of waves per second. A larger frequency brings the waves closer together and gives a higher pitch, while the loudness stays the same.

(b) Frequency and pitch (2 marks)

Pitch is the sensation by which we tell a shrill sound from a deep sound. It is not a physical quantity and cannot be measured directly, but it can be found from the frequency of the wave, because it describes the number of vibrations produced in one second. Hence pitch is directly proportional to frequency:

A high frequency gives a high pitch (shrill) and a low frequency gives a low pitch (deep). Examples: a bird gives a high-pitched sound and the roar of a lion is low-pitched; the voice of a woman has a higher pitch than that of a man.

Expansion of liquids

Liquids expand when heated. Their particles gain kinetic energy and push each other further apart. The attractive forces between liquid particles are weaker than in solids, so liquids expand more than solids for the same rise in temperature. A liquid cannot be heated on its own, so it is heated in a container. The volume change must therefore be split into two types: real expansion and apparent expansion.

Real volume expansion

The real volume expansion is the increase in the volume of the liquid when heat is applied to it directly. Its coefficient is \gamma_r, which is the fractional increase in real volume for a rise of 1 K:

Apparent volume expansion

The apparent volume expansion is the expansion of the liquid as it appears in the container, without considering the expansion of the container. Its coefficient is \gamma_a:

Experiment with a flask

A coloured liquid is kept in a flask with a long narrow neck (book Figure 11.8). When the flask is heated from below, the liquid level first falls from V_1 to V_2, because the glass flask expands first and its volume grows. The heat then reaches the liquid, which expands and rises from V_2 to V_3.

The rise of the liquid seen against the glass is the apparent expansion (V1 to V3). The real expansion is the rise from V2 to V3, measured from the level after the flask has grown. The three quantities are related by

where \Delta V_g is the expansion of the flask. Dividing by V_0\,\Delta T gives the relation between the coefficients (book equation 11.9):

So the real coefficient is always greater than the apparent coefficient, by the coefficient of the container. Different liquids have different coefficients, as Table 11.3 shows: for example \beta=113\times10^{-5}\,\mathrm{K^{-1}} for methanol and 18\times10^{-5}\,\mathrm{K^{-1}} for mercury.

Water is an exception

Almost all liquids expand on heating and contract on cooling. Water does not behave in this way between 4\,^\circ\mathrm{C} and 0\,^\circ\mathrm{C}: as it cools from 4\,^\circ\mathrm{C} to 0\,^\circ\mathrm{C} it expands, so ice floats on liquid water (book Science Tidbits).

(a) Derivation (3 marks)

(b) Numerical (2 marks)

(a) Step-up and step-down transformers (3 marks)

A transformer is a device that increases or decreases an alternating voltage. It has a primary coil, a secondary coil and a laminated iron core. The changing field made by the a.c. in the primary induces an e.m.f. in the secondary, and

In an ideal transformer I_pV_p=I_sV_s, so when the voltage is raised the current falls, and when the voltage is lowered the current rises.

(b) Numerical (2 marks)

Principle (3 marks)

A burglar alarm detects an intruder and sounds a loud bell to warn others. The book's simple burglar alarm is built with an AND gate that has two inputs: a person sensor (input A) and an alarm switch (input B). The gate output is X=A\cdot B.

Circuit diagram (2 marks)

A diode conducts when it is forward biased and blocks current when it is reverse biased, so it lets current pass in one direction only. This is why it is used as a rectifier: it changes alternating current into one-way (direct) current. Option D is correct.

Reducing voltage is the job of a resistor, amplifying current is the job of a transistor, and storing charge is the job of a capacitor. None of these is the main function of a diode.

The critical angle of a medium in air is given by \sin\theta_c=\dfrac{1}{n} (formula list). For polystyrene, \sin\theta_c=\dfrac{1}{1.49}=0.671, so \theta_c=\sin^{-1}(0.671)=42.2^{\circ}.

The tempting option C (45^{\circ}) would need n=\sqrt2=1.41, B (60^{\circ}) would need n=1.15, and A (32.2^{\circ}) would need n=1.88. None of these is the index of polystyrene.

When two different materials are rubbed together, the loosely held outer electrons pass from the material whose atoms hold them less strongly to the one that attracts them more strongly (section 15.3.1). The material that loses electrons becomes positive and the one that gains them becomes negative.

Protons and neutrons are bound inside the nucleus and are not removed by rubbing, so B and C are wrong. Whole atoms (A) are not transferred either; only electrons move.

An OR gate has X=A+B. Its output is 1 (HIGH) if at least one input is 1, so it is 0 (LOW) only when all the inputs are 0 (Table 18.3). Option C is correct.

Option A is the tempting one: with one input LOW and the other HIGH the OR output is still HIGH. That rule (output LOW when any input is LOW) belongs to the AND gate, not the OR gate.

