WJEC A-Level Physics Revision

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WJEC · A-Level Physics1420QSExam years · 2027

Assessment AS Units 1–2: 90 minutes each, 20% each. A2 Unit 3: 2 hours 15 minutes, 25%; Unit 4: 2 hours, 25%, with one option. Unit 5: separate external practical examination, 10%, with a 90-minute Experimental Task and 60-minute Practical Analysis Task. Ask your centre for the 2027 topic notice; reading is not assessed performance.

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Open a point to read what to know, how to use it in an assessment, a plain-language explanation and a self-check. Answers stay hidden until you choose to reveal them.

Options and source

A2 Unit 4 Section B option

Option A: Alternating Currents
Option B: Medical Physics
Option C: The Physics of Sports
Option D: Energy and the Environment

Summary of Assessment and A2 Unit 4: Section B is a choice of one out of four options.

Units, Vectors, and StaticsCore
Scope: Core · AS Unit 1 §1 BASIC PHYSICS; AS Unit 1 §1 BASIC PHYSICS specified practical work
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What to know
SI has seven base units. The six used in this specification’s Physics calculations are: kilogram (kg) for mass, metre (m) for length, second (s) for time, Ampere (A) for current, mole (mol) for substance, and Kelvin (K) for temperature. Derived units are built from these base units, often modified by prefixes like milli or kilo to adjust scale.
Equations must be homogeneous. This means the base unit composition of the left side must equal the right side. If units do not match, the equation is physically incorrect. This check is a vital tool for identifying errors in algebraic manipulation.
Quantities are classified as scalars or vectors. Scalars, such as time and speed, have magnitude only. Vectors, such as displacement, velocity, acceleration, and force, require both magnitude and direction.
Coplanar vectors are added by joining them tip-to-tail. Subtraction is performed by reversing the direction of the vector to be subtracted and adding it. For two perpendicular vectors, the resultant magnitude is found using the Pythagorean theorem, √ (a² + b²), while the direction is determined using inverse trigonometry.
Resolving a vector involves splitting it into perpendicular components along chosen axes using trigonometry: the component adjacent to the angle uses cosine, and the opposite component uses sine.
Density (ρ) is the ratio of mass (m) to volume (V), expressed as ρ = m / V. Practical measurement requires using a sensitive balance for mass and a water displacement method or callipers for volume, ensuring scale interpolation for maximum precision.
A force exerts a turning effect called a moment. A moment is calculated as the product of the force and its perpendicular distance from a pivot. The principle of moments states that at equilibrium, the total clockwise moment must perfectly balance the total counter-clockwise moment.
The centre of gravity is the point where the total weight of an object acts. For uniform objects, it lies at the geometric centre: the midpoint for a beam, the centre for a sphere, and the central axis midpoint for a cylinder. Stability is improved when the centre of gravity is kept low and vertically within the support base.
Equilibrium requires two conditions: the vector sum of all forces must be zero, and the net moment about any pivot must be zero. Practically, unknown masses are determined by placing them on a beam and balancing them against known weights at varying distances.
Worked Example: A 2.0 kg mass is placed 0.5 m from a pivot. To balance this with a 5.0 kg mass, we set moments equal: (2.0 kg × 9.81 N/kg) × 0.5 m = (5.0 kg × 9.81 N/kg) × d. Solving gives d = 1.0 m / 5.0 = 0.2 m.
A uniform cuboid (including a rectangular beam) has its centre of gravity at its geometric centre; for a uniform sphere it is the centre, and for a uniform cylinder the midpoint on its axis. Treat weight as acting through that point when calculating moments. An object topples when the vertical line of action of its weight falls outside its base: a wider base and lower centre of gravity increase stability.
Density practical: measure the solid’s mass with a zeroed balance. For a regular solid, measure dimensions with appropriate callipers or a micrometer and calculate volume (for a cylinder, V=πd²l/4). For an irregular insoluble solid, fully submerge it and measure the increase in water volume, reading the meniscus at eye level. Convert volume to m³ and calculate ρ=m/V. Repeat readings, check zero errors and estimate the uncertainties in mass and dimensions or the two volume readings.
Unknown-mass practical: first balance a uniform beam with its pivot at its centre of gravity, so its own weight has no turning moment. Put a known mass at a measured perpendicular distance on one side and an unknown mass on the other; adjust until horizontal. From mgd=MgD, m=MD/d. Keep the pivot and beam fixed, measure distances from the pivot to each weight’s line of action, repeat with different positions, and consider pivot friction and distance uncertainty.
What to do in an assessment
Record experimental measurements carefully using analogue instruments like meter rules or scales.
Use interpolation between scale markings to improve the precision of your recorded readings.
Calculate mean values for repeated measurements to reduce random uncertainty.
Manage risk during investigations involving heavy equipment to ensure a safe laboratory environment.
In plain language
This lesson details the foundational SI base units, the mathematical treatment of vectors, the calculation of density, and the principles governing moments and equilibrium.
Self-check
If a body is in equilibrium, what are the two required conditions for the resultant force and net moment?
Show the answer
The resultant force must be zero and the net moment must be zero.
Rectilinear and Projectile MotionCore
Scope: Core · AS Unit 1 §2 KINEMATICS; AS Unit 1 §2 KINEMATICS specified practical work
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What to know
Kinematics is the study of motion without considering its causes. Displacement is the vector change in position from a starting point, distinct from scalar distance. Speed is the scalar rate of change of distance, whereas velocity is the vector rate of change of displacement. Acceleration is defined as the vector rate of change of velocity.
Mean values represent motion over a finite time interval, while instantaneous values describe the motion at a specific, infinitesimal point in time. These are visualised on graphs: displacement-time graphs show velocity via their gradient, and velocity-time graphs show acceleration via their gradient and displacement via the area under the curve.
Equations for uniform linear acceleration are derived from the constant gradient of a velocity-time graph. The fundamental equations are: v = u + at, s = (u + v)t / 2, s = ut + 0.5at², and v² = u² + 2as. These assume the acceleration is constant throughout the motion.
Bodies falling in a gravity field experience uniform acceleration in a vacuum. With air resistance, the net force on an object is weight minus drag. As velocity increases, drag increases until it equals weight, where the net force becomes zero and the object reaches a constant terminal velocity.
Projectile motion is analysed by treating horizontal and vertical components as independent. Horizontally, assuming no air resistance, velocity remains constant because no force acts in that direction. Vertically, the body experiences constant acceleration due to gravity, g, directed downwards.
The motion is combined by solving for each axis separately. For example, a ball thrown horizontally at 15 m/s from a height of 10 m has a vertical time of flight calculated as t = sqrt(2h / g) = sqrt(20 / 9.81) ≈ 1.43 s. The horizontal displacement is then s = vt = 15 m/s × 1.43 s = 21.45 m.
Practically, g is measured using a freefall apparatus. An object is dropped through two light gates separated by a vertical distance. Using s = ut + 0.5at², the timer measures the time t taken to traverse the known gap. Uncertainty is minimised by using high-precision gates and ensuring the object falls vertically.
The independence of motion allows us to resolve any velocity vector into perpendicular horizontal and vertical components, enabling complex paths to be broken into simpler, solvable equations.
This approach ensures that every kinematic calculation remains consistent with the principles of vector decomposition and uniform acceleration models.
Derive the constant-acceleration equations, rather than only quoting them. The straight velocity-time graph has gradient a=(v−u)/t, giving v=u+at. Its trapezium area is displacement s=(u+v)t/2. Substitute v=u+at to obtain s=ut+½at². Eliminate t using t=(v−u)/a to obtain s=(v²−u²)/(2a), so v²=u²+2as. These equations require acceleration constant throughout the chosen interval and a consistent signed direction.
On a displacement-time graph, instantaneous velocity is the gradient of the tangent. A curve with an increasingly steep gradient represents increasing velocity; acceleration need not be constant. On a velocity-time graph, instantaneous acceleration is the tangent gradient, and signed displacement is the area between the curve and the time axis. For changing acceleration, estimate that area in strips or trapezia rather than applying constant-acceleration equations to the whole journey.
What to do in an assessment
Use light gates to minimise human reaction time errors in timing.
Graph velocity-time data to calculate acceleration from the slope.
Apply standard kinematic formulas to both independent axes consistently.
Verify results by checking units for homogeneity.
In plain language
This lesson covers the mathematics of constant acceleration, the independence of motion components, and the experimental determination of gravitational acceleration.
Self-check
A ball is launched horizontally at 8.0 m s⁻¹ from 5.0 m above level ground. Ignoring air resistance, calculate its flight time and horizontal range using g=9.81 m s⁻².
Show the answer
Taking downward as positive, initial vertical speed is zero and 5.0=½×9.81×t², so t=√(10/9.81)=1.01 s. Horizontal speed stays 8.0 m s⁻¹, giving range=8.0×1.01=8.1 m. The same flight time links the independent horizontal and vertical motions; these constant-acceleration equations require negligible air resistance.
View diagrams
Non-uniform motion graphs and centripetal velocity triangle
Constructed non-uniform example x = t², v = 2t and a = 2 in consistent SI units: the tangent gradient on x-t gives instantaneous v, area under v-t gives displacement, and area under a-t gives Δv. A separate equal-speed vector triangle shows Δv = v₂ − v₁ directed approximately toward the centre in circular motion. No measured motion is implied.
Use the labelled model alongside the explanation. Idealised curves are not measured data.
Forces and MomentumCore
Scope: Core · AS Unit 1 §3 DYNAMICS; AS Unit 1 §3 DYNAMICS specified practical work
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What to know
Force represents an interaction changing motion. Newton's 3rd Law dictates that for every force A exerts on B, B exerts an equal and opposite force on A, existing solely as interaction pairs. Free body diagrams isolate a body to map all external forces acting upon it, ignoring internal forces.
Newton's 2nd Law states the resultant force ΣF equals the product of mass m and acceleration a, valid for constant mass. Linear momentum p = mv is a vector quantity defined by the product of mass and velocity.
Force is fundamentally the rate of change of momentum, expressed as F = Δp / Δt. In systems with constant mass, this reduces to F = ma, confirming that resultant force causes acceleration.
The Principle of Conservation of Momentum states that in any closed system, total momentum is constant. Elastic collisions conserve both momentum and total kinetic energy (ΣEk), whereas inelastic collisions dissipate some kinetic energy, often as heat or sound.
Safety systems like crumple zones and airbags increase the duration of an impact (Δt). Given F = Δp / Δt, increasing the time for a fixed change in momentum (Δp) significantly reduces the average impulsive force exerted on passengers.
The investigation of Newton's 2nd law involves a trolley on a track. By applying a constant force (often via a hanging mass over a pulley) and measuring acceleration using light gates, one plots force against acceleration to observe the linear relationship.
Worked example: A 1500 kg vehicle decelerates from 20 m/s to 10 m/s over 2 s. The change in momentum is Δp = m(v - u) = 1500 * (10 - 20) = -15000 kg m/s. The resultant force is F = Δp / Δt = -15000 / 2 = -7500 N, with the negative sign indicating the direction is opposite to initial motion.
To perform such practical work, one must use appropriate analogue instruments such as meter rules or stopwatches, ensuring readings are recorded with proper care to minimise parallax error and uncertainty.
Always apply consistent sign conventions for momentum vectors, treating the direction of motion as positive. Risk assessments are essential when using accelerating masses, ensuring equipment is secured safely before trials.
Significant figures must be maintained throughout calculations to reflect the precision of experimental data. Area under force-time graphs provides the impulse, which equals the total change in momentum, validating the dynamics observed during collisions.
Force is a vector with magnitude and direction. Balanced forces acting on the same body give zero resultant force and therefore zero acceleration, not necessarily zero velocity. Newton’s third-law forces act on different bodies, so they are not two cancelling entries on one free-body diagram. Resolve the forces on the chosen body before applying resultant F=ma.
Newton’s second-law practical: use a low-friction trolley connected over a pulley to a hanging mass, with light gates or a motion sensor measuring acceleration. Measure the total moving mass, including hanger and added masses. For the force investigation, transfer masses from the trolley to the hanger so total moving mass stays constant while the pulling force changes. For the mass investigation, keep the pulling force fixed and add trolley masses. A level track does not remove friction: minimise it, estimate its effect or use a teacher-approved compensation. Plot a against resultant F at fixed mass, or a against 1/m at fixed force. Repeat and assess gate spacing, timing, friction and pulley inertia.
What to do in an assessment
Use appropriate analogue instruments to ensure recording accuracy.
Apply correct sign conventions for momentum vectors.
Perform risk assessments for experiments involving accelerating masses.
Use significant figures consistently in momentum calculations.
Analyse the area under force-time graphs to interpret impulse.
In plain language
This lesson establishes the principles of force, Newton's laws, linear momentum, and collision mechanics through theoretical analysis and experimental validation.
Self-check
A 2.0 kg object moving at 5 m/s hits a stationary 3.0 kg object and sticks to it. Determine the final velocity of the combined mass.
Show the answer
Using conservation of momentum (m1u1 + m2u2 = (m1+m2)v): (2.0 * 5) + (3.0 * 0) = (2.0 + 3.0)v; 10 = 5v; v = 2.0 m/s.
Work, Energy, and PowerCore
Scope: Core · AS Unit 1 §4 ENERGY CONCEPTS
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What to know
Work is fundamentally the process of energy transfer. When a constant force acts on an object, the work done is defined as the product of that force and the distance the object moves in the direction of the force. If the force is applied at an angle θ relative to the displacement, the component of force along the motion is F cos θ, making work done = Fx cos θ.
The Principle of Conservation of Energy dictates that energy cannot be created or destroyed, only transformed between states. Common mechanical energy forms include Gravitational Potential Energy (GPE = mgΔh), Elastic Potential Energy (EPE = ½kx²) stored in springs, and Kinetic Energy (KE = ½mv²).
The work-energy relationship links mechanical work directly to motion changes. The work done by the net force acting on an object is equal to the change in its kinetic energy, expressed as Fx = ½mv² − ½mu², where v is final velocity and u is initial velocity.
Power quantifies the rate of energy transfer, defined as energy per unit time. Systems rarely operate with perfect energy conversion due to dissipative forces. Friction and drag transfer energy out of the mechanical system, typically into thermal energy, which reduces the overall system efficiency.
Efficiency is calculated as the ratio of useful energy transfer to total energy input, expressed as a percentage: Efficiency = (Useful Energy Output / Total Energy Input) × 100%. Improving efficiency requires minimising dissipative losses.
Consider a 50 kg mass accelerated from rest (u=0) to 4 m/s over a distance of 2 m by a constant horizontal force. First, calculate the work done using the work-energy theorem: Fx = ½m(v² − u²) = 0.5 × 50 × (4² − 0) = 400 J. Given x = 2 m, the required force is F = 400 J / 2 m = 200 N.
In practical applications, modelling energy systems requires careful unit management. All energy must be expressed in Joules (J), force in Newtons (N), and distance in meters (m) to maintain physical consistency.
Energy models help evaluate power generation. By comparing useful output against total energy input, engineers determine the viability of different power sources. Conservation of energy remains the primary tool for modelling these transformations.
To check your understanding, consider a motor that consumes 8000 J of electrical energy to lift a weight, performing 2400 J of mechanical work. Calculate the efficiency of this motor. Solution: Efficiency = (2400 / 8000) × 100% = 30%.