Warm air is less dense than cool air, so it rises, and the denser cool air sinks to take its place. This circulation of the moving fluid itself carries heat around the room. It is convection.

Conduction (D) needs direct contact between particles of a solid, and the air particles do not pass heat along a fixed chain like that. Radiation (B) is heat carried by electromagnetic waves and does not need a moving fluid. Reflection (A) is not a method of heat transfer.

The force on a current-carrying conductor in a magnetic field is perpendicular to both the field and the current (Fleming's left-hand rule). Reversing the current turns the middle finger the other way, so the thumb, which shows the force, also turns the other way. The force reverses (A) but its size does not change, so options B, C and D are wrong. Option B would be true only if both the current and the field were reversed together.

Current is the charge passing per second, I=\dfrac{Q}{t}=\dfrac{10\,\mathrm{C}}{5\,\mathrm{s}}=2\,\mathrm{A}. Option D (5 A) comes from dividing by the wrong number, and option A (10 A) is just the charge, not the charge per second.

Linear thermal expansion is the change in one dimension, the length, of a solid on heating, given by \Delta L=\alpha L_0\,\Delta T (option D).

The mass does not change on heating (A). A change in area is area expansion (B), and a change in volume is volume expansion (C), which are different from linear expansion.

The number of half-lives is n=\dfrac{\Delta t}{T_{1/2}}=\dfrac{16}{8}=2, so the mass left is N=N_0\left(\tfrac12\right)^{2}=\dfrac{40}{4}=10\,\mathrm{g}. The answer is option C.

Option B (20\,\mathrm{g}) is what is left after only one half-life (8 days), and option D (5\,\mathrm{g}) would need three half-lives (24 days). Do not take 40-16=24\,\mathrm{g} or subtract the days: each half-life halves the amount that is left.

A longitudinal wave is made of compressions (particles close together, higher pressure) and rarefactions (particles spread apart, lower pressure). Option B is wrong because a transverse wave has crests and troughs, not compressions and rarefactions. Option D is also wrong: electromagnetic waves are transverse and need no medium to be compressed.

An electric motor takes electrical energy from the supply and gives rotational mechanical energy, because a current-carrying coil in a magnetic field experiences a couple and turns. The DC generator (C) is the tempting wrong option: it does the reverse and converts mechanical energy into electrical energy. A capacitor stores charge and a transformer only changes an alternating voltage, so neither gives mechanical energy.

In a solid the particles are tightly packed (closely spaced and strongly bound), so the solid is much denser than a gas. Each particle is close to its neighbour and passes the vibration on quickly, so sound travels fastest in solids. Of the four options only higher density matches this.

Options C and D describe a gas, where the particles are far apart and the vibration is passed on slowly. Option A is wrong because the speed of sound in a solid does not come from low pressure.

Isotopes are atoms of the same element that have the same atomic number (the same number of protons) but different mass numbers, because they have different numbers of neutrons.

Example: hydrogen has three isotopes, protium {}^{1}_{1}\mathrm{H} (no neutron), deuterium {}^{2}_{1}\mathrm{H} (one neutron) and tritium {}^{3}_{1}\mathrm{H} (two neutrons). All have one proton.

Chemical properties: yes, the isotopes of an element have similar (identical) chemical properties. Chemical behaviour depends on the electrons, and isotopes of an element have the same number of electrons, since they have the same number of protons. Only their masses differ, so they cannot be separated by chemical methods but only by methods based on mass, such as mass spectrometry.

Electric field (1 mark)

An electric field is the region around a charge in which it exerts a force on other charges. The charges do not have to touch: any charge brought into the region feels a force.

Its strength is measured by the electric field intensity E, the force per unit positive test charge, E=\dfrac{F}{q_0}, with SI unit \mathrm{N\,C^{-1}}.

Effect on a test charge (2 marks)

Rearranging E=F/q_0 gives the force on a charge q placed in a field of strength E:

• A positive test charge feels a force of size qE in the same direction as the field. It is pushed along the field, away from a positive source charge and towards a negative one.
• A negative test charge feels a force of the same size in the opposite direction to the field.
• The test charge does not have to touch the source charge, and the force is larger where the field is stronger (nearer the source).

A diode is a PN junction that conducts when it is forward biased and blocks the current when it is reverse biased. Its two main functions follow from this.

1. Rectification (0.75 mark for the name, 0.75 for the reason). A diode is used as a rectifier. Because it allows current in one direction only, it changes alternating current (which reverses its direction) into current that flows in one direction only.
2. One-way switch (0.75 mark for the name, 0.75 for the reason). A diode acts like a closed switch (a conductor) when forward biased, with a forward current of a few milliamperes. It acts like an open switch (an insulator) when reverse biased, with only a leakage current of a few microamperes.

A light-emitting diode is a special diode with a further use: it gives out light when forward biased, so it is used in display devices and decorative lamps.

Wave form (1 mark). A transverse wave has crests and troughs. Its particles vibrate up and down about the rest position while the wave moves along.

Energy transfer (2 marks). The source (for example a hand moving the end of a rope up and down) makes the first particle vibrate. Each particle pulls its neighbour with it, so its neighbour starts vibrating a little later, and the disturbance passes from particle to particle along the wave. The particles themselves only vibrate about their mean positions at right angles to the wave and do not travel with it. Only the energy is carried forward, in the direction of travel of the wave.

Series. The positive terminal of each cell is joined to the negative terminal of the next, so the emfs add: \varepsilon_{net}=\varepsilon_1+\varepsilon_2+\cdots+\varepsilon_n.

Refractive index (1 mark). The refractive index of a medium is the ratio of the speed of light in vacuum to the speed of light in that medium. It measures how much a light ray bends when it enters the medium from vacuum. It has no unit and is never less than 1.

Lenz's law: the direction of the induced current in a circuit is always such that it opposes the cause which produces it. (1 mark)

How it fixes the direction (2 marks)

The induced current produces its own magnetic field. Lenz's law says this field must oppose the change (the movement of the magnet) that causes the current, so the direction of the current is the one whose field does this.

In each case the rule gives the pole formed at the near end of the coil, and the right-hand grip rule then gives the direction of the current round the coil.

Direct current (d.c.) flows steadily in one fixed direction. Alternating current (a.c.) keeps changing direction, going forward for half the time and backward for the other half.

• Direction: d.c. does not change its direction, while a.c. reverses its direction continuously.
• Graph: the I-t graph of d.c. is a horizontal line (or a curve on one side of the time axis), while that of a.c. is a wave that goes above and below the time axis.

Water has a large specific heat (4200\,\mathrm{J\,kg^{-1}\,K^{-1}}), while dry land has a much smaller one (about 800\,\mathrm{J\,kg^{-1}\,K^{-1}}, five times smaller). Land therefore heats up and cools down quickly, but the sea warms and cools slowly.

The sea near a coast absorbs and stores a lot of heat from the Sun in summer and releases it in winter, so the temperature changes little between day and night and between summer and winter. In Karachi the average temperature varies only from 19^\circ\mathrm{C} to 32^\circ\mathrm{C}. Inland, the land has no such store of heat, so the temperature varies much more, up to about 45^\circ\mathrm{C} to 50^\circ\mathrm{C} in summer and down to about 0^\circ\mathrm{C} in winter. Sea and land breezes help the coast further.

Echo (1 mark). An echo is a distinct sound that comes back to the listener after the sound wave strikes an obstacle and is reflected from it. It is heard separately from the original sound.

How it is produced (2 marks). When a source makes a sound, the wave travels to a hard, rigid surface such as a cliff, a hill or a wall, and bounces back by reflection, like a rubber ball bouncing from a wall. The reflected wave is heard as a second, weaker sound.

The sound travels to the obstacle and back, so the total distance covered is twice the distance d of the obstacle. The ear keeps the sensation of a sound for about 0.1\,\mathrm{s}, so the reflected wave is heard separately only if it returns at least 0.1\,\mathrm{s} after the original sound:

With v=340\,\mathrm{m\,s^{-1}} the obstacle must be at least 17\,\mathrm{m} away. If the time gap is less than 0.1\,\mathrm{s}, the reflected sound overlaps the original and no separate echo is heard (reverberation).

An insulator has no free electrons, so a charge placed on it cannot leak away through the material. Exposing it to moist (humid) air discharges it (section 15.3.4).

Water molecules in damp air stick to the surface of the insulator. They are polar molecules, so they interact with the charged areas and form a thin conducting layer of water on the surface. The charge can now move along this layer and escape, so the insulator is discharged.

The ions present in humid air also help: they are attracted to the charged surface and neutralise the static charge on it. This is why static electricity is much more noticeable on dry days than on humid ones.

The regions of the electromagnetic spectrum in order of increasing wavelength are:

1. Gamma rays
2. X-rays
3. Ultraviolet
4. Visible light
5. Infrared
6. Microwaves
7. Radio waves

Gamma rays have the shortest wavelength (below 10^{-12}\,\mathrm{m}) and radio waves the longest (above 1\,\mathrm{mm}). Any six of the seven regions, in this order, earn the marks.

Ohm's law

The current through a conductor is directly proportional to the potential difference across its ends, as long as the temperature and physical state of the conductor stay constant. That is, I\propto V, or V=IR.

The half-life T_{1/2} of a radioactive substance is the time in which half of the unstable nuclei of a sample decay into daughter nuclei.

Example: iodine-131 has a half-life of 8 days. If we start with 40\,\mathrm{g}, then 20\,\mathrm{g} is left after 8 days, 10\,\mathrm{g} after 16 days and 5\,\mathrm{g} after 24 days. The amount left after n half-lives is

A convex lens (and a concave mirror) can form a real image, for example the image on a screen. A plane mirror, a concave lens and a convex lens used as a magnifying glass form virtual images.