What to do in an assessment
Record experimental measurements of force and distance using standardised SI units to ensure calculations remain consistent.
Utilise trigonometry to resolve forces into perpendicular components, ensuring only the force component parallel to motion is used for work calculations.
Identify and isolate dissipative energy losses, such as heat from friction, to accurately analyse system efficiency.
Apply the work-energy theorem to bridge the gap between force-based dynamics and energy-based motion analysis.
In plain language
This lesson establishes the relationships between mechanical work, the conservation of energy, power, and efficiency in physical systems.
Self-check
Define the work-energy relationship in terms of kinetic energy.
Show the answer
The work done by a net force is equal to the change in kinetic energy.
Solids Under StressCore
Scope: Core · AS Unit 1 §5 SOLIDS UNDER STRESS; AS Unit 1 §5 SOLIDS UNDER STRESS specified practical work
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What to know
Hooke’s Law defines the linear relationship between force (F) and extension (x) as F = kx, where k is the spring constant. Beyond this proportionality, we define tensile stress (σ = F/A) and tensile strain (ε = Δl/l). The Young modulus (E) measures stiffness: E = σ/ε. When deforming a material, the work done equals the area under the force-extension graph; if Hooke’s Law holds, this area is 0.5Fx.
Solids are categorised by internal structure as crystalline (metals), amorphous (glass), or polymeric (rubber). In metals, elastic strain is reversible, while plastic strain is permanent. Dislocations allow layers to slide; strengthening is achieved by adding foreign atoms or increasing grain boundaries to block dislocation movement. Ductile materials exhibit necking before fracture.
Brittle materials like glass undergo elastic strain until catastrophic fracture. This failure is driven by crack propagation from surface imperfections. Increasing breaking stress requires minimising imperfections, such as drawing material into thin fibres, or using surface compression techniques like pre-stressing concrete or manufacturing toughened glass.
Rubber displays unique behaviour where Hooke’s Law is only a rough approximation. Its low Young modulus results from the straightening of long chain molecules against thermal opposition. When loaded and then unloaded, rubber follows different paths, resulting in a hysteresis loop where energy is dissipated as heat.
Experimental determination of the Young modulus for a metal wire involves using micrometers to measure diameter with high precision, calculating cross-sectional area (A = πd²/4), and recording extensions under varying loads. The Young modulus is then found from the gradient of the stress-strain graph.
Rubber investigation requires measuring force-extension during a full loading-unloading cycle to observe hysteresis. Digital calipers help track dimensions accurately. Uncertainties in measurements must be calculated, often by estimating the smallest scale division or observing the repeatability of readings.
Worked Example: A 20 N force acts on a 3 m wire with a cross-sectional area of 2 × 10⁻⁶ m², causing an extension of 0.0015 m. First, calculate stress: σ = 20 / (2 × 10⁻⁶) = 1 × 10⁷ Pa. Next, calculate strain: ε = 0.0015 / 3 = 0.0005. Finally, the Young modulus is E = 1 × 10⁷ / 0.0005 = 2 × 10¹⁰ Pa.
In metals, plastic deformation involves dislocations moving through the lattice. Alloying introduces foreign atoms, work-hardening introduces additional dislocations, and grain boundaries interrupt slip; these obstacles restrict dislocation movement and increase strength. In a brittle material, cracks concentrate stress. Reducing surface flaws or placing the surface under compression makes tensile crack growth harder, as in toughened glass; do not confuse higher breaking stress with greater ductility.
What to do in an assessment
Use micrometers for diameter to minimise measurement uncertainty.
Perform a full loading and unloading cycle for rubber to observe hysteresis.
Plot stress-strain graphs to distinguish between elastic and plastic regions.
Ensure consistent units (SI) are used for all stress and strain calculations.
In plain language
This lesson details mechanical properties of materials, covering Hooke’s Law, Young Modulus, and the distinct stress-strain behaviours of metals, brittle substances, and polymers.
Self-check
What is meant by hysteresis in rubber?
Show the answer
Hysteresis refers to the energy dissipated during a loading-unloading cycle of a polymer, represented by the area enclosed between the loading and unloading curves on a force-extension graph.
View diagrams
Stress-strain curves for ductile and brittle materials
Schematic tensile stress-strain curves compare ductile and brittle responses. The initial gradient is Young modulus; the ductile trace shows yielding and plastic extension before fracture, while the brittle trace fractures after a mostly elastic response. The graph is conceptual, with no fabricated measured values.
Use the labelled model alongside the explanation. Idealised curves are not measured data.
Stellar RadiationCore
Scope: Core · AS Unit 1 §6 USING RADIATION TO INVESTIGATE STARS
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What to know
Stellar spectra provide critical diagnostic information about stars. A star emits a continuous spectrum from its dense, hot core. As this radiation passes through the cooler, tenuous outer atmosphere, specific wavelengths are absorbed, creating a line absorption spectrum. This combination allows astronomers to determine stellar composition and physical states.
A black body is an idealised object that absorbs all incident radiation and emits thermal radiation characteristic of its temperature. Stars function as excellent approximations to black bodies. The intensity of radiation emitted by a black body depends on its surface temperature and wavelength.
The black body spectrum exhibits a characteristic shape with a peak wavelength (λ_max). Wien’s displacement law states that λ_max is inversely proportional to absolute temperature (T). The temperature in Kelvin (K) is calculated from the Celsius temperature (θ) using T = θ + 273.15.
Stefan’s Law relates the total power emitted (Luminosity, L) to the surface area (A) and the absolute temperature (T) of the object, expressed as L = σAT^4, where σ is the Stefan-Boltzmann constant. Because a star is spherical, its surface area is 4πr^2, allowing calculation of stellar radius (r).
The inverse square law describes how observed brightness (b) decreases with distance (d) from a source. Since L = 4πd^2b, if the distance to a star doubles, the brightness decreases to 1/4 of its original value. This law enables researchers to calculate distances to stars.
Multiwavelength astronomy observes the cosmos across the entire electromagnetic spectrum. By examining a region at different wavelengths, such as X-ray, ultraviolet, visible, and infrared, scientists observe different photon energies, revealing distinct astrophysical processes that a single waveband might hide.
To illustrate Wien’s Law, consider a star with a peak emission wavelength of 500 nm (500 × 10^-9 m). Given the constant (k = 2.9 × 10^-3 m K), the surface temperature is calculated as T = k / λ_max. Thus, T = 2.9 × 10^-3 / 500 × 10^-9 = 5800 K.
In practical stellar analysis, flux measurements must account for the inverse square law. If a star's distance from Earth increases by a factor of 3, the brightness observed on Earth decreases by a factor of 3^2 = 9. This calculation is essential for mapping galactic distances.
What to do in an assessment
Use Kelvin for all thermodynamics calculations.
Apply standard form when handling small wavelengths and large distances.
Use stellar luminosity and flux ratios to isolate unknown variables like radius or distance.
Interpret peak wavelength shifts on black body curves to compare stellar surface temperatures.
In plain language
This lesson explains how continuous and line absorption spectra, combined with Wien’s, Stefan’s, and inverse square laws, enable astronomers to determine fundamental stellar properties like temperature, radius, and distance.
Self-check
What is a black body, and how does its spectral peak relate to temperature?
Show the answer
A black body is an object that absorbs all incident electromagnetic radiation; its spectrum peaks at a wavelength that is inversely proportional to its absolute temperature.
View diagrams
Blackbody spectral radiance against wavelength
Planck spectral-radiance curves per unit wavelength for ideal blackbodies at 4500 K and 6000 K, plotted against wavelength in nm (not frequency). The higher temperature gives a higher peak and shorter peak wavelength, consistent with Wien’s displacement law. Curves are theoretical, not measured star data.
Use the labelled model alongside the explanation. Idealised curves are not measured data.
Particles and Nuclear StructureCore
Scope: Core · AS Unit 1 §7 PARTICLES AND NUCLEAR STRUCTURE
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What to know
Matter is built from fundamental entities: leptons and quarks. The first generation includes the electron (e⁻) with charge -1, the electron neutrino (νe) with charge 0, the up quark (u) with charge +2/3, and the down quark (d) with charge -1/3. These particles are characterized by lepton numbers and specific charges.
Antiparticles mirror these properties. An antiparticle, such as a positron (e⁺) or an anti-up quark (ū), possesses the same mass as its counterpart but reverses the sign of all additive quantum numbers, such as charge and lepton number. When a particle meets its antiparticle, they annihilate.
Quarks do not exist freely. They are bound into hadrons via the strong force. Baryons consist of three quarks, while mesons contain a quark-antiquark pair. The proton is composed of uud quarks (charge +2/3 + 2/3 - 1/3 = +1), and the neutron is composed of udd quarks (charge +2/3 - 1/3 - 1/3 = 0).
Charged pions are examples of mesons. A π⁺ is an u d̄ pair, and a π⁻ is a ū d pair. Hadrons are classified by their quark structure, which determines their interactions. The strong force acts on all quarks, whereas electromagnetic forces couple to charge, including the charged quarks inside neutral hadrons.
Four fundamental interactions govern particle physics. Gravitational interaction acts on all matter but is negligible at the subatomic scale. Electromagnetic interaction has an infinite range, affecting charged particles. The strong force, with a short range, binds quarks within hadrons. The weak interaction has a very short range and is experienced by all quarks and leptons. Neutrinos have no electric charge and do not experience the strong interaction; their particle reactions involve the weak interaction, though they also gravitate.
Weak interaction is unique because it permits quark flavour changes and involves neutrinos. During such processes, fundamental conservation laws must be maintained: charge, lepton number, and baryon number.
Consider the neutron decay reaction: n → p + e⁻ + ν̄e. Charge: 0 → +1 - 1 + 0 = 0 (conserved). Baryon number: 1 → 1 + 0 + 0 = 1 (conserved). Lepton number: 0 → 0 + 1 - 1 = 0 (conserved). This confirms the interaction is consistent with physical laws.
The electron and electron neutrino have lepton number +1; their antiparticles have −1. Quarks have lepton number zero. Each quark has baryon number +⅓ and each antiquark −⅓, so baryons have +1, antibaryons −1 and mesons zero. An antibaryon contains three antiquarks. Three generations of quarks and leptons exist, but this course’s required particle questions use first-generation particles. Charge values here are multiples of the elementary positive charge e. The four interactions differ in relative strength and range: strong interactions are strongest and the force between nucleons acts over about 10⁻¹⁵ m; electromagnetic forces have infinite range and are weaker than the strong interaction; weak interactions have range about 10⁻¹⁸ m and cause flavour-changing processes; gravity has infinite range but is extraordinarily weak at particle scales. Neutrinos participate in weak interactions and gravity, not electromagnetic or strong interactions. Conserved quantum numbers alone do not prove that a reaction has enough energy to occur: beta-plus conversion of a proton happens in an energetically allowed nucleus, not as spontaneous decay of a free proton.
Use a bar to identify antiparticles: ū and d̄ are anti-up and anti-down quarks; p̄ is an antiproton (ūūd̄) and n̄ an antineutron (ūd̄d̄). The positron is e⁺ and the electron antineutrino ν̄ₑ. Antiparticle symbols change the additive quantum numbers, not the rest mass.
Read the interaction comparison by four properties. Gravity: experienced by all matter, infinite range, extremely weak on particle scales. Weak: experienced by all leptons and quarks and hence hadrons, very short range, significant where electromagnetic and strong processes cannot cause the change. Electromagnetic: infinite range, acts on electric charge; neutral hadrons can still interact through their charged constituent quarks. Strong: experienced by quarks and hence hadrons, short range between nucleons; it binds quarks into hadrons and produces the residual nuclear binding interaction.
What to do in an assessment
Create a table comparing particle properties including charge and lepton numbers.
Practice identifying the quark content of various mesons and baryons.
Calculate conservation of charge and lepton number for decay equations.
Use Feynman-style diagrams to visualise the four fundamental interactions.
In plain language
This lesson details the structure of matter via quarks and leptons, explains the four fundamental forces, and demonstrates how to apply conservation laws to particle reactions.
Self-check
A π⁺ meson contains u and d̄. Calculate its charge and baryon number. Then check charge, lepton and baryon numbers for n → p + e⁻ + ν̄ₑ.
Show the answer
u has charge +⅔e and d̄ has +⅓e, so π⁺ has charge +e. Baryon number is +⅓−⅓=0. In neutron beta-minus decay, charge is 0=+1−1+0; baryon number is 1=1+0+0; lepton number is 0=0+1−1. The antineutrino is essential for lepton-number conservation. These checks establish conservation, not the energy balance of every proposed reaction.

Conduction and Electrical Current DynamicsCore
Scope: Core · AS Unit 2 §1 CONDUCTION OF ELECTRICITY
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What to know
Electric charge is measured in coulombs (C), with the elementary charge e representing a fraction of a coulomb. Conductors facilitate charge flow. Current I is defined as the rate of flow of charge Q over time t, expressed as I = ΔQ/Δt. Measured in ampères (A), 1 A is equivalent to 1 C s⁻¹.
In metals, conduction occurs via the drift of free electrons. Conventional current is defined as moving from positive to negative, whereas electron drift involves actual electrons moving in the opposite direction, reflecting the kinetic movement of charge carriers.
To derive I = nAve, consider a wire section with cross-sectional area A and length x = vΔt, where v is the average drift velocity. The volume of this segment is AvΔt. If n is the number density of free electrons, the total number of electrons in this volume is nAvΔt. Total charge ΔQ = nAvΔt * e. Substituting this into I = ΔQ/Δt yields I = nAve.
Worked Example: A copper wire (area 2.0e-7 m²) carries 2 A current. If n = 8.5e28 m⁻³ and e = 1.6e-19 C, calculate drift velocity v. Using v = I / (nAe), v = 2 / (8.5e28 * 2.0e-7 * 1.6e-19) = 7.35e-4 m s⁻¹.
The elementary charge has magnitude e=1.602×10⁻¹⁹ C. Conventional current follows the direction of positive-charge flow; free electrons in a metal drift in the opposite direction. In I=nAve, v is drift-speed magnitude, not the speed at which the electric-field disturbance travels. Current is rate of charge flow I=ΔQ/Δt; over steady time t, Q=It.
What to do in an assessment
1. Memorise the fundamental definitions of charge, current, and potential difference.
2. Practice deriving I = nAve and Snell's Law from first principles.
3. Sketch and label I-V characteristic graphs for resistors, lamps, and diodes.
4. Review experimental setups for measuring internal resistance and resistivity.
5. Master the photon and wave equations by performing calculations in standard units.
In plain language
This lesson synthesizes the principles of electrical conduction, circuit analysis, wave properties, optics, and quantum physics into a unified framework for understanding electromagnetism and modern physics.
Self-check
Calculate the current in a wire with electron density 8.0e28 m⁻³, area 1.5e-7 m², and drift velocity 5.0e-4 m s⁻¹ using e = 1.6e-19 C.
Show the answer
0.96 A
Resistance and Electrical CharacteristicsCore
Scope: Core · AS Unit 2 §2 RESISTANCE; AS Unit 2 §2 RESISTANCE specified practical work
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What to know
Potential difference is defined as the energy transferred per unit charge, measured in volts (V), where 1 V = 1 J C⁻¹. Resistance R is defined via Ohm's law, V = IR, measured in ohms (Ω), where 1 Ω = 1 V A⁻¹. Power dissipation follows P = IV = I²R = V²/R.