Effect (1.5 marks). Diffraction is the spreading of waves as they pass through a gap or around an obstacle. For a gap of a given size, a longer wavelength diffracts more and a shorter wavelength diffracts less.

A wave whose wavelength is large compared with the gap spreads out widely on the far side. A wave whose wavelength is much smaller than the gap passes almost straight through with very little spreading. Diffraction is greatest when the gap is less than or equal to the wavelength. The wavelength and speed of the wave do not change in diffraction.

Example (1.5 marks). Infrared light, with the longer wavelength, diffracts more than ultraviolet light, which has the shorter wavelength, through the same gap (Figure 12.17 of the book). Long radio waves bend round hills and reach valleys for the same reason.

Both boiling and evaporation change a liquid into vapour, but they differ as follows (book Table 11.4).

Other differences that can be written instead: evaporation is slow and boiling is fast; evaporation uses energy from the surroundings and causes cooling, while boiling needs a continuous external source of heat; evaporation depends on the surface area, boiling does not.

Colour of the sky (1 mark)

On a clear day the sky is blue.

How scattering gives this colour (2 marks)

Scattering is the sending of light in different directions by the particles in its path. Sunlight contains all the colours, from red (longest wavelength) to violet (shortest). The air is mostly oxygen and nitrogen molecules, which are very small and comparable in size to the short wavelengths of light. Shorter wavelengths are scattered more than longer ones, so the molecules scatter blue (with indigo and violet) strongly in all directions.

The longer wavelengths (red, orange, yellow) are not scattered much and pass straight through. Wherever you look in the sky, some of the scattered blue light comes to your eyes, so the whole sky looks blue (Figure 20.15).

(a) Nuclear fusion (2 marks)

Nuclear fusion is the process in which two light nuclei combine to form a comparatively heavy nucleus. The mass of the new nucleus is less than the total mass of the nuclei that formed it. This loss of mass (the mass defect) appears as energy, according to E=mc^{2}. An example is the proton-proton chain in the Sun, which converts hydrogen into helium and releases about 26.3\,\mathrm{MeV} per fusion. Its three steps are

Why very high temperature is needed

Both nuclei are positively charged, so they repel each other strongly. To fuse, they must be brought extremely close together. At very high temperature the nuclei move with very large kinetic energy, so they collide hard enough to overcome their electrostatic repulsion and combine. This is why the energy needed to start fusion is available only in the surroundings of stars, including the Sun.

(b) Energy from 55.56 kg of mass (3 marks)

(a) Factors affecting loudness and pitch

Loudness is the characteristic of a sound by which we tell a loud sound from a faint sound. It depends on the amplitude of the wave, and it is proportional to the square of the amplitude:

The physical factors affecting loudness are:

1. Vibrational amplitude of the source: a larger amplitude of vibration gives a louder sound.
2. Surface area of the source: a larger vibrating surface gives a louder sound.
3. Distance from the source: the farther the listener, the fainter the sound; a listener near the source hears it louder.
4. Sensitivity of the listener's ears: more sensitive ears feel a greater loudness.

Pitch is the characteristic by which we tell a shrill (high) sound from a grave (deep) sound. It depends on the frequency of the wave (the number of vibrations per second):

A larger frequency gives a higher pitch and a smaller frequency gives a lower pitch. Pitch does not depend on the amplitude. A bird gives a high-pitched sound and the roar of a lion is low-pitched.

(b) Effect of the amplitude on loudness

The amplitude is the maximum displacement of the particles of the medium, and it measures the energy carried by the wave. A larger amplitude means more energy reaches the ear every second, so the sound is louder. Doubling the amplitude gives (2A)^{2}=4A^{2}, that is four times the loudness. The frequency stays the same, so the pitch does not change.

Examples: a drum struck hard vibrates with a larger amplitude and sounds louder than the same drum struck gently; turning up the volume of a loudspeaker makes its cone vibrate with a larger amplitude; a speaker who shouts produces a larger amplitude than one who whispers.

Derivation (3 marks)

Numerical (2 marks)

(a) Principle (1 mark)

A transformer works on the principle of electromagnetic induction: a changing magnetic field in the iron core, produced by an alternating current in the primary coil, induces an alternating e.m.f. in the secondary coil.

(b) Working and formula (2 marks)

If N_s>N_p the transformer is step-up (V_s>V_p); if N_s<N_p it is step-down (V_s<V_p). A steady d.c. supply cannot be used, because its field does not change and no e.m.f. is induced.

(c) Construction (2 marks)

• A primary coil of N_p turns, connected to the a.c. supply.
• A secondary coil of N_s turns, which gives the output voltage.
• A laminated iron core; the two coils are wound on two different limbs of this core.

What an LED is

A light-emitting diode (LED) is a PN junction diode, made from gallium arsenide phosphide (GaAsP) or gallium phosphide (GaP), that emits energy in the form of light when an electric current passes through it. It is enclosed in a transparent cover so that the light can be seen.

Passing current in one direction only

• Forward bias. The positive terminal of the supply is joined to the p-type side and the negative terminal to the n-type side, with a resistor in series to limit the current. The depletion region becomes narrow and the potential barrier is lowered, so electrons and holes cross the junction and a forward current of a few milliamperes flows.
• Reverse bias. If the connections are reversed, the depletion region widens and the barrier rises, so the majority carriers cannot cross. Only a very small leakage current flows, and the LED does not glow.
• So, like any diode, the LED passes current in one direction only, and it must be forward biased to work.

Emission of light

In forward bias the free electrons of the conduction band of the n-region cross the lowered barrier and enter the p-region. There they fall into holes lying in the valence band. Each electron therefore drops from a higher energy level to a lower energy level, and the energy it loses is radiated as light. LEDs can give red, green or blue light.

Diagram

A diode conducts when it is forward biased: the positive terminal of the supply is connected to the p-type side and the negative terminal to the n-type side. The depletion region becomes narrow, the barrier is reduced and a forward current flows. Option C is correct.

Reverse bias widens the depletion region and blocks the current (only a microampere leakage current flows). With no bias the barrier of the junction stays in place, so there is no current, and heating is not the condition that makes a diode conduct.

From n=\dfrac{c}{v} we get v=\dfrac{c}{n}=\dfrac{3\times10^{8}}{1.5}=2\times10^{8}\,\mathrm{m\,s^{-1}}.

Option C is the speed of light in vacuum, which would need n=1. Options A and D are larger than c, which is impossible, because the speed of light in a material medium is always less than in vacuum.

Only the loosely bound outer electrons move when two materials are rubbed, and electrons carry negative charge. The material that loses electrons becomes positive and the one that gains them becomes negative (section 15.3.1).

Option B is the tempting one because one body ends up positive, but that is only because it has lost electrons. The protons stay fixed in the nuclei, so positive charge is not transferred. A neutral charge (C) does not exist, and D is wrong because only one type moves.

A NOR gate is an OR gate followed by a NOT gate, so X=\overline{A+B} (the bar covers the whole sum). Option C is correct.

Option A is the expression of a NAND gate, option B is an OR gate and option D is an AND gate. The bar in front of the whole sum is what makes it NOR.

The metal of the pan has many free electrons, so heat from the flame is conducted quickly through the metal base to the food. The pan heats up quickly mainly by conduction.

Convection (C) occurs in fluids and is not how heat moves through the solid metal. Radiation (B) from the flame does reach the pan, but it is a smaller part of the heating than the conduction through the metal. Evaporation (A) is not a method of heat transfer into the pan.

The direction of the force depends on the directions of both the field and the current. Reversing only the field turns the forefinger of Fleming's left hand the other way, so the thumb (force) reverses (A). The size of the force stays the same, so C and D are wrong. The force would remain unchanged (B) only if the current were reversed as well.

Since I=\dfrac{Q}{t}, with t fixed the current is directly proportional to the charge. Doubling Q gives I'=\dfrac{2Q}{t}=2I. Option B (becomes half) would be true if the time were doubled instead.

In a gas the particles are far apart and the attractive forces between them are almost zero, so a gas expands the most for the same rise in temperature (option D). In a liquid the forces are weaker than in a solid, so a liquid expands more than a solid, but still much less than a gas.

Option C (liquids) is the tempting choice only if gases are left out. The book compares solids and liquids: liquids expand more than solids because of the weaker forces. Gases have the weakest forces of all, so they expand the most. Option A is wrong because the three states do not expand equally.

An \alpha-particle is a helium nucleus. It is heavy and has a charge of +2e, so it ionizes strongly and loses its energy in a very short distance. A thin sheet of paper (or a few centimetres of air) stops it. The answer is option D.

Beta particles (C) pass through paper and need a few millimetres of aluminium. X-rays (A) and gamma rays (B) are the most penetrating and are only reduced by thick lead or concrete, so a thin sheet of paper does not stop them.

Wave speed is the distance moved by a wave in one second. In one time period T the wave moves one wavelength \lambda, so v=\dfrac{\lambda}{T}=f\lambda. Option C (\lambda/f) is wrong: it has the units \mathrm{m\,s}, not \mathrm{m\,s^{-1}}, because it divides by f where it should divide by T (or multiply by f).

The split-ring commutator turns with the coil. Each half of the ring changes brushes as the coil passes the vertical position, so the current in the coil is reversed every half-turn and the torque keeps the same sense. The brushes (A) are the tempting wrong option: they only carry current to the ring and stay fixed. The armature (B) is the rotating coil and the field magnet (C) only supplies the magnetic field.