At the microscopic level, electrical resistance arises from collisions between free electrons and lattice ions. As these collisions increase the random vibration energy of ions, the metal's temperature rises. Consequently, resistance typically increases with temperature.
Resistivity ρ relates geometry to resistance via R = ρl/A, where l is length and A is cross-sectional area. Superconductivity occurs when a material's resistance drops to zero below a specific transition temperature. Most metals exhibit this near absolute zero (-273 °C), while high-temperature superconductors function above the boiling point of liquid nitrogen (-196 °C). Practical uses include MRI scanners and particle accelerators.
In the specified practical I-V investigation, a circuit with a power supply, ammeter, and voltmeter is used to plot characteristics for a lamp and resistor. A metal wire shows linear V-I behaviour (Ohmic), while a lamp shows a curve as its resistance rises with heat. For resistivity, one measures the diameter of a wire (using a micrometer) and length, then calculates R for varying lengths to plot R against l; the slope is ρ/A. For temperature variation, a wire coil is heated in an oil bath, recording R via an ohmmeter against temperature.
Example: A wire of 0.5 mm diameter (r = 0.25e-3 m) and 2 m length has R = 0.8 Ω. Area A = π(0.25e-3)² ≈ 1.96e-7 m². Using ρ = RA/l = (0.8 * 1.96e-7) / 2 = 7.84e-8 Ω m.
Potential difference V is energy transferred (work done) per unit charge: V=W/Q, in J C⁻¹. Resistance is R=V/I, in ohms. A metal wire at constant temperature has an I-V straight line through the origin, so resistance is constant. A filament lamp heats as current rises; increased lattice vibration causes more scattering and increasing resistance, so its I-V curve becomes less steep. Draw and label both positive and negative quadrants for these non-polarised components.
For the specified I-V investigation, connect an ammeter in series and a voltmeter across the component, using a variable low-voltage supply or resistor. Record I and V in both polarities and plot I vertically against V horizontally. Keep the metal wire’s temperature constant using small currents and brief readings; the lamp’s temperature changes are part of its behaviour. For the separate resistivity practical, measure wire diameter at several positions with a micrometer, calculate A=πd²/4, measure several lengths and R=V/I, then plot R against l: gradient=ρ/A. Avoid heating and investigate contact/lead resistance through the intercept.
For the separate metal-resistance temperature practical, place the metal specimen and thermometer in a controlled bath, allow thermal equilibrium at each temperature, and measure R using a small current. Plot R against temperature and repeat on cooling where feasible. Superconductivity is different from an ordinary metal’s gradual resistance reduction: below a material-dependent transition temperature resistance becomes zero. Practical superconducting magnets require suitable cryogenic cooling; not every superconductor has the same transition temperature.
What to do in an assessment
Sketch I-V graphs for resistors, filaments, and diodes to identify linear versus non-linear regions.
Practice rearranging R = ρl/A to solve for cross-sectional area and radius.
Review how internal energy of metal ions increases due to electron collisions.
Memorise the definitions of transition temperatures for standard vs high-temperature superconductors.
In plain language
This lesson covers the fundamental physics of resistance, resistivity, and temperature effects on metals, including practical circuit analysis and the phenomenon of superconductivity.
Self-check
If a metal wire's temperature increases, why does its resistance rise according to the collision model?
Show the answer
A hotter metal lattice has greater ion vibration. Free electrons are scattered more frequently, so for a given potential difference their drift speed/current is lower and R=V/I is larger. It is not the temperature rise being caused by the definition of resistance; state the mechanism for the already hotter wire.
Direct Current Circuits: Principles and Internal ResistanceCore
Scope: Core · AS Unit 2 §3 D.C. CIRCUITS; AS Unit 2 §3 D.C. CIRCUITS specified practical work
Open revision guidance
What to know
Electric circuits operate on the fundamental principles of conservation of charge and energy. In a parallel circuit, current from the source splits into branches; the total current entering a junction equals the sum of currents leaving it, demonstrating conservation of charge. In a series circuit, the total supply potential difference (pd) equals the sum of individual pd values across components, reflecting energy conservation as charges transfer energy to components.
Potential difference is defined by the energy J per unit charge C, measured in Volts. In parallel configurations, the pd across each branch is identical. Combined resistance is calculated as the sum for resistors in series, or via the reciprocal sum (1/R_total = 1/R1 + 1/R2) for parallel branches.
A potential divider uses series resistors to output a fraction of the source voltage. By substituting a fixed resistor with an LDR or thermistor, the output voltage becomes sensitive to ambient light or temperature changes.
Electromotive force (emf) represents the energy per unit charge supplied by a source, measured in the same unit as pd. Real cells possess internal resistance (r), meaning terminal pd (V) is less than emf (E) when current (I) flows, expressed as V = E - Ir.
To measure internal resistance, plot terminal voltage (V) against current (I) across a variable load. The intercept on the V-axis is emf (E), and the gradient is -r. Practical precautions include using a high-impedance voltmeter to minimise load impact and limiting current to prevent overheating.
Example: A cell has E=1.5V, r=0.5Ω. With a 2.5Ω load, I = 1.5/(2.5+0.5) = 0.5A. Terminal V = 1.5 - (0.5*0.5) = 1.25V.
Series resistors carry the same current and their potential differences add, so Rtotal=R₁+R₂+…. Parallel branches have the same potential difference and their currents add, so 1/Rtotal=1/R₁+1/R₂+…. For cells in series, add emfs algebraically according to polarity and add their internal resistances: I=Etotal/(Rload+rtotal). Identical aiding cells double both emf and internal resistance; a reversed cell opposes the others.
For the internal-resistance practical, draw the circuit with cell, switch, ammeter and variable load in series, and voltmeter across the cell terminals. Vary the load without short-circuiting the cell; record paired terminal V and I readings, opening the switch between readings to limit heating and discharge. Plot V against I: V=E−rI, so intercept is emf E and gradient is −r. Estimate meter uncertainties and use plausible steepest/shallowest lines to assess r; a changing cell condition or meter loading can produce systematic errors.
What to do in an assessment
Draw circuit diagrams labelling current flow and nodes.
Derive V=E-Ir by rearranging energy conservation equations.
Compare series versus parallel rules for every variable.
Analyse potential divider behaviour under changing sensor resistance.
In plain language
This lesson establishes D.C. circuit rules based on conservation laws and the practical determination of internal resistance in electrical sources.
Self-check
If a cell has an emf of 12V and an internal resistance of 1Ω, what is the terminal voltage when the circuit current is 2A?
Show the answer
Using V = E - Ir, V = 12V - (2A * 1Ω) = 10V.
Wave Properties and PolarisationCore
Scope: Core · AS Unit 2 §4 THE NATURE OF WAVES; AS Unit 2 §4 THE NATURE OF WAVES specified practical work
Open revision guidance
What to know
A progressive wave transfers energy without transferring matter.
Transverse waves oscillate perpendicular to the direction of energy flow, while longitudinal waves oscillate parallel to it.
Polarisation occurs when transverse waves are restricted to a single plane of oscillation. Only transverse waves can be polarised.
Wave terms: displacement is distance from equilibrium; amplitude is maximum displacement; wavelength is distance between successive identical points; period is time for one oscillation; frequency is oscillations per second; wave speed is distance travelled per unit time.
The wave equation c = f * lambda relates speed, frequency, and wavelength.
Graphical representations include displacement-time and displacement-position plots, restricted to transverse waves.
Wavefronts are lines where points oscillate in phase; rays represent direction of energy flow, always perpendicular to wavefronts.
Practical Method: Polarisation. Apparatus: light source, two polarising filters, light intensity sensor. Rotate one filter relative to the other. Measure intensity versus rotation angle. Plot intensity against cos squared theta to observe Malus law. Safety: do not look directly into high-intensity beams. Uncertainty: monitor background light levels.
Worked Example: A wave with frequency 50 Hz and speed 340 m/s has a wavelength of lambda = 340 / 50 = 6.8 m.
Points are in phase when separated by integer multiples of lambda, and in antiphase when separated by odd half-integer multiples.
Polarisation experiment measures how intensity varies, confirming the transverse nature of electromagnetic waves.
Ensure all calculations use standard SI units, checking significant figures for accuracy.
What to do in an assessment
Distinguish clearly between transverse and longitudinal motion.
Memorise the wave equation and practice rearranging it.
Understand that polarisation intensity follows the angle squared relationship.
Sketch both types of displacement graphs to differentiate position and time.
In plain language
This lesson covers the fundamentals of progressive waves, their graphical analysis, and the investigation of transverse properties through polarisation.
Self-check
What is the physical significance of the ray relative to the wavefront?
Show the answer
The ray indicates the direction of energy propagation and is always perpendicular to the wavefront.
Wave Interference and DiffractionCore
Scope: Core · AS Unit 2 §5 WAVE PROPERTIES; AS Unit 2 §5 WAVE PROPERTIES specified practical work
Open revision guidance
What to know
Diffraction occurs when waves encounter obstacles or slits. If wavelength λ is much smaller than slit width, minimal diffraction occurs. For λ ≥ slit width, waves spread as semicircular wavefronts; for smaller slits, the beam spreads less than 180 degrees.
Two-source interference requires coherent sources. Coherent sources are monochromatic with continuous wavefronts and a constant phase relationship. Examples include laser light (coherent) versus incandescent bulbs (incoherent).
Superposition is the principle where displacements add algebraically. Constructive interference occurs at path difference nλ, destructive at (n + 0.5)λ. Young’s experiment demonstrated light's wave nature using path difference. The approximation λ = aΔy/D relates wavelength λ to slit separation a, fringe spacing Δy, and screen distance D.
Diffraction gratings use d sin θ = nλ. A small grating spacing d spreads orders significantly, while many slits sharpen bright fringes.
Stationary waves result from superposition of two equal progressive waves travelling in opposite directions. Internodes occur at λ/2 spacing. Unlike progressive waves, they do not transport matter.
Practical 1: Measure λ using Young’s slits. Apparatus: laser, double slit, screen. Measured: D, a, Δy. Control: constant laser position. Uncertainty: slit distance measurement. Safety: never look into laser beams.
Practical 2: Measure λ using a diffraction grating. Measured: n, θ, d. Useful graph: sin θ against n (slope = λ/d). Practical 3: Speed of sound using stationary waves (resonance tube).
Numerical Example: A 500 lines/mm grating (d = 2.0x10^-6 m) illuminated by 600 nm light. For n=1, sin θ = (1 * 600x10^-9) / 2.0x10^-6 = 0.3. Thus, θ = 17.5 degrees.
To derive the grating equation, consider rays from adjacent slits separated by d, leaving at angle θ to the grating normal. Their path difference is d sinθ. A bright principal maximum requires the waves in phase, so this path difference equals a whole number n of wavelengths: d sinθ=nλ. Order n=0 is central; use the absolute order for either side and reject solutions with |sinθ|>1.
For Young’s two-slit pattern, a path difference of one wavelength separates adjacent bright fringes. At small angles, sinθ≈tanθ≈y/D, giving fringe spacing Δy=λD/a or λ=aΔy/D. D is screen distance, a slit separation and Δy spacing between adjacent fringes; measure several spacings and divide by their number to reduce uncertainty. The approximation needs fringe displacement small compared with D, not every imaginable screen geometry.
Adjacent nodes of a stationary wave are λ/2 apart; adjacent antinodes are also λ/2 apart. A node and its neighbouring antinode are λ/4 apart. All particles in one segment between nodes oscillate in phase; adjacent segments oscillate in antiphase. Energy is not carried continuously along the stationary pattern as in a single progressive wave.
For the sound stationary-wave practical, use a known-frequency loudspeaker with a microphone and oscilloscope, or a teacher-provided resonance-tube arrangement. With microphone scanning, locate successive amplitude minima or maxima and measure several adjacent-node or adjacent-antinode separations: λ=2×mean separation, then c=fλ. With a closed resonance tube, successive resonant air-column lengths differ by λ/2, which cancels the end correction approximately. Record frequency and positions, repeat, consider end effects and resolution, and avoid excessive sound levels.
What to do in an assessment
1. Sketch interference and diffraction patterns to visualise wavefront overlap.
2. Memorise the path difference rules for constructive and destructive interference.
3. Practice deriving the diffraction grating equation from geometry.
4. Distinguish between stationary waves and progressive waves using amplitude and phase characteristics.
In plain language
This lesson covers the principles of wave interference, diffraction patterns, and stationary waves with practical applications for determining wavelength and sound speed.
Self-check
How does the slit separation d in a diffraction grating affect the spacing and sharpness of interference orders compared to a double-slit?
Show the answer
A smaller d increases the angular separation between orders, while a higher number of slits results in sharper, more intense bright maxima due to increased destructive interference between orders.
View diagrams
Superposition of two waves
Use the labelled model alongside the explanation. Idealised curves are not measured data.
Refraction and Wave PropagationCore
Scope: Core · AS Unit 2 §6 REFRACTION OF LIGHT; AS Unit 2 §6 REFRACTION OF LIGHT specified practical work
Open revision guidance
What to know
Refraction is the change in direction of a wave crossing a boundary between media with different refractive indices. The refractive index n is defined as n = c/v, where c is the vacuum light speed and v is the speed in the medium.
As waves cross a boundary, frequency remains constant, but speed v and wavelength lambda change. Snell law n1 sin theta1 = n2 sin theta2 relates these properties. Using the wave model, consider plane wavefronts hitting a boundary; as one part of the wavefront enters the slower medium, the wavefront pivots, changing the ray direction.
Total internal reflection occurs when moving from a high to low refractive index medium (n1 > n2) if the incidence angle exceeds the critical angle theta_c, where sin theta_c = n2/n1.
For a refractive index practical, one typically uses a glass block, light box, and protractor. Measure incidence angles i and refraction angles r. Plot sin i against sin r. The gradient equals the refractive index n of the block. Ensure the block is perpendicular to the ray path, estimate uncertainty in angles, and wear laser safety goggles.
Worked Example: If light enters glass (n=1.5) from air (n=1.0) at 30 degrees, sin r = (1.0 * sin 30) / 1.5 = 0.333. Thus, r = 19.5 degrees.
Optical fibres use total internal reflection to guide light. Multimode fibres carry multiple modes; however, different paths have different lengths, leading to multimode dispersion which limits data rates and distance.
Monomode fibres have a small core diameter such that only one mode propagates. This minimises dispersion, allowing much higher bandwidth and longer transmission distances.
Step 1: Define n as c/v and learn the Snell law formula. Step 2: Sketch wavefront diagrams to visualise refraction. Step 3: Derive the critical angle relation using n1 sin theta = n2 sin 90. Step 4: Compare multimode and monomode fibre constraints.
Derive the critical-angle relation using Snell’s law for passage from index n₁ into lower index n₂. At the critical angle, the refracted ray is at 90° to the normal, so n₁sinθc=n₂sin90°=n₂ and sinθc=n₂/n₁. Total internal reflection needs n₁>n₂ and incident angle greater than θc. At the boundary, frequency stays fixed: slower speed means shorter wavelength, with wavefronts closer together and rays bending towards the normal.
What to do in an assessment
Define refractive index as the ratio of vacuum light speed to speed in a medium.
Sketch ray and wavefront diagrams to illustrate how wave velocity changes affect direction.
Derive the critical angle formula by setting the refraction angle to 90 degrees in Snell law.
Contrast the data transmission limitations of multimode versus monomode optical fibres.
In plain language
This lesson covers light refraction physics, total internal reflection, Snell law derivations, and the application of fibre optics technology.
Self-check
Explain why multimode dispersion limits data transmission in multimode optical fibres.
Show the answer
Multimode fibres allow light to travel via multiple paths (modes) of different lengths, causing signals to spread in time and overlap, which restricts the achievable data rate and transmission distance.
View diagrams
Reflection, refraction and total internal reflection
Rays show equal reflection angles, refraction towards the normal in a slower medium, and total internal reflection from an optically denser medium above its critical angle. Plane wavefronts are perpendicular to the rays and closer together in the slower medium.
Use the labelled model alongside the explanation. Idealised curves are not measured data.
Quantum Physics of Photons and MatterCore
Scope: Core · AS Unit 2 §7 PHOTONS; AS Unit 2 §7 PHOTONS specified practical work
Open revision guidance
What to know
Light behaves as discrete energy packets termed photons, where energy E equals hf. The photoelectric effect confirms this, where illumination of a metal surface releases electrons if the photon energy exceeds the work function.
In a vacuum photocell experiment, incident light releases photoelectrons. Applying a reverse potential until current stops defines stopping voltage Vs, where Ek_max = e * Vs. Measuring Ek_max against radiation frequency f yields a linear plot.
Einstein's relation, Ek_max = hf - phi, explains this. The gradient of the Ek_max-f graph is Planck constant h, the intercept is the negative work function -phi, and the x-intercept is the threshold frequency f0.
The visible spectrum ranges from 700 nm (red) to 400 nm (violet). Photon energy varies across the electromagnetic spectrum, with gamma-ray photons being significantly more energetic than radio photons.
Atoms produce discrete line emission spectra when electrons drop between energy levels, emitting specific energy photons (delta E = hf). Line absorption occurs when photons are absorbed, matching energy gaps.
Energy level diagrams display these discrete states. Ionisation energy is the energy required to lift an electron from the ground state to the zero energy level (n = infinity). A diffraction grating can resolve these lines.
Matter exhibits wave properties; electron diffraction displays wave-like aspects. The de Broglie relation p = h / lambda applies universally to both photons and particles of matter.
Radiation pressure occurs as photons exert force. A surface absorbing photons of energy E receives momentum p = E / c, while reflection doubles this momentum change.
Practical Method: Determining h using LEDs. Apparatus: LED, variable supply, ammeter, voltmeter, spectroscope. Measure the turn-on voltage V where current begins to flow. V is proportional to f, and using V = hf / e, h can be determined.
Safety and Uncertainty: Avoid looking directly into LEDs. Use small increments of voltage near the threshold to reduce uncertainty. The LED limitation is that the emission range affects the precision of V.
Worked Example: A photon has f = 6.0e14 Hz. Its energy E = 6.63e-34 * 6.0e14 = 3.98e-19 J. In eV, E = 3.98e-19 / 1.6e-19 = 2.49 eV.
Representative wavelength orders, not hard universal boundaries: radio can be metres to kilometres; microwaves around 10⁻² m; infrared around 10⁻⁵ m; visible around 4×10⁻⁷–7×10⁻⁷ m; ultraviolet around 10⁻⁸ m; X-rays around 10⁻¹⁰ m; gamma around 10⁻¹² m. Use E=hc/λ to compare photon energies: a 10⁻¹⁰ m photon has about 2.0×10⁻¹⁵ J≈12 keV, far above a visible photon’s few eV. Bands are approximate and X-rays/gamma can overlap in wavelength.
Through a diffraction grating, an excited low-pressure gas produces separate bright coloured lines at particular angles, each wavelength satisfying d sinθ=nλ. A continuous source viewed through a cooler gas instead shows dark absorption lines at the matching transition wavelengths. The grating spreads wavelengths into their angular positions; it does not create the atom’s discrete energies.
For radiation incident normally on area A, absorbing photons transfers momentum E/c and perfect reflection transfers 2E/c. For incident power P, force is P/c for complete absorption or 2P/c for ideal reflection. Divide by area: pressure=I/c or 2I/c, with intensity I=P/A in W m⁻². For I=600 W m⁻², absorption pressure=600/(3.0×10⁸)=2.0×10⁻⁶ Pa; ideal reflection gives 4.0×10⁻⁶ Pa. These are pressures, not optical intensities or electric currents.
What to do in an assessment
Memorise the definitions of work function and threshold frequency as critical parameters.
Sketch the Ek_max versus f graph frequently to internalize the physical meaning of the gradient and intercepts.
Practice converting between Joules and electron-volts to avoid unit errors.
Relate the de Broglie equation to both light and matter to grasp the concept of wave-particle duality.
In plain language
This lesson details the quantum behaviour of light and matter, covering the photoelectric effect, atomic spectra, de Broglie wave-particle duality, and experimental methods to determine fundamental constants.
Self-check
If the threshold frequency of a metal surface is 5.0e14 Hz, what is the work function in Joules?
Show the answer
phi = h * f0 = 6.63e-34 * 5.0e14 = 3.32e-19 J.
Principles and Operations of LasersCore
Scope: Core · AS Unit 2 §8 LASERS
Open revision guidance
What to know
Lasers rely on stimulated emission, where an incoming photon interacts with an excited atom, triggering it to release a second photon identical in phase, frequency, and direction, resulting in coherent light.
To achieve amplification, a population inversion is necessary, where the number of atoms in an upper energy state (N2) exceeds those in a lower state (N1). In a simple two-level system, this is generally impossible because the rate of stimulated absorption balances stimulated emission, keeping N1 > N2.
Practical lasers use three-level or four-level systems. Pumping is the process of supplying energy to excite electrons from the ground state to higher levels. Four-level systems are more efficient as they allow population inversion between intermediate levels, avoiding the need to empty the ground state entirely.
In a three-level laser, pumping excites atoms from the ground level to a high level. They quickly drop without emitting the laser photon into a longer-lived metastable upper laser level. The laser transition returns them to the ground level, so more than half the relevant atoms must be excited to make the upper population exceed the lower population. In a four-level laser, the laser transition ends at a level above the ground state which empties rapidly. That lower laser level stays sparsely populated, so inversion can be sustained with much less pumping. It is Nupper>Nlower for the laser transition, not necessarily more excited atoms than ground-state atoms.
Laser structure consists of an amplifying medium placed between two mirrors. One mirror is fully reflective while the other is partially transmissive, allowing a beam of coherent light to escape.
Semiconductor lasers are widely used in devices such as CD and DVD players and telecommunications. They are favored for being compact, inexpensive, and significantly more efficient than gas or crystal lasers.
Numerical Worked Example: An electron transition releases a photon with frequency 4.74e14 Hz. Calculate energy E = hf where h = 6.63e-34 J s. Result: E = 3.14e-19 J.
What to do in an assessment
Review the energy level diagrams for 3-level vs 4-level systems.
Practice deriving the population inversion necessity.
Compare the efficiency of semiconductor lasers against gas lasers.
Analyse the role of the resonator mirrors in building optical gain.
In plain language
This lesson covers the quantum mechanics of stimulated emission, the necessity of population inversion for optical gain, and the practical implementation of semiconductor lasers.
Self-check
Why is a four-level energy system more effective than a two-level system for creating a laser?
Show the answer
Pumping a two-level system drives both absorption and stimulated emission on the same transition; ordinary optical pumping approaches equal populations rather than maintaining inversion. A four-level route pumps to a high level, relaxes into a relatively long-lived upper laser level, emits into a rapidly emptied lower laser level, and returns to the ground state. It can therefore sustain Nupper>Nlower with a much smaller excited fraction. A three-level laser’s lower laser level is the ground state, so inversion is harder.

Circular Motion PrinciplesCore
Scope: Core · A2 Unit 3 §1 CIRCULAR MOTION
Open revision guidance
What to know
Circular motion describes an object moving at constant speed along a circular path. Although speed remains constant, the velocity vector is continuously changing direction, necessitating a centripetal acceleration. This acceleration is directed towards the centre of the circle.
The radian is defined as the angle subtended at the centre of a circle by an arc equal in length to the radius. An angle in radians is given by arc length divided by radius, making it a dimensionless measure of rotation.
Angular velocity omega is the rate of change of angular position, measured in radians per second. It relates to linear speed v via the equation v = omega r. The period T is the time for one full rotation, related to frequency f by T = 1/f. Consequently, omega = 2 pi f = 2 pi / T.
Centripetal force is the resultant force directed towards the circle centre required to maintain circular motion; it is not a new or extra force added to the system.
The fundamental equations are a = omega^2 r, a = v^2 / r, F = m v^2 / r, and F = m omega^2 r. These equations define the dynamics of particles in uniform circular motion.
Worked Example: A 0.5 kg mass moves in a circle of radius 2.0 m at an angular velocity of 3 rad/s. Calculating force: F = m omega^2 r = 0.5 * (3)^2 * 2.0 = 9 N.
Physics of motion requires distinguishing between linear velocity components and radial accelerations. Understanding that centripetal force arises from physical interactions like tension or friction is essential.
Safety during practical work involves ensuring mounts are secure when rotating masses and using protective screens if objects might detach at high speeds.
The angular frequency ω used to describe SHM is the angular speed of its corresponding uniform circular-motion phase: ω=2πf=2π/T. A sinusoidal projection of uniform circular motion oscillates, although its actual displacement is along a line and its instantaneous linear velocity changes. Do not equate ω with that changing linear velocity.
What to do in an assessment
Define the period and frequency in terms of circular rotation.
Apply the radian unit to convert between arc length and angular displacement.
Identify the resultant centripetal force in diverse mechanical contexts.
Perform calculations using the standard circular motion equations.
In plain language
This lesson covers the kinematics and dynamics of uniform circular motion, defining centripetal force as the resultant directed towards the centre, and establishing the relationship between angular and linear variables.
Self-check
What is the centripetal acceleration of an object moving at 5 m/s in a circle of radius 2 m?
Show the answer
Using a = v^2 / r, the acceleration is (5^2) / 2 = 12.5 m/s^2.
Simple Harmonic Motion and OscillationsCore
Scope: Core · A2 Unit 3 §2 VIBRATIONS; A2 Unit 3 §2 VIBRATIONS specified practical work
Open revision guidance
What to know
Simple Harmonic Motion (SHM) is defined as motion where the acceleration is directly proportional to the displacement from a fixed equilibrium position and is always directed towards that position. The defining mathematical equation is a = -ω²x, where a is acceleration, ω is angular frequency, and x is displacement.
For an object in SHM, displacement over time is given by x = Acos(ωt + ε), where A is amplitude and ε is the phase constant. Velocity is the first derivative, v = -Aωsin(ωt + ε). Acceleration is the second derivative, confirming a = -ω²x. Graphs of these functions show displacement as a cosine wave, velocity as a negative sine wave, and acceleration as a negative cosine wave.
The period T of an oscillator relates to frequency f and angular frequency ω by T = 1/f = 2π/ω. For a mass-spring system, T = 2π√(m/k), where k is stiffness. For a simple pendulum undergoing small-angle oscillations, T = 2π√(l/g).
Energy in an undamped SHM system oscillates between kinetic and potential forms. Total energy is conserved. At maximum displacement (x = A), potential energy is maximum and kinetic energy is zero. At equilibrium (x = 0), kinetic energy is maximum and potential energy is zero.
To measure the acceleration due to gravity (g) with a pendulum, suspend a bob on a string of length l. Measure the time for multiple oscillations to find T. Use the gradient of a graph of T² against l (where T² = 4π²l/g) to calculate g. Minimise uncertainty by using a fiduciary marker and timing over many periods.
Numerical Example: A mass of 0.2 kg on a spring of constant 50 N/m oscillates with amplitude 0.05 m. Calculate maximum acceleration. Substituting: ω² = k/m = 50/0.2 = 250 rad²/s². Thus, a_max = ω²A = 250 * 0.05 = 12.5 m/s².
What to do in an assessment
Memorise the defining equation a = -ω²x and the derivative-based solutions for displacement and velocity.
Practice rearranging period equations for different variables and ensure units are consistent (e.g., kg, m, s, N).
Understand that g is determined from the gradient of a T² vs l graph, ensuring experimental setup includes a plumb line for precision.
Interpret resonance curves by noting how damping lowers amplitude and broadens the frequency response range.
In plain language
This lesson covers the kinematics of SHM, energy conservation in oscillators, damped/forced vibrations, kinetic theory of gases, thermal physics laws, and experimental methods for determining g.
Self-check
A 0.20 kg mass on a spring of stiffness 50 N m⁻¹ oscillates with amplitude 0.040 m. Calculate its period and maximum speed, assuming undamped small oscillations.
Show the answer
ω=√(k/m)=√(50/0.20)=15.8 rad s⁻¹. T=2π/ω=0.397 s≈0.40 s. Maximum speed is Aω=0.040×15.8=0.632 m s⁻¹≈0.63 m s⁻¹, at equilibrium; speed is zero at the turning points. The amplitude is in metres, not centimetres.
View diagrams
Simple harmonic motion graphs and phasor
For x = A cos(ωt), v = −ωA sin(ωt) and a = −ω²A cos(ωt). The aligned time traces show the quarter-cycle phase relationships; the unit-circle phasor rotates anticlockwise and its horizontal projection is x/A. Normalised, dimensionless curves are mathematical, not measurements.
Use the labelled model alongside the explanation. Idealised curves are not measured data.
Oscillations: Resonance and DampingCore
Scope: Core · A2 Unit 3 §2 VIBRATIONS; A2 Unit 3 §2 VIBRATIONS specified practical work
Open revision guidance
What to know
Circular motion defines angular velocity as omega equals change in angle over time, where a full circle is 2pi radians. Frequency f equals 1 over period T. The inward resultant force, centripetal force, is not a new force but a vector sum acting toward the centre. At constant speed v, velocity changes direction, hence acceleration a equals omega squared r or v squared over r, with force F equal to m omega squared r.
Simple harmonic motion (SHM) is defined by a equals -omega squared x. The solution x equals A cos(omega t + epsilon) gives displacement. Velocity v is the derivative, -A omega sin(omega t + epsilon). Acceleration is directly proportional to negative displacement. Mass-spring periods follow T equals 2pi sqrt(m/k), while small-angle pendulums use T equals 2pi sqrt(l/g).
Kinetic theory distinguishes N (number of molecules) from n (moles). Pressure p equals 1/3 rho mean squared speed <c²>. Internal energy for an ideal monatomic gas is 3/2 nRT. Molecules collide with walls to exert pressure. Thermal physics defines internal energy as the sum of potential and kinetic energy. The first law is delta U equals Q - W, where W is p delta V.
Damping removes energy from oscillating systems. Under-damping allows oscillations to decay; over-damping returns to equilibrium without oscillation; critical damping returns to equilibrium as quickly as possible, crucial for car suspensions.
Forced oscillations involve a driving frequency. Resonance occurs when the driving frequency matches the natural frequency, maximising amplitude. Damping broadens the resonance curve and shifts the peak.
Microwave cooking utilises dielectric heating where electromagnetic waves drive water molecule polar rotations within cavity modes, not an isolated water resonance. Bridges must avoid resonance to prevent structural failure.