Sound travels fastest in solids, slower in liquids and slowest in gases. The particles of a solid are tightly packed, so they pass the vibrations on most quickly (over 5000\,\mathrm{m\,s^{-1}} in steel).

Liquids (C) come second, about 1500\,\mathrm{m\,s^{-1}} in water, and gases (B) are slowest, about 340\,\mathrm{m\,s^{-1}} in air. In a vacuum (A) there are no particles, so sound cannot travel at all.

**\alpha-particles** are helium nuclei, each made of two protons and two neutrons bound together, {}^{4}_{2}\mathrm{He}. They carry a charge of +2e and are emitted from the nuclei of very large atoms (high atomic number).

• They are positively charged, so they are attracted towards the negative plate in an electric field; being heavy, their deflection is small.
• They have the strongest ionizing effect but the weakest penetrating power: they are stopped by a thin sheet of paper.

Example of an alpha-decay reaction: radon-222 changes into polonium-218 by releasing an \alpha-particle. The nucleon number falls by 4 and the proton number by 2.

Check: 222=218+4 and 86=84+2, so the equation balances.

Specific heat capacity is the amount of heat absorbed or lost to change the temperature of 1\,\mathrm{kg} of a substance by 1\,\mathrm{K} (or 1^\circ\mathrm{C}).

Mathematical expression:

Here Q is the heat absorbed or lost, m is the mass and \Delta T is the change in temperature. Its SI unit is \mathrm{J\,kg^{-1}\,K^{-1}}. Equivalently Q=mc\,\Delta T, the form given in the formula list of the paper.

Electric field (1 mark)

An electric field is the region around a charge in which it exerts a force on other charges. The charges do not have to touch: any charge brought into the region feels a force.

Its strength is measured by the electric field intensity E, the force per unit positive test charge, E=\dfrac{F}{q_0}, with SI unit \mathrm{N\,C^{-1}}.

Positive test charge in the field (2 marks)

The direction of the electric field at a point is defined as the direction of the force on a positive test charge placed there. So a positive test charge placed in an electric field feels a force F=qE in the same direction as the field.

It is pushed along the field: away from a positive source charge (repelled) and towards a negative source charge (attracted). The force is larger where the field is stronger, that is, closer to the source charge, since the field of a point charge falls off with distance as an inverse square law.

Role of the diode (2 marks)

Rectification means changing alternating current (ac) into current that flows in one direction only. A diode does this because it allows current in one direction only: it conducts when it is forward biased and blocks the current when it is reverse biased.

When an ac source is joined in series with a diode and a load resistor R, the diode is forward biased in the half-cycle in which its p-side (arrow side) is positive, and current flows through R. In the next half-cycle the polarity reverses, the diode is reverse biased and no current flows. The current through R therefore flows in pulses in one direction only (a pulsating direct current), which is why the diode is called a rectifier.

Diagram (1 mark)

Transverse wave (1.5 marks). The particles vibrate at right angles to the direction in which the wave (energy) travels. The wave form has crests and troughs.

Longitudinal wave (1.5 marks). The particles vibrate parallel to the direction in which the wave (energy) travels, along the same line. The wave form has compressions and rarefactions.

Series. The positive terminal of each cell is joined to the negative terminal of the next, so the emfs add: \varepsilon_{net}=\varepsilon_1+\varepsilon_2+\cdots+\varepsilon_n.

Principle (1 mark). Optical fibres work on total internal reflection. Light enters the core at an angle greater than the critical angle of the core and cladding boundary, so it is totally reflected again and again and travels along the fibre.

Advantages (any two, 2 marks).

• High bandwidth: a fibre carries much more data per second than a copper wire.
• Resistance to electrical interference: the signal is light, so electrical noise does not affect it.
• Also: faster speed (data travel as light pulses), long distance without much loss of signal, and low power use.

Lenz's law: the direction of the induced current in a circuit is always such that it opposes the cause which produces it. (1 mark)

Why it must oppose the change (2 marks)

Suppose the induced current helped the motion instead. A magnet pushed towards a coil would then be pulled in faster, the current would grow, and the magnet would go on speeding up with no one doing work. That would create energy from nothing. Energy cannot be created, so the induced current must oppose the change; the work done against this opposition is the energy that appears as the electrical energy of the induced current.

For example, a north pole moving towards a coil makes the near end of the coil a north pole, which repels the magnet. The person moving the magnet must do work against this repulsion, and this work becomes the electrical energy of the current.

Alternating current is preferred for domestic use because of the following reasons.

1. Its voltage can be changed (stepped up or down) easily, so it can be sent over long distances at high voltage and brought down to a safe value (about 220 V) for homes.
2. Generators produce a.c. directly, so it is easy to generate and supply to homes.
3. Most household appliances such as lights, heaters, fans and motors work directly on a.c. mains, and where d.c. is needed (electronic circuits) a.c. can be converted into it.

Land has a small specific heat and the sea has a large one, so by day the land becomes hotter than the sea and at night the sea stays hotter than the land.