The spring-damping experiment involves observing the rate of decay of oscillations under varying viscous loads to measure energy loss. Data plotting amplitude versus cycle count allows calculation of the damping coefficient and uncertainty analysis.
Example calculation: A system with k = 100 N/m and m = 0.25 kg. Period T = 2 * 3.14159 * sqrt(0.25 / 100) = 0.314 s. Using v = omega r: if r = 0.05 m and f = 3 Hz (omega = 18.85 rad/s), then v = 0.94 m/s.
Nuclear decay is spontaneous and random. Alpha particles have high ionisation/low range; beta have moderate; gamma have low ionisation/high range. Background radiation must be subtracted from measured counts.
Activity A = lambda N. Exponential decay follows N = N0 e^(-lambda t). Lambda is decay constant. Derivation: T_half = ln 2 / lambda. Gamma-distance practical requires safety shielding and inverse-square verification.
Nuclear energy: Binding energy per nucleon indicates stability. Fission of heavy nuclei and fusion of light nuclei release energy based on the binding energy curve. E = mc² applies to mass defects where initial mass exceeds final mass.
A free oscillation follows an initial displacement or impulse without a continuing periodic driving force. Its natural frequency depends on the system; real free oscillations may be damped, so “free” does not mean “no damping”. A forced oscillation is maintained by an external periodic force, such as repeated pushes on a swing or periodic machinery vibration. Resonance gives a large response when driving frequency is near the natural frequency; damping reduces the peak and broadens the response.
For the spring-damping practical, displace the mass safely and release without an extra push. Record successive turning-point amplitudes and times, using a ruler/video or displacement sensor; repeat with controlled changes in damping while keeping mass and spring fixed. Plot amplitude against time, compare decay and oscillation period, and, where approximately exponential, plot ln amplitude against time to estimate the decay rate. Lost mechanical energy explains the shrinking amplitude. Extra Q-factor formulae are not needed merely to label this investigation complete.
What to do in an assessment
Distinguish clearly between angular quantities (omega) and linear kinematic variables.
Graphically plot acceleration versus displacement and kinetic energy versus time for SHM.
Calculate period for systems using mass-spring and pendulum equations accurately.
Analyse resonance curves, noting the trade-off between damping magnitude and peak sharpness.
Verify all energy and mass conservation laws in nuclear interactions.
In plain language
This lesson integrates the dynamics of circular motion and SHM with thermal kinetic theory, nuclear decay statistics, and resonance phenomena.
Self-check
If a system is critically damped, how does its displacement-time graph compare to an under-damped system?
Show the answer
A critically damped system returns to equilibrium in the shortest possible time without oscillating, whereas an under-damped system oscillates with decreasing amplitude until it reaches equilibrium.
Kinetic Theory and Thermal Physics of Ideal GasesCore
Scope: Core · A2 Unit 3 §3 KINETIC THEORY
Open revision guidance
What to know
Kinetic theory models gases using N molecules of mass m in volume V. Pressure arises from molecular collisions, modelled by p = 1/3 * rho * <c²>, where <c²> is the mean squared speed, not the squared mean speed. Assumptions include random motion and negligible inter-molecular forces. Distinguish N (total molecules) from n (moles). Molar mass M (kg/mol) relates to Mr via M = Mr/1000, and n = total mass / molar mass.
The ideal gas law is pV = nRT = NkT, with R the molar constant and k = R/NA the Boltzmann constant (NA is the Avogadro constant). Combining pV = 1/3 * Nmc² and pV = NkT yields the mean translational kinetic energy of a molecule: E_k = 3/2 * kT. For a mole, this total energy is U = 3/2 * RT. This applies strictly to monatomic gases where internal energy is purely translational.
Thermal energy refers to the internal energy (U) sum of potential and kinetic molecular energies. In ideal monatomic gases, U = 3/2 * nRT. Absolute zero is the temperature of minimum internal energy, not zero motion/energy. Thermal equilibrium occurs when no net heat flows.
Heat (Q) is energy in transit, not a state function. Work (W) done by gas is p * deltaV. The first law of thermodynamics states Delta U = Q - W. A positive Q means heat added to the system, and positive W means work done BY the gas. For liquids/solids, work is negligible, so Q = Delta U = mc * delta theta.
Practicals: Estimate absolute zero by graphing p against T (extrapolating to p=0) and measure specific heat capacity for solids using calorimetry. Accuracy is improved by insulation and using digital thermometers.
Numerical Example: Find the mean kinetic energy of a molecule at 300 K. Use E = 3/2 * kT, where k = 1.38e-23 J/K. E = 1.5 * 1.38e-23 * 300 = 6.21e-21 J.
The kinetic model assumes many molecules moving randomly in all directions with a random distribution of molecular energies, negligible molecular volume compared with the gas, negligible forces except during collisions, and elastic collisions. Individual speeds are not equal. The pressure equation uses mean squared speed ⟨c²⟩, not the square of the mean speed. Avogadro constant Nₐ is the number of specified particles per mole (6.02214076×10²³ mol⁻¹); N=nNₐ and k=R/Nₐ. The historical carbon-12 definition is not the current SI definition.
Combining pV=⅓Nm⟨c²⟩ and pV=NkT gives ½m⟨c²⟩=3kT/2, the mean translational kinetic energy per molecule. Multiplying by Nₐ gives 3RT/2 for one mole. Total internal energy U=3nRT/2 applies to a monatomic ideal gas where this translational energy is the whole internal energy, not to every gas with rotation or vibration.
What to do in an assessment
Confirm the distinction between molecule count N and amount n in moles.
Verify all calculations use Kelvin for temperature and standard SI units.
Ensure the 3/2 factor is only applied to internal energy for monatomic gases.
Apply the sign convention for the first law correctly: heat into the system is positive.
In plain language
This lesson establishes the kinetic molecular model of gases to relate microscopic motion to macroscopic pressure and internal energy, governed by the first law of thermodynamics.
Self-check
If the absolute temperature of an ideal monatomic gas is doubled, what happens to the mean translational kinetic energy of the molecules?
Show the answer
Since mean kinetic energy = 3/2 * kT, doubling the temperature T doubles the mean kinetic energy.
View diagrams
Maxwell-Boltzmann speed distributions
For the same ideal gas and particle number, each Maxwell-Boltzmann speed distribution has equal total area. Raising temperature broadens the distribution, moves the most probable speed right, and lowers the peak. The curves use nitrogen at 300 K and 600 K; marked most-probable, mean and rms speeds are 422, 476 and 517 m s⁻¹ at 300 K, and 597, 674 and 731 m s⁻¹ at 600 K.
Use the labelled model alongside the explanation. Idealised curves are not measured data.
Thermal PhysicsCore
Scope: Core · A2 Unit 3 §4 THERMAL PHYSICS; A2 Unit 3 §4 THERMAL PHYSICS specified practical work
Open revision guidance
What to know
Internal energy is defined as the sum of the potential and kinetic energies of all molecules within a system. Heat is energy in transit transferred across boundaries due to temperature differences, whereas thermal equilibrium occurs when no net heat flows between systems, indicating equal temperatures.
Absolute zero represents the state where a system possesses minimum internal energy, though it does not imply total cessation of motion. For an ideal monatomic gas, internal energy is strictly kinetic, expressed as U = 3nRT/2. Work done by a gas is energy in transit defined by W = pΔV at constant pressure, or the area under a p-V graph if pressure varies.
The first law of thermodynamics states ΔU = Q - W. A positive Q indicates heat entering the system, while positive W represents work done by the system. For solids or liquids, volume changes are negligible, simplifying the expression to Q = ΔU. Specific heat capacity c is defined by Q = mcΔθ.
Practical 1: To estimate absolute zero, use a gas law apparatus with a sealed volume of gas immersed in a water bath. Measure pressure at varying temperatures, plot p against θ (Celsius), and extrapolate the linear graph to p = 0 to find the intercept at -273 degrees Celsius.
Practical 2: To measure specific heat capacity of a solid, provide a known power P to a heater embedded in the solid mass m. Measure temperature change Δθ over time t, calculate energy Q = Pt, and rearrange Q = mcΔθ to c = Pt/(mΔθ). Use insulation to minimise losses.
Worked example: 100 J of heat enters a gas and the gas does 30 J of expansion work. With Q positive into the gas and W positive done by the gas, ΔU=Q−W=100−30=70 J. For compression W is negative, so work done on the gas increases its internal energy. Separately, heating a 2.0 kg solid with c=400 J kg⁻¹ K⁻¹ through 50 K requires Q=mcΔT=2.0×400×50=40,000 J if losses are neglected; a solid block’s thermal expansion work is normally negligible, not 10 kJ.
Ensure all experimental data includes uncertainties from analogue or digital equipment. Maintain safety by wearing eye protection when handling hot materials and ensuring gas apparatus is secure. Analyse graphs for linearity and interpret intercepts carefully to avoid systematic errors.
What to do in an assessment
Define internal energy versus energy in transit.
Apply the first law of thermodynamics correctly with sign conventions.
Distinguish between ideal gas internal energy and solid calorimetry.
Execute practical methods with precise data recording and uncertainty analysis.
In plain language
This lesson covers the principles of internal energy, thermodynamics, and thermal properties of matter including specific heat capacity and gas law applications.
Self-check
A gas loses 80 J of heat while 25 J of work is done on it. Find its internal-energy change using ΔU=Q−W, with W positive for work done by the gas.
Show the answer
Heat leaves, so Q=−80 J. Compression work is done on the gas, so W=−25 J. ΔU=−80−(−25)=−55 J. Internal energy decreases by 55 J; state the convention before substituting.
Nuclear Decay and Exponential LawsCore
Scope: Core · A2 Unit 3 §5 NUCLEAR DECAY; A2 Unit 3 §5 NUCLEAR DECAY specified practical work
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What to know
Nuclear decay is a spontaneous and random process where an unstable nucleus transforms into a more stable state by emitting alpha, beta, or gamma radiation. Alpha particles are helium nuclei with high ionization and low penetration, beta are high-energy electrons/positrons, and gamma are high-energy photons with high penetration. Transformation equations use the A-Z notation, where A is the mass number and Z is the atomic number.
Activity A is defined as the rate of decay, measured in Becquerels (Bq), representing decays per second. The decay constant lambda is the probability of decay per unit time, related by A = lambda*N. Experimental measurements must always subtract the background radiation count to obtain the true source activity.
The exponential decay law N = N_0 * e^(-lambda*t) describes the number of remaining nuclei at time t, where N_0 is the initial count. Alternatively, for non-integer half-lives, N = N_0 / 2^x where x = t/T_half. The half-life T_half is the time for the activity or number of nuclei to reduce to half the initial value.
Deriving the relationship between decay constant and half-life: at t = T_half, N = N_0/2. Substituting into N = N_0*e^(-lambda*t) gives 1/2 = e^(-lambda*T_half). Taking natural logarithms on both sides results in ln(1/2) = -lambda*T_half, which simplifies to -ln 2 = -lambda*T_half, yielding lambda = ln 2 / T_half.
The dice analogy practical uses dice to simulate spontaneous decay: each die representing a nucleus, where rolling a 6 might signify decay. This illustrates probability, as each die has a 1/6 chance of decaying regardless of its history. In gamma distance practicals, intensity follows an inverse-square law; ensure safety by keeping sources in lead-lined boxes, using tongs, and maximising distance from the body.
Worked Numerical Example: A sample has an initial activity A_0 = 800 Bq and a half-life of 10 seconds. Find the activity after 15 seconds. Given x = t / T_half = 15 / 10 = 1.5. Using A = A_0 / 2^x, we have A = 800 / 2^1.5 = 800 / 2.828 = 282.8 Bq.
Circular Motion: Radians define angle theta = s/r; a full circle is 2pi radians. Angular velocity omega = delta_theta/delta_t. Frequency f = 1/T, and omega = 2pi/T = 2pi*f. Centripetal force F = mv^2/r = m*omega^2*r is the resultant inward force; velocity direction changes constantly, keeping speed constant.
SHM: Defined by a = -omega^2*x. Displacement x = A*cos(omega*t + epsilon). Velocity v = -A*omega*sin(omega*t + epsilon). Kinetic energy is max at equilibrium, potential max at amplitude. For a pendulum T = 2pi*sqrt(l/g), use small angle approximations. Practical: Measure g by timing swings.
Damping/Resonance: Free oscillations occur without external driving. Damping (under/over/critical) removes energy, important for vehicle suspension. Resonance happens when driving frequency matches natural frequency; increased damping lowers and broadens the amplitude peak. Microwave dielectric heating uses oscillating fields to rotate polar molecules, not a 2.45 GHz resonance.
Kinetic Theory: N is molecule count, n is moles. Mr is relative molecular mass. p = (1/3)*rho*<c^2> uses mean squared speed. Assumptions: random motion, negligible volume, elastic collisions. Average KE = (3/2)kT per molecule or (3/2)RT per mole (monatomic).
Thermal Physics: Internal energy U is kinetic plus potential. Absolute zero implies minimum motion, not zero. Equilibrium means equal temperature. Work W = p*deltaV. First law: deltaU = Q - W. Q = mc*deltaT/mL. Practical: measure c by electric heating.
What to do in an assessment
Define radioactive decay as a random and spontaneous statistical process.
Use N = N_0 * e^(-lambda*t) for calculations where time is not a simple multiple of half-life.
Apply the subtraction of background count to all raw data before performing decay analysis.
Connect the mathematical derivation of lambda = ln 2 / T_half to the exponential decay definitions.
In plain language
This lesson covers the statistical nature of radioactive decay, the derivation of decay constants from half-lives, and the practical methods for analysing ionizing radiation.
Self-check
What is the relationship between the decay constant and half-life, and how is it derived from the exponential law?
Show the answer
The relationship is lambda = ln 2 / T_half. It is derived by setting the number of nuclei N to half the initial value N_0 at t = T_half in the equation N = N_0 * e^(-lambda*t), resulting in 0.5 = e^(-lambda*T_half), which simplifies via logarithms to lambda = ln 2 / T_half.
Nuclear Energy and StabilityCore
Scope: Core · A2 Unit 3 §6 NUCLEAR ENERGY
Open revision guidance
What to know
The mass-energy equivalence principle states that mass and energy are interchangeable via E=mc², where c is the speed of light in a vacuum. A unified atomic mass unit (u) is used for nuclear masses; in calculations, one must ensure consistency by using either nuclear masses or atomic masses (accounting for electron cancellation).
Mass defect is the difference between the mass of a nucleus and the sum of the individual masses of its constituent nucleons. This mass loss is released as binding energy when the nucleus forms. Binding energy per nucleon provides a measure of nuclear stability. A nucleus with higher binding energy per nucleon is more tightly bound and stable.
Nuclear fission occurs in heavy nuclei, while fusion occurs in light nuclei. Both processes are governed by the conservation of mass-energy. The binding energy per nucleon versus nucleon number curve shows that both fission and fusion lead to products with higher binding energy per nucleon, indicating a more stable state.
Example calculation: A nucleus has a mass defect of 0.030 u. Given 1 u = 1.66e-27 kg and c = 3.00e8 m/s, the energy released is E = (0.030 * 1.66e-27 kg) * (3.00e8 m/s)² = 4.48e-12 J.
Simple Harmonic Motion (SHM) is defined by a=−ω²x. The displacement solution is x=Acos(ωt+ε), with velocity v=−Aωsin(ωt+ε) derived from the time derivative. Acceleration is proportional to displacement but opposite in direction. A mass-spring system has period T=2π√(m/k) and a simple pendulum has T=2π√(l/g).
For the pendulum practical, use a small-angle assumption (<10°) to ensure simple harmonic behaviour. Measure period by timing multiple oscillations with a stopwatch to reduce percentage uncertainty. Plot T² against length l; the gradient is 4π²/g.
Damping dissipates energy, categorised as under, over, or critical damping. Resonance occurs when driving frequency matches natural frequency, increasing amplitude; damping broadens and shifts the resonance curve. Microwave cooking uses dielectric heating where electromagnetic cavity modes couple with polar molecules like water, causing rotation and heating; this is not simple resonance at a fixed 2.45 GHz frequency.
Mass defect is the difference between the mass of separated nucleons and that of the bound nucleus: Δm=Zmp+(A−Z)mn−mnucleus. Binding energy is Δmc² and binding energy per nucleon is Δmc²/A. Use masses in kg with c in m s⁻¹ for joules, or convert atomic mass units consistently using 1 u c²≈931.5 MeV. Nuclear and atomic masses must not be mixed without accounting for electrons; using neutral atom masses with hydrogen-atom masses is a different consistent bookkeeping choice.
The binding-energy-per-nucleon curve rises rapidly for light nuclei, reaches a broad maximum in the iron/nickel region, then declines gradually towards very heavy nuclei. A transformation releases energy when the products have greater total binding energy, so moderate heavy nuclei can release energy by fission and light nuclei by fusion. Do not say every possible fusion releases energy or that the peak is exactly at one nuclide irrespective of the convention.
What to do in an assessment
Calculate mass defect using unified mass units before converting to kilograms.
Ensure consistent units for energy, mass, and velocity in all equations.
Refer to the binding energy curve to explain why fission and fusion release energy.
Distinguish clearly between absolute nuclear mass and atomic mass when performing defect calculations.
In plain language
Nuclear energy processes like fission and fusion release energy due to the conversion of mass defect into binding energy as defined by E=mc².
Self-check
If a nucleus has a mass defect of 0.025 u, calculate the equivalent energy in Joules. (1 u = 1.66 × 10^-27 kg; c = 3.00 × 10^8 m/s)
Show the answer
Mass defect = 0.025 × 1.66 × 10^-27 kg = 4.15 × 10^-29 kg. Energy E = mc² = (4.15 × 10^-29 kg) × (3.00 × 10^8 m/s)² = 3.735 × 10^-12 J.
View diagrams
Binding energy per nucleon and a worked energy release
The schematic binding energy per nucleon curve peaks near the iron/nickel region. Constructed worked example only: initial total binding energy = 240 × 7.6 = 1824 MeV; final total = 2 × 120 × 8.5 = 2040 MeV; Q = final − initial = +216 MeV, so 216 MeV is released. These are illustrative nuclei, not a named isotope reaction or measured data.
Use the labelled model alongside the explanation. Idealised curves are not measured data.

Capacitance: Fundamentals and DynamicsCore
Scope: Core · A2 Unit 4 §1 CAPACITANCE; A2 Unit 4 §1 CAPACITANCE specified practical work
Open revision guidance
What to know
A parallel plate capacitor comprises two metal plates separated by an insulator like air or vacuum. Charge transfer between these plates creates equal and opposite charges, maintaining net electrical neutrality.
Capacitance (C) is defined by the ratio of charge (Q) to potential difference (V), expressed as C = Q/V. For a vacuum-spaced parallel plate capacitor, C = (ε₀ * A) / d, where A is plate area and d is separation; dielectrics increase this capacitance.
The electric field (E) between plates is uniform, defined by E = V/d. Energy (U) stored is calculated as U = 1/2 * Q * V. When capacitors are in series, 1/C_total = 1/C1 + 1/C2; in parallel, C_total = C1 + C2.
Charging and discharging through a resistor follow exponential laws characterized by the time constant RC. The equations are Q = Q0(1 - e^(-t/RC)) for charging and Q = Q0 * e^(-t/RC) for discharging.
Practical investigation requires identifying the RC time constant by recording current or voltage over time. Safety is paramount; ensure capacitors are safely discharged before circuit manipulation to avoid shock hazards.
Numerical example: A 100 µF capacitor is charged to 10 V. Calculate the energy. U = 0.5 * Q * V = 0.5 * (C * V) * V = 0.5 * 100e-6 * 10^2 = 0.005 J.
Measurements involve using multimeters and DC supplies. Graphs of voltage against time yield exponential decay curves, allowing for logarithmic plotting to linearize data.
Practical apparatus includes capacitors, resistors, DC power sources, and timing equipment. Controls involve maintaining stable components, while uncertainties arise from meter precision and timing errors.
Students must practise data recording and error analysis to interpret these scientific behaviours accurately.
To derive the stored energy, gradually move charge onto the plates. The potential rises as V=Q/C, so the graph with V on the vertical axis and Q on the horizontal axis is a straight line of gradient 1/C. Work is the area under V against Q: U=½QV=½CV²=Q²/(2C). Energy is stored in the electric field produced by charge separation, not in a net excess of charge on the whole capacitor.
For the time-constant practical, use a low-voltage supply, appropriately rated capacitor, known resistor and high-resistance voltmeter or data logger across the capacitor. Charge to V₀, disconnect the supply and discharge through R while recording V and time. Plot ln(V/V₀) against t; its gradient is −1/(RC). Alternatively, find the time for V to fall to V₀/e. Keep R and C constant, repeat, and assess meter loading, timing and component tolerance. During charging from zero, V rises to V₀ while current falls; Q₀ means the final charge during charging and initial charge during discharge.
For the separate stored-energy practical, charge the capacitor to several measured low voltages and investigate the energy released on discharge into a calibrated load. One approach records current and load voltage versus time and sums small energy intervals ΔE=VIΔt to estimate total energy transferred. Compare this with ½CV² and plot energy against V²: the predicted gradient is C/2. Account for internal resistance, unrecorded discharge energy and measurement uncertainty. Use teacher-supervised equipment, observe polarity/ratings and safely discharge before changing the circuit; never improvise high-voltage arrangements.
What to do in an assessment
Review derivation of C = Q/V and parallel plate formulas.
Practice sketching exponential charging and discharging graphs.
Perform RC circuit calculations using standard scientific notation.
Verify experimental safety procedures for handling high-voltage capacitors.
In plain language
This lesson covers the physical principles, mathematical definitions, and experimental dynamics of capacitors in electric circuits.
Self-check
A 50 µF capacitor is connected to a 12 V supply. Calculate the charge stored.
Show the answer
Using C = Q/V, Q = C * V = (50 * 10^-6 F) * 12 V = 6.0 * 10^-4 C.
View diagrams
Capacitor discharge circuit and exponential graphs
A source-free circuit with 100 kΩ resistance and 10.0 µF capacitance has τ = RC = 1.00 s. Starting at 10.0 V gives Q₀ = 100 µC and I₀ = 0.10 mA. Q and V decay as e⁻ᵗ/τ; current is plotted negative because the stated reference direction is positive for charging. At t = τ, Q = 36.8 µC, V = 3.68 V and I = −0.0368 mA.
Use the labelled model alongside the explanation. Idealised curves are not measured data.
Electrostatic and Gravitational Fields of ForceCore
Scope: Core · A2 Unit 4 §2 ELECTROSTATIC AND GRAVITATIONAL FIELDS OF FORCE
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What to know
A field describes force at each position, without requiring the interacting objects to touch. Gravitational field strength g is force per unit test mass: g=F/m, in N kg⁻¹, directed towards the attracting mass. Electric field strength E is force per unit positive test charge: E=F/q, in N C⁻¹ or V m⁻¹. A negative charge experiences force opposite to E. The field is not the same as the force: force also depends on the mass or charge placed there.
Newton’s gravitational force law is F=Gm₁m₂/r² for point masses, or outside spherically symmetric bodies with separation measured between their centres. Gravity between these masses is attractive. Coulomb’s electric force magnitude is F=|q₁q₂|/(4πε₀r²) in vacuum; like charges repel and unlike charges attract. Both are inverse-square interactions. Gravitational sources are mass; electric sources are charge, which can have either sign.
Field lines point along the force on a positive test charge or a test mass, and closer spacing represents stronger field. Around a positive point charge they point outward; around a negative charge inward. Around a spherical mass they point inward. Parallel, equally spaced lines describe a uniform field, such as the approximate electric field between large parallel plates away from their edges. Fields from several sources add as vectors, so direction matters.
Gravitational potential φg is potential energy per unit mass, in J kg⁻¹. Electric potential V is potential energy per unit charge, in J C⁻¹ (volts). Potential is a scalar. Choose zero at infinity for isolated sources: φg=−GM/r, while V=Q/(4πε₀r). Positive-charge potential is positive and negative-charge potential negative; gravitational potential is negative because work must be done to remove an attracted test mass to infinity.
A potential difference tells us a change in potential energy: ΔU=mΔφg for mass or ΔU=qΔV for charge. Work done by the field is −ΔU. In an approximately uniform gravitational field, raising mass through height Δh increases potential energy by mgΔh. Define the direction and reference before assigning a sign; volts and joules must not be treated as interchangeable.
Along a radial coordinate, signed field components are gᵣ=−dφg/dr and Eᵣ=−dV/dr. A field points towards decreasing potential for a positive test object. For a positive point charge, V decreases outward and Eᵣ is outward; for a mass, φg increases outward and gᵣ is inward. This explains the negative gradient relation and distinguishes field strength from potential.
Worked example: an electron with q=−1.60×10⁻¹⁹ C moves from 2.0 V to 10.0 V. Its potential-energy change is qΔV=(−1.60×10⁻¹⁹)(10.0−2.0)=−1.28×10⁻¹⁸ J. If only the electric field does work, kinetic energy increases by 1.28×10⁻¹⁸ J. A negative charge accelerates towards higher potential, opposite to the electric-field direction.
When comparing the two fields, separate force (a vector), field strength (a vector) and potential (a scalar). At one point, potentials from several sources add algebraically while fields require vector components. The inverse-square magnitude applies to isolated point or spherical sources; it does not describe the approximately uniform field near a small region of Earth’s surface or inside an ideal parallel-plate capacitor.
What to do in an assessment
Construct a comparative table for gravitational and electrostatic force laws and field strengths.
Sketch field lines and equipotential surfaces for both positive and negative point charges.
Practice rearranging the field strength and potential equations to solve for distance or source magnitude.
Ensure all experimental safety protocols regarding HV supplies are reviewed.
Derive orbital speed by equating centripetal force to the gravitational force.
In plain language
This lesson details the mathematical and physical properties of electrostatic and gravitational fields, including their inverse-square laws, potential definitions, and applications in orbital mechanics and cosmology.
Self-check
A positive charge 2.0×10⁻⁶ C moves from 12 V to 5 V. Find its potential-energy change and the work done by the electric field.
Show the answer
ΔU=qΔV=(2.0×10⁻⁶)(5−12)=−1.4×10⁻⁵ J. The electric field does W=−ΔU=+1.4×10⁻⁵ J. Potential energy decreases and, with no other energy transfer, kinetic energy increases. State the charge sign and initial/final potentials.
View diagrams
Gravitational field, equipotentials and logarithmic plots
A spherical-mass field has radial g ∝ 1/r² and gravitational potential Φ ∝ −1/r. The first panel shows inward field lines crossing concentric equipotentials at right angles; the second plots log |g| and log |Φ| against log r, with slopes −2 and −1. Curves use Earth mass as a worked reference and are not a business-style chart.
Use the labelled model alongside the explanation. Idealised curves are not measured data.
Orbits and the Wider UniverseCore
Scope: Core · A2 Unit 4 §3 ORBITS AND THE WIDER UNIVERSE
Open revision guidance
What to know
Kepler’s first law says a planet follows an ellipse with the Sun at one focus. The second says the line from the Sun to a planet sweeps equal areas in equal times, so the planet travels faster nearer the Sun. The third says T² is proportional to a³ for planets orbiting the same central mass, where a is the ellipse’s semi-major axis. A circular orbit has a=r.
Newton’s law is F=Gm₁m₂/r², an attractive force between spherically symmetric masses with centre-to-centre separation r. For a small satellite of mass m orbiting a much larger mass M, GMm/r²=mv²/r. Therefore v²=GM/r. Substitute v=2πr/T to obtain T²=4π²r³/(GM). Do not use height above a surface as the orbital radius: add the central body’s radius.
Rearrange these relations to find a central mass: M=v²r/G or M=4π²r³/(GT²). These circular approximations assume gravity provides the resultant inward force and the satellite’s mass is negligible relative to M. They let us estimate stellar or planetary mass without weighing the object directly.
Two significant masses instead orbit their common centre of mass. With separation a=r₁+r₂, balance moments about that point: m₁r₁=m₂r₂. Thus r₁=m₂a/(m₁+m₂), and r₂=m₁a/(m₁+m₂). For circular motion their common period obeys T²=4π²a³/[G(m₁+m₂)]. A heavier component lies closer to the centre of mass and moves more slowly.
For an edge-on circular binary, sinusoidal radial-velocity curves reveal speeds v₁ and v₂ from their amplitudes. Their common period is the curve’s repeat time. Then a=(v₁+v₂)T/(2π), m₁/m₂=v₂/v₁, and m₁+m₂=T(v₁+v₂)³/(2πG). Combine the total mass and ratio to find each mass. A system viewed at an inclination other than edge-on gives projected speeds, so these uncorrected masses are not valid.
Spiral galaxies often have nearly flat outer rotation curves: orbital speed does not fall as the visible matter alone would predict. From v²=GM(r)/r, a flat speed implies enclosed mass M(r) keeps increasing with radius. This supports an extended dark-matter component, inferred through gravity rather than detected light. The Higgs discovery motivates research into proposed connections with unseen particles, but the Higgs boson itself is not an established explanation of dark matter and such connections remain hypotheses.
A spectral line shifted from its laboratory wavelength λ to λ+Δλ gives radial velocity v≈cΔλ/λ when |v| is much smaller than c. Positive Δλ is redshift and recession; negative Δλ is blueshift and approach. This measures only motion along the observer’s line of sight, not the full space velocity. Identify the same atomic line before comparing wavelengths.
Hubble’s law v=H₀D relates nearby-galaxy recession speed and distance. Convert units before using it: H₀=70 km s⁻¹ Mpc⁻¹ means 70,000/(3.086×10²²)=2.27×10⁻¹⁸ s⁻¹. Then 1/H₀=4.41×10¹⁷ s, about 14.0 billion years. This is a characteristic expansion timescale: the universe’s actual age depends on how expansion has changed, so it is not an exact clock.
To derive critical density in the specification’s simplified spherical energy model, take matter of mass m at radius r receding at v=H₀r. The marginally unbound condition is ½mv²−GMm/r=0. Write enclosed mass M=4πr³ρ/3 and substitute v. Dividing by mr² gives ½H₀²=4πGρ/3, hence ρc=3H₀²/(8πG). Critical density is the reference density associated with a spatially flat universe; the derivation states its idealised assumptions rather than describing every contribution in modern cosmology.