Sea breeze (day). The air above the hot land is heated, expands and rises. Cool air from the sea moves in over the land to fill the gap. This cools the coast during the day.

Land breeze (night). The land cools faster than the water, so the air above the sea is warmer and rises. Cool air from the land moves out over the sea. This keeps the night temperature of the coast from falling too low.

These two convection currents blow continuously, cool the coast by day and moderate it at night, so the coastal climate stays moderate.

Minimum time (1 mark). The sensation of a sound stays in the brain for about 0.1\,\mathrm{s}, so the echo must reach the ear at least 0.1\,\mathrm{s} after the original sound. The minimum time is 0.1\,\mathrm{s}.

Small room (2 marks). The sound travels to the wall and back, a distance 2d, in the time t. For an echo t\ge0.1\,\mathrm{s}, which needs the wall to be at least

away. In a small room the walls are nearer than 17\,\mathrm{m}. Take a wall at 5\,\mathrm{m}: the sound returns after t=2d/v=(2\times5)/340\approx0.03\,\mathrm{s}, which is less than 0.1\,\mathrm{s}. The reflected sound therefore reaches the ear before the sensation of the original sound has faded, and the two cannot be told apart. They overlap (reverberation) and make the sound seem louder and prolonged, but no separate echo is heard.

An insulator cannot lose its charge through its own material because it has no free electrons. Holding it over a flame changes its surroundings so that the charge can be neutralised (section 15.3.4).

The heat of the flame excites electrons and ionises the air around the insulator, so the air becomes conducting. Ions of the opposite sign are attracted to the charged surface and neutralise the static charge on it.

The heat also temporarily increases the surface conductivity of the insulator, so the static charges can move and escape from it. In this way the insulator is discharged.

Written from the higher to the lower wavelength, the order is:

1. Radio waves
2. Microwaves
3. Infrared
4. Visible light
5. Ultraviolet
6. X-rays
7. Gamma rays

Radio waves have the longest wavelength (above 1\,\mathrm{mm}) and gamma rays the shortest (below 10^{-12}\,\mathrm{m}). Any six of the seven regions, in this order, earn the marks.

Ohm's law

The current through a conductor is directly proportional to the potential difference across its ends, as long as the temperature and physical state of the conductor stay constant. That is, I\propto V, or V=IR.

The half-life is the time in which half of the unstable nuclei in a sample of a radioactive substance decay. For example, iodine-131 has a half-life of 8 days: half of any sample is left after 8 days and a quarter after 16 days.

Why it is characteristic of an isotope:

• Its value depends only on the nature of the radioactive nucleus, and not on temperature, pressure, humidity or the chemical compound the atoms are in.
• Each radioisotope has its own fixed value, from a short time for very unstable nuclei to 4.53\times10^{9} years for uranium-238 (carbon-14 has 5730 years and iodine-131 has 8 days), so the half-life identifies the isotope and tells how quickly it decays.

A convex lens or a concave mirror can form a real image. A plane mirror, a concave lens, or a convex lens with the object inside its focal length form a virtual image.

Narrow gap (1.5 marks). When the gap is less than or equal to the wavelength, diffraction is greatest. The waves spread out in all directions beyond the gap and become nearly circular waves (Figure 12.16 (a) of the book).

Wide gap (1.5 marks). When the gap is much larger than the wavelength, diffraction is minimal. The central part of the wave passes straight through and only the part at the edges bends, so most of the energy keeps its original direction (Figure 12.16 (b)). The wavelength and speed of the wave stay the same in both cases.

The rate of evaporation depends on the following factors (any three, with the reason for each).

1. Temperature. A higher temperature gives the molecules more kinetic energy, so more of them can escape from the surface and evaporation is faster.
2. Surface area. A larger surface lets more molecules escape at the same time, so evaporation is faster. This is why wet clothes are spread out to dry.
3. Humidity. In dry air (low humidity) the air can take in more water vapour, so evaporation is faster. In humid air it is slower.
4. Wind speed. Moving air blows away the moist air near the surface, so more molecules can leave and evaporation is faster.

Particle nature of light (2 marks)

Light also behaves as a stream of tiny particles called photons. A photon is a massless packet (quantum) of light energy. It carries energy and momentum but no charge, and in a vacuum it always travels at the speed of light. Max Planck introduced this idea in the early 20th century, calling the packets quanta of light.

Here h=6.63\times10^{-34}\,\mathrm{J\,s} is Planck's constant. Light shows both wave properties (interference, diffraction, polarisation) and particle properties, which is its dual nature.

One application (1 mark)

Radiation pressure and solar sails. Because each photon has momentum p=h/\lambda, light that strikes a surface exerts a very small force on it. A large, light, mirror-like solar sail in space is pushed by the photons of sunlight and can move a spacecraft without fuel, which suits long deep-space missions.