Worked example: an edge-on circular binary has v₁=40,000 m s⁻¹, v₂=60,000 m s⁻¹ and period 10.0 days=864,000 s. Using G=6.674×10⁻¹¹ N m² kg⁻², total mass=864,000(100,000)³/(2π×6.674×10⁻¹¹)=2.06×10³⁰ kg. Since m₁/m₂=60,000/40,000=1.50, m₁=0.600 of the total=1.24×10³⁰ kg and m₂=8.24×10²⁹ kg.
What to do in an assessment
Review derivation of Kepler's 3rd law using centripetal force.
Practice using the Doppler shift formula for radial velocity.
Explain the evidence for dark matter in galactic rotation curves.
Derive the critical density equation using energy conservation.
In plain language
This unit covers the mechanics of planetary orbits and the cosmological principles describing the expansion and composition of the universe.
Self-check
A circular satellite orbit has radius 7.00×10⁶ m around a mass 5.97×10²⁴ kg. Calculate orbital speed and period using G=6.674×10⁻¹¹ N m² kg⁻².
Show the answer
v=√(GM/r)=√[(6.674×10⁻¹¹)(5.97×10²⁴)/(7.00×10⁶)]=7.54×10³ m s⁻¹. Then T=2πr/v=2π(7.00×10⁶)/(7.54×10³)=5.83×10³ s, about 97.2 minutes. Radius is measured from the centre; the model assumes a circular orbit and negligible satellite mass.
Magnetic Fields and ForcesCore
Scope: Core · A2 Unit 4 §4 MAGNETIC FIELDS; A2 Unit 4 §4 MAGNETIC FIELDS specified practical work
Open revision guidance
What to know
Magnetic fields exert forces on moving charges and current-carrying conductors. The force F on a conductor of length l carrying current I in a field B is F = BIl sin θ, where θ is the angle between the current and field. Directions are found using Fleming's Left-Hand Rule.
For a charge q moving at velocity v, the force is F = Bqv sin θ. Because this force acts perpendicular to motion, the magnetic field performs no work on the charge, resulting in circular paths for particles injected perpendicular to uniform fields with radius r = mv / Bq.
Field geometries are specific: long straight wires produce circular fields with B = μ₀I / (2πa). Solenoids create uniform fields internally where B = μ₀nI, with strength enhanced by high-permeability iron cores.
Practical investigations include measuring force on a current-carrying wire using a balance to determine B, and using a Hall probe to map flux density. Hall probes utilise the Hall effect, where VH ∝ B for constant I.
Ion beams in uniform fields allow for precise deflection control. This principle underpins particle accelerators including linear accelerators, cyclotrons, and synchrotrons which use combined electric and magnetic fields to accelerate and guide particles.
Numerical example: A wire of length 0.05m carries 2.0A at 90 degrees to a 0.5T field. F = BIl sin(90) = 0.5 * 2.0 * 0.05 * 1 = 0.05N.
Measurements require careful apparatus setup. Use multimeters for current, digital balances for force, and ensure stability during readings. Identify systematic uncertainties in alignment and control temperature to maintain resistance stability.
Safety is paramount. Ensure power supplies are managed properly and avoid exceeding current ratings which may cause excessive heating in conductors.
Each current-carrying wire produces a magnetic field. Parallel wires carrying currents in the same direction attract; opposite currents repel. Determine the field at the second wire using the right-hand grip rule, then its force direction using the motor rule with conventional current. These forces are on two different conductors, not balanced forces on one wire.
For an ion beam entering a uniform electric field perpendicular to its initial speed v, force is qE and acceleration qE/m. If field length is L, travel time is L/v and transverse displacement within the field is y=½(qE/m)(L/v)², assuming the longitudinal speed is unchanged: the path is parabolic. In a perpendicular uniform magnetic field, |q|vB=mv²/r, so r=mv/(|q|B): the path is circular and the magnetic force does no work. Crossed-field undeflected selection requires E=vB; charge sign changes direction, not the selected speed E/B.
What to do in an assessment
Memorise Fleming's Left-Hand Rule for force directions.
Practice deriving circular motion radius from F = Bqv.
Distinguish between wire and solenoid field equations.
Review Hall probe methodology for field measurement.
In plain language
This lesson covers magnetic field interactions, forces on currents and charges, geometric field derivations, and practical measurement techniques for flux density.
Self-check
A particle with charge 1.6x10^-19C moves at 2x10^6 m/s perpendicular to a 0.2T magnetic field. Calculate the force.
Show the answer
F = Bqv = 0.2 * 1.6x10^-19 * 2x10^6 = 6.4x10^-14 N.
View diagrams
Electric and magnetic fields: charged-particle paths
Between parallel plates the electric field points from + to −; equal-mass particles with equal and opposite charge curve in opposite directions. In a uniform magnetic field into the page, equal-magnitude charges with the same initial velocity also bend oppositely because F = q(v × B). The matched tracks are a constructed direction model, not experimental data.
Use the labelled model alongside the explanation. Idealised curves are not measured data.
Electromagnetic Induction PrinciplesCore
Scope: Core · A2 Unit 4 §5 ELECTROMAGNETIC INDUCTION
Open revision guidance
What to know
Electromagnetic induction describes how a changing magnetic environment produces an electromotive force (emf). The fundamental physical quantity is magnetic flux, defined as Φ = AB cos θ, where A is the area of the surface and θ is the angle between the magnetic field lines and the normal to the surface. Flux linkage, NΦ, represents the total flux threading a coil of N turns.
Faraday's Law states that the magnitude of the induced emf is equal to the rate of change of flux linkage. Lenz's Law complements this, providing the physical direction of the induced current such that it opposes the change in flux that caused it, ensuring the conservation of energy. Together, these are expressed as emf = -d(NΦ)/dt.
When a linear conductor moves through a uniform magnetic field at right angles, an emf is induced. This motion creates a change in area through which the field passes, resulting in a potential difference across the conductor ends. If the conductor forms part of a closed circuit, a current will flow.
Rotating a coil in a magnetic field results in an induced emf related to the coil's instantaneous position, the flux density, the cross-sectional area, and the angular velocity. This is the fundamental principle behind generator operation, where rotational kinetic energy is converted into electrical energy.
Consider a coil with 500 turns and an area of 0.02 m^2 placed in a 0.5 T magnetic field. If the field changes from 0 to 0.5 T in 0.1 s, the induced emf is calculated as N * A * (ΔB/Δt). Here, emf = 500 * 0.02 * (0.5 / 0.1) = 50 V.
Practical measurements of magnetic fields often utilise a search coil connected to an oscilloscope or a Hall probe. Ensuring precise alignment of the coil area relative to the field lines is essential to minimise errors in flux calculations.
Control variables in induction experiments include the consistency of the conductor's velocity and the orientation of the magnetic field. Uncertainties primarily arise from fluctuations in movement speed and measurement inaccuracies in the field strength.
Safety is paramount when working with induction apparatus, especially high-voltage transformers or power supplies. Always ensure proper insulation, avoid contact with exposed conductors, and disconnect power sources when adjustments are required.
In summary, induction relies on the coupling between motion, magnetic fields, and charge separation within conductors.
For a coil rotating in uniform B, flux linkage is NBAcosθ, with θ measured from the coil normal. Linkage is maximum when the normal is parallel to B, but its rate of change is then zero and instantaneous emf zero. When the coil plane is parallel to B, linkage is zero but its change is fastest and emf magnitude maximum. Increasing B, A, N or angular speed increases peak emf, for the same geometry; ε=NBAωsin(ωt) with a chosen time origin.
What to do in an assessment
Verify the orientation of the area vector relative to the magnetic field normal before calculating flux.
Always define the direction of current using Lenz's law to satisfy energy conservation principles.
Practice deriving the induced emf for a rotating coil by considering the varying component of the field through the cross-sectional area.
Ensure all apparatus for magnetic field mapping are checked for calibration and zero-error before testing.
In plain language
This lesson details the quantitative and qualitative aspects of electromagnetic induction, covering flux, flux linkage, Faraday and Lenz laws, and their application to moving conductors and rotating coils.
Self-check
Calculate the average induced emf in a 100-turn coil if the flux changes from 0.01 Wb to 0.05 Wb in 0.2 seconds.
Show the answer
The change in flux linkage Δ(NΦ) = 100 * (0.05 - 0.01) = 4 Wb. The emf = Δ(NΦ) / Δt = 4 / 0.2 = 20 V.

Sinusoidal AC and Rotating CoilsCore
Scope: Core · A2 Unit 4 Section B option: any of Option A: Alternating Currents · A2 Unit 4 Option A
Open revision guidance
What to know
Alternating current (AC) is defined by periodic variation. A rotating coil in a uniform magnetic field serves as the fundamental generator. The flux linkage NΦ is expressed as BAN cos(ωt), where ωt is the angle θ between the coil normal and the field.
Faraday’s law dictates that the induced electromotive force (emf) is the negative rate of change of flux linkage. Deriving this via calculus shows the instantaneous emf is V = ωBAN sin(ωt). This produces a sinusoidal waveform.
Key parameters include frequency (f), the period (T=1/f), the peak value (V₀ or I₀), and the root mean square (rms) value. The rms value represents the effective power-dissipating capacity compared to DC.
The relationships between peak and rms values are Iᵣₘₛ = I₀/√2 and Vᵣₘₛ = V₀/√2. These relations assume pure sinusoidal waveforms.
In a pure resistor, the mean power dissipated is given by P = IᵣₘₛVᵣₘₛ = Iᵣₘₛ²R = Vᵣₘₛ²/R. It is critical not to confuse rms values with peak values when calculating thermal energy transfer.
An oscilloscope allows visual measurement of these voltages and frequencies. The trace represents the instantaneous potential difference versus time.
Inductors introduce reactive behaviour. Specifically, the current lags the voltage by a 90-degree phase shift in a sinusoidal AC circuit. This occurs because the induced back-emf opposes the rate of change of current.
For a numerical example: if a coil has a peak voltage of 10V, the Vᵣₘₛ = 10/√2 = 7.07V. If this is connected to a 5Ω resistor, mean power P = (7.07)²/5 = 10W.
The generator derivation is NΦ=NBAcos(ωt), followed by ε=−d(NΦ)/dt=−NBA[−ωsin(ωt)]=NBAωsin(ωt), for uniform B, fixed coil area A and constant angular speed. For sinusoidal current I=I₀sin(ωt), instantaneous resistor power is I₀²Rsin²(ωt). The cycle average of sin² is ½, so mean power is I₀²R/2=Iᵣₘₛ²R and Iᵣₘₛ=I₀/√2. The analogous voltage derivation gives Vᵣₘₛ=V₀/√2.
On an oscilloscope, multiply the peak vertical divisions from the zero line by volts per division to find peak voltage; peak-to-peak voltage must be halved for a centred sine wave. Multiply horizontal divisions for one complete cycle by seconds per division to find T, then f=1/T. A DC offset shifts the trace, while AC coupling removes that offset. Voltage across a known small series resistor can be used to infer current, with suitable supervised isolation and equipment ratings.
What to do in an assessment
Memorise the derivation of V=ωBANsin(ωt) by differentiating flux linkage.
Practice converting between peak and rms values to avoid calculation errors.
Draw phasor diagrams to visualise the 90-degree phase lag in inductors.
Use real-world data from oscilloscope traces to calculate frequency.
In plain language
This lesson covers the generation of sinusoidal AC via rotating coils, the relationship between peak and rms values, power dissipation in resistors, and the inductive phase lag.
Self-check
If a generator produces an emf V = 100sin(100πt), what is the peak voltage and the Vᵣₘₛ?
Show the answer
The peak voltage V₀ is 100V. The Vᵣₘₛ is 100/√2 = 70.7V.
AC Circuit Dynamics and ResonanceCore
Scope: Core · A2 Unit 4 Section B option: any of Option A: Alternating Currents · A2 Unit 4 Option A
Open revision guidance
What to know
In sinusoidal AC circuits, root mean square (rms) values represent the DC equivalent for power dissipation. Peak current I_0 relates to rms current I_rms via I_rms = I_0 / sqrt(2). Resistive components convert electrical energy to heat, with mean power P = I_rms^2 * R, unlike purely reactive components where mean power dissipation is zero.
Reactance characterizes opposition to current flow in reactive components. For an inductor, X_L = V_L/I_rms = ωL. For a capacitor, X_C = V_C/I_rms = 1/(ωC). Inductive current lags potential difference by 90 degrees, whereas capacitive current leads by 90 degrees.
Impedance Z = V_rms/I_rms measures total circuit opposition. For series circuits, voltages across R, L, and C are summed using phasors due to their differing phase angles. Phasor-vector addition follows V_total = sqrt(V_R^2 + (V_L - V_C)^2), yielding Z = sqrt(R^2 + (X_L - X_C)^2).
Resonance occurs in RCL circuits when inductive and capacitive reactances cancel, specifically X_L = X_C. Substituting ωL = 1/(ωC) and ω = 2πf, we derive the resonance frequency f = 1 / (2π * sqrt(LC)).
The Q factor signifies circuit selectivity and sharpness of resonance. At resonance, Q = V_L/V_R = V_C/V_R. This ratio indicates the magnification of potential across reactive components relative to the resistive component.
Consider an RCL series circuit with R = 50 ohms, L = 0.1 H, C = 100 microfarads. At resonance, f = 1 / (2 * 3.14 * sqrt(0.1 * 10^-4)) = 50.3 Hz. Given a supply of 10 Vrms, V_R = 10 V, and at resonance, V_L = I_rms * X_L = (10/50) * (2 * 3.14 * 50.3 * 0.1) = 6.32 V.
The Q factor for this specific circuit is Q = V_L/V_R = 6.32 / 10 = 0.632. Note that apparent power is V_rms * I_rms (VA), distinct from real power dissipated solely in the resistor.
Assumptions include ideal components with negligible internal resistance unless specified and pure sinusoidal waveforms. Limits include frequency dependence of reactances where X_L vanishes at DC and X_C becomes infinite.
Practical applications include radio tuning circuits which exploit high Q resonance to isolate specific frequencies from background signals, and AC power systems where phase correction minimises energy losses.
Understanding phasor diagrams is essential to visualise how individual component voltages combine to produce total supply voltage.
Differentiating between rms and peak values is crucial to avoid power calculation errors; always use rms for mean power.
Resonance sharpness is directly proportional to Q; higher Q circuits offer narrower bandwidths.
The energy oscillates between the electric field of the capacitor and the magnetic field of the inductor, resulting in zero net work over a full cycle.
Taking current as the horizontal phasor reference, Vᵣ is in phase, Vₗ is +90° and V꜀ is −90°. The phase angle by which supply voltage leads current satisfies tanφ=(Xₗ−X꜀)/R. For RL, omit X꜀; for RC, omit Xₗ, giving a negative φ. At resonance, Vₗ and V꜀ cancel, Z=R and supply voltage equals Vᵣ. Therefore Q=Vₗ/Vᵣ=(Iω₀L)/(IR)=ω₀L/R=1/(ω₀CR), independent of the chosen current; voltage magnification can exceed one in a high-Q circuit.
What to do in an assessment
Draw phasor diagrams for RL, RC, and RCL circuits to confirm phase relationships.
Practice substituting values into the impedance formula while ensuring frequency is in rad/s.
Verify resonance frequency using the derived RCL formula on varied component values.
Contrast the power behaviour of resistors versus inductors/capacitors using graph sketches.
In plain language
This lesson details AC circuit behaviour through phasors, reactive components, and RCL resonance properties governed by frequency-dependent reactance.