(a) The main energy source of the Sun (2 marks)

The main source of the Sun's energy is nuclear fusion: hydrogen nuclei fuse into helium nuclei in the Sun's core. The Sun is a medium-sized, self-luminous sphere of hot gas, held together by gravity, with a photosphere at about 6000\,\mathrm{K} made of about 75% hydrogen and 25% helium by mass.

• The dominant reaction is the proton-proton chain: two protons form deuterium, a proton joins it to form helium-3, and two helium-3 nuclei fuse to give helium-4 and two protons (about 26.3\,\mathrm{MeV} per fusion).
• It starts because of the very high temperature and pressure in the core, which make the hydrogen nuclei collide with enough energy to overcome their electrostatic repulsion.
• Every second about 6.0\times10^{11}\,\mathrm{kg} of hydrogen is converted into 5.96\times10^{11}\,\mathrm{kg} of helium and 4.0\times10^{26}\,\mathrm{J} of energy. The lost mass appears as energy according to E=mc^{2}.
• The Sun has been fusing hydrogen for about 5 billion years and is expected to go on for another 5 billion years.

(b) Controlled nuclear fission in reactors (3 marks)

Each fission of uranium-235 releases about 2.5 neutrons. If every one of them caused a new fission, the number of fissions would grow in each generation and the energy would be released in an instant, as in an atomic bomb (uncontrolled chain reaction). In a nuclear reactor the chain reaction is kept controlled: on average only one neutron from each fission is allowed to cause a new fission, so the number of fissions per second, and the power, stays steady. The energy is then released slowly and can be put to use.

Main parts of the reactor

1. Fuel rods: uranium-235 (natural uranium has a little less than 1% of it, so the proportion is increased before it is used as fuel). The fissions take place here.
2. Moderator (for example graphite or heavy water): the neutrons from a fission are fast, but slow (thermal) neutrons are the ones that cause fission in uranium-235. The moderator slows them down by collisions.
3. Control rods (boron or cadmium): they absorb neutrons. Pushing them further in absorbs more neutrons and slows the reaction; pulling them out lets more neutrons cause fission and raises the power. Pushed fully in, they shut the reactor down.
4. Coolant (water or a gas): it flows through the core, takes away the heat released in fission and carries it to a heat exchanger, where steam is made. The steam turns a turbine and generator to produce electricity.

(a) Effect of changing amplitude and frequency

Amplitude. The amplitude is the maximum displacement of the particles of the medium and it measures the energy of the wave. Increasing the amplitude makes the sound louder, and decreasing it makes the sound fainter. The loudness is proportional to the square of the amplitude, and the pitch does not change.

Frequency. The frequency is the number of waves produced per second. Increasing the frequency makes the waves come closer together and raises the pitch (a shriller sound); decreasing it lowers the pitch. The loudness does not change.

(b) Loudness and pitch compared

Diagrams: the first graph above shows loudness (same frequency, larger amplitude is louder). The second graph shows pitch (same amplitude, the wave with more cycles in the same distance has the higher pitch).

(a) Mutual induction in a transformer (3 marks)

Mutual induction means that a changing current in one coil induces an e.m.f. in a neighbouring coil, because the changing magnetic field of the first coil passes through the second. This is exactly how the two coils of a transformer are linked.

(b) Energy transformation (2 marks)

Electrical energy supplied to the primary coil is changed into the energy of the magnetic field in the iron core, and this field then gives electrical energy in the secondary coil. So the energy goes electrical, then magnetic, then electrical again, at a different voltage.

In an ideal transformer no energy is lost, so the power in the primary equals the power in the secondary:

A step-up transformer raises the voltage and lowers the current in the same ratio; a step-down transformer does the opposite. The total energy is not changed.

(a) Parallel combination (2.5 marks)

(b) Series combination (2.5 marks)

Principle

An electric motor converts electrical energy into mechanical energy. A current-carrying coil placed in a magnetic field experiences a couple, so the coil rotates.

Parts

• Coil (armature): a rectangular coil of many turns on an axle, between the poles.
• Magnets: permanent magnets (or an electromagnet) giving the magnetic field.
• Split-ring commutator: a ring split into two halves, which turns with the coil.
• Brushes: pieces of graphite that touch the two halves of the ring and carry current from the battery into the coil.

Operation

A truth table lists the output of a gate for every possible combination of its inputs. A gate with two inputs has 2^{2}=4 rows. The symbols and Boolean expressions are shown first, then the truth tables (1 mark for each gate).

AND, OR, NAND and NOR (two inputs A and B)

NOT (one input A)

Rule for each gate

• AND: the output is 1 only when all the inputs are 1.
• OR: the output is 0 only when all the inputs are 0.
• NAND: the AND output turned over, so the output is 0 only when all the inputs are 1.
• NOR: the OR output turned over, so the output is 1 only when all the inputs are 0.
• NOT: the output is the opposite of the input.