Self-check
What is the resonance frequency and Q factor of a circuit with R=100 ohms, L=0.5 H, and C=10 microfarads?
Show the answer
ω₀=1/√(LC)=1/√(0.5×10×10⁻⁶)=447 s⁻¹. f₀=ω₀/(2π)=71.2 Hz. Q=ω₀L/R=(447×0.5)/100=2.24, dimensionless. No supply current or voltage is needed because the current cancels in Vₗ/Vᵣ.
Medical Imaging PhysicsCore
Scope: Core · A2 Unit 4 Section B option: any of Option B: Medical Physics · A2 Unit 4 Option B
Open revision guidance
What to know
X-rays are high-energy electromagnetic waves characterized by their high penetrating power. They are produced when high-speed electrons strike a metal target, resulting in bremsstrahlung and characteristic spectra. Intensity is controlled by filament current, while photon energy depends on the accelerating potential difference.
Clinical use distinguishes between therapy, requiring high-energy photons to destroy localized cells, and diagnostic imaging, utilising lower-energy photons for structure visualisation. The attenuation of X-rays through tissue follows the exponential law I = I0 exp(-μx), where I0 is initial intensity, μ is the linear attenuation coefficient, and x is tissue thickness.
Medical applications include conventional radiography with digital receptors and real-time fluoroscopy using image intensifiers for moving targets. X-ray computed tomography (CT) scanners rotate an X-ray source around a patient to construct detailed cross-sectional images, providing better depth resolution than standard X-rays.
Ultrasound utilises high-frequency sound waves above human hearing, generated and detected by piezoelectric transducers that convert electrical energy to pressure waves. Diagnostic scans include A-scans for distance measurement and B-scans for structural mapping.
Acoustic impedance (Z) is defined as Z = ρc, where ρ is material density and c is the speed of sound. Reflection occurs at tissue boundaries where Z differs; the intensity reflection coefficient is given by the formula Ir/I0 = (Z2-Z1)^2 / (Z2+Z1)^2.
Impedance mismatches cause significant reflection; therefore, a coupling medium (gel) is used to match the Z of the transducer to the skin, minimising signal loss. The Doppler shift is applied in blood flow measurement, proportional to 2v cos(theta) / c.
Example: If an X-ray beam with intensity 100 W/m² passes through 2 cm of tissue (μ = 0.5 cm^-1), the transmitted intensity I = 100 * exp(-0.5 * 2) = 100 * exp(-1) = 36.8 W/m². For ultrasound, if Z1 = 1.5e6 kg/m²s and Z2 = 1.6e6 kg/m²s, the reflection coefficient is ((1.6-1.5)/(1.6+1.5))^2 = (0.1/3.1)^2 = 0.00104 or 0.104%.
Assumptions include monochromatic beams for attenuation and continuous tissue interfaces for impedance. Limits apply regarding non-linear attenuation in complex tissues and the need for acoustic coupling at every interface to prevent total reflection.
A-scan ultrasound plots echo strength against return time along one beam, useful for measuring distances between eye structures. B-scans combine many beam directions into a two-dimensional brightness image, used for fetal imaging and examining soft tissues. Pulse-echo depth is ct/2 because sound travels out and back. Acoustic impedance Z=ρc depends on density and sound speed; the ideal intensity reflection fraction [(Z₂−Z₁)/(Z₂+Z₁)]² assumes normal incidence. Coupling gel removes an air gap whose large impedance mismatch would reflect most energy.
What to do in an assessment
Memorise the exponential attenuation equation and the definition of acoustic impedance.
Practice rearranging I = I0 exp(-μx) to solve for x or μ using natural logarithms.
Understand that the coupling medium is essential for minimising reflections at skin boundaries.
Distinguish clearly between X-ray production mechanisms and ultrasound generation mechanisms.
In plain language
This lesson covers the principles of medical imaging through X-ray attenuation physics, CT scanning technology, and ultrasound properties including acoustic impedance and Doppler shift applications.
Self-check
What is the intensity reflection coefficient at an interface between two tissues with impedances 1.4 x 10^6 kg/m²s and 1.7 x 10^6 kg/m²s?
Show the answer
Using the formula (Z2-Z1)^2 / (Z2+Z1)^2, we get (1.7 - 1.4)^2 / (1.7 + 1.4)^2 = (0.3)^2 / (3.1)^2 = 0.09 / 9.61 = 0.00936 or approximately 0.94%.
Medical Imaging and DosimetryCore
Scope: Core · A2 Unit 4 Section B option: any of Option B: Medical Physics · A2 Unit 4 Option B
Open revision guidance
What to know
Medical physics employs wave phenomena and nuclear interactions to visualise internal anatomy. Diagnostic ultrasound utilises the Doppler effect, defined by the equation Δf/f₀ = 2v cos θ/c, where v is blood velocity, θ is the angle between the ultrasound beam and blood flow, and c is the speed of sound in tissue, allowing non-invasive assessment of circulatory health.
Magnetic Resonance Imaging (MRI) relies on the nuclear magnetic resonance of protons. When exposed to a strong external magnetic field, hydrogen nuclei precess. Resonance occurs when radio-frequency pulses match the Larmor frequency, calculated as f = 42.6 × 10^6 B, where B is the magnetic flux density in Tesla. Following excitation, nuclei relax, providing spatial data to construct images of internal structures.
Clinical imaging choices require weighing trade-offs between modalities. Ultrasound is portable and non-ionizing but limited by tissue boundaries. MRI provides superior soft-tissue contrast but requires long scan times and strictly controlled environments due to high magnetic fields. X-ray based methods remain vital for skeletal and rapid screening applications.
Radiation protection is quantified using specialised units. Absorbed dose (D) is defined as the energy deposited per unit mass, measured in Grays (Gy, where 1 Gy = 1 J/kg). Equivalent dose (H) adjusts for radiation type via a weighting factor (WR), expressed as H = D × WR, measured in Sieverts (Sv). Effective dose (E) further accounts for tissue sensitivity using a weighting factor (WT), calculated as E = H × WT.
Radionuclides, notably Technetium-99m, serve as tracers. These emit gamma radiation, which is detected externally by a gamma camera. The camera features a lead collimator to ensure only gamma photons originating from specific directions are recorded, a scintillation crystal to convert gamma rays into light, and photomultiplier tubes to amplify signals into images.
Positron Emission Tomography (PET) scanning utilises radionuclides that emit positrons. When a positron annihilates with an electron in the patient, two gamma photons are emitted in opposite directions. Detecting these simultaneous events allows for precise tumor localization.
Radiation risks include potential cellular damage from ionizing alpha, beta, and gamma emissions. Protection protocols minimise exposure by limiting activity, increasing distance, and using shielding consistent with the radiation type.
Example: Calculate the Larmor frequency for a proton in an MRI scanner with a field strength of 1.5 T. Using f = 42.6 × 10^6 B, we calculate: f = 42.6 × 10^6 × 1.5 = 63.9 × 10^6 Hz or 63.9 MHz.
Ionising radiation can ionise molecules in living cells, producing chemical changes and DNA damage. Cells may die, or mutations may later cause cancer. Alpha particles cause dense ionisation over a short range: intact skin largely stops external alpha radiation, but an alpha-emitting material inside the body can cause substantial local damage. Beta particles penetrate further and can damage skin and internal tissues. Gamma photons penetrate much more deeply, exposing internal organs even when the source is outside the body. Damage depends on absorbed energy, radiation type, tissue sensitivity and exposure, not just whether a detector records a count. Compare benefit with risk and reduce unnecessary exposure; clinical decisions belong to trained professionals.
In a gamma camera, a collimator admits photons travelling along selected directions to a scintillation crystal. The crystal emits light when a gamma photon deposits energy. An array of photomultiplier tubes, or a suitable CCD light-detection system as specified in the course, detects that light to estimate the event position and energy; it is not a lens taking an ordinary visible photograph of the tracer.
What to do in an assessment
Memorise the definitions of Absorbed, Equivalent, and Effective dose and their respective SI units.
Practice rearranging the Doppler equation to solve for blood flow velocity (v) in clinical scenarios.
Draw diagrams of a gamma camera to identify the specific purpose of the collimator and scintillation crystal.
Compare the risks of ionizing radiation against the diagnostic benefits provided by nuclear tracers.
In plain language
This lesson covers medical physics diagnostic principles including ultrasound Doppler shifts, MRI Larmor frequencies, nuclear tracer applications, and radiation dosimetry.
Self-check
A patient receives an equivalent dose of 0.05 Sv from an alpha source with a radiation weighting factor of 20. Calculate the absorbed dose in Grays.
Show the answer
Using H = D × WR, rearrange to D = H / WR. D = 0.05 Sv / 20 = 0.0025 Gy.
Mechanics of Sporting MotionCore
Scope: Core · A2 Unit 4 Section B option: any of Option C: The Physics of Sports · A2 Unit 4 Option C
Open revision guidance
What to know
Sporting performance relies on physical principles of stability and rotation. Stability is maintained when the vertical line through the centre of gravity falls within the base of support. Toppling occurs if this line falls outside the base, creating a restoring moment.
The principle of moments states that for equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments. In human muscle systems, lever systems acting on joints balance external loads via forces produced by muscle contraction.
Newton’s 2nd law for impulse is written as Ft = mv - mu. This describes the change in momentum caused by a force acting over time, essential for calculating impact forces in sports like ball strikes.
The coefficient of restitution, e, measures elasticity: e = relative speed after collision / relative speed before collision. Assuming negligible air resistance and constant gravity, dropping a ball from H and measuring bounce height h yields e = sqrt(h/H).
Moment of inertia, I, defines a body's resistance to angular acceleration. For a solid sphere, I = (2/5)mr^2, while for a thin spherical shell, I = (2/3)mr^2. Distribution of mass relative to the axis of rotation dictates these values.
Angular acceleration, alpha, is the rate of change of angular velocity: alpha = (omega2 - omega1) / t. Torque, tau, is defined as tau = I * alpha. This relationship shows that applying torque to an object with high moment of inertia results in lower angular acceleration.
Example calculation: A solid bowling ball (m = 5.0 kg, r = 0.1 m) starts from rest and reaches 10 rad/s in 2.0 s. First, I = (2/5) * 5.0 * 0.1^2 = 0.02 kg m^2. Then, alpha = (10 - 0) / 2.0 = 5.0 rad/s^2. Finally, torque tau = 0.02 * 5.0 = 0.1 Nm.
The centre of gravity is the point through which the resultant weight acts. Stability depends on its height and the base of support: an athlete can widen their stance or lower their body to keep the weight’s vertical line within the base. Once that line falls outside the base, weight produces a toppling moment about the edge.
Muscle-moment example: a forearm holds a 40 N load 0.30 m from the elbow, and the muscle’s perpendicular moment arm is 0.040 m. Ignoring the forearm’s own weight, static balance requires Fmuscle×0.040=40×0.30, giving 300 N. A short muscle moment arm requires a large muscle force. Include the limb’s weight and pivot reaction if the question specifies them; measure perpendicular distances, not arbitrary lengths.
Coefficient of restitution e is relative speed of separation divided by relative speed of approach along the impact line. For a ball dropped vertically onto a stationary rigid surface and rebounding, e=vup/vdown=√(h/H), ignoring air drag and the ball’s finite size. Moment of inertia describes mass distribution about a chosen axis: I=Σmr² for point masses. Mass farther from the axis contributes more, so pulling mass towards a spin axis reduces I.
What to do in an assessment
Analyse stability by drawing free-body diagrams for athletes in various poses.
Practice rearranging the impulse equation to solve for force given impact duration.
Compare moments of inertia for different mass distributions to understand rotational difficulty.
Memorise definitions of angular variables and their vector relationships.
In plain language
This lesson covers the application of mechanical principles including stability, moments, impulse, restitution, and rotational dynamics to sporting activities.
Self-check
A 40 N load acts 0.30 m from an elbow pivot. A supporting muscle has perpendicular moment arm 0.040 m. Ignoring the forearm’s weight, find the muscle force required for rotational equilibrium.
Show the answer
Clockwise and anticlockwise moments balance: F×0.040=40×0.30, so F=300 N. Use perpendicular distances to the force lines. The elbow reaction acts through the pivot and contributes no moment about that pivot; the arm’s weight must be included if supplied.
Rotational Dynamics and Fluid Mechanics in SportsCore
Scope: Core · A2 Unit 4 Section B option: any of Option C: The Physics of Sports · A2 Unit 4 Option C
Open revision guidance
What to know
Angular momentum L=Iω describes the rotational motion of bodies. Moment of inertia I measures resistance to angular acceleration, determined by mass distribution relative to the rotation axis, such as a solid sphere I=2mr²/5 or shell I=2mr²/3.
The conservation of angular momentum states that in the absence of external torques, L_initial = L_final. A diver tucking in reduces their radius r, thereby reducing I, which causes an increase in ω to conserve L.
Rotational kinetic energy is defined as KE_rot = 1/2 Iω². Total energy conservation includes gravitational, elastic, linear, and rotational components.
Projectile motion remains a core sporting analysis tool. Bernoulli's equation, p = p0 - 1/2 ρv², explains pressure drops in moving fluids. Assuming steady, incompressible, non-viscous flow, as velocity v increases, pressure p must decrease.
Drag force acts opposite to motion, calculated by F_D = 1/2 ρv²AC_D. A is the cross-sectional area, ρ is fluid density, and C_D is the dimensionless drag coefficient.
Numerical Example: A gymnast of mass 50 kg acts as a cylinder (I = 1/2mr²) with radius 0.2 m. If they spin at 2 rad/s, KE_rot = 0.5 * (0.5 * 50 * 0.2²) * 2² = 0.5 * 1 * 4 = 2 J.
Substitution: I = 0.4 * 0.4 * 0.1² = 0.0016 kg m². KE_rot = 0.5 * 0.0016 * 5² = 0.02 J.
Limitations include air turbulence during high-speed movement and variations in human body shape preventing simple geometric modelling for I.
Application includes improving cycle aerodynamics by minimising A or optimising sports balls via drag coefficient design.
Practical use of Bernoulli's principle includes lift generation on shaped surfaces like ski jumpers or ball flight path curvature.
Students must ensure consistency of SI units: kg for mass, m for radius, rad/s for ω, and J for energy.
What to do in an assessment
Sketch 2D cross-sections of 3D sporting objects to determine rotation axes.
Convert all rotational speeds to radians per second before substitution.
Check that units for drag force equate to Newtons.
Practice combining linear and rotational energy conservation problems.
In plain language
This lesson covers rotational dynamics, angular momentum conservation, energy principles, and fluid mechanics relevant to athletic performance.
Self-check
Calculate the rotational kinetic energy of a solid sphere (I=2/5mr²) of mass 0.4 kg and radius 0.1 m spinning at 5 rad/s.
Show the answer
I=(2/5)mr²=(2/5)×0.4×0.1²=0.0016 kg m². Rotational kinetic energy=½Iω²=½×0.0016×5²=0.020 J. The first factor 2/5 is the solid-sphere coefficient, not a second mass; ω is in rad s⁻¹ and the axis is through the sphere’s centre.
Energy Balance and Renewable PowerCore
Scope: Core · A2 Unit 4 Section B option: any of Option D: Energy and the Environment · A2 Unit 4 Option D
Open revision guidance
What to know
Earth's temperature is governed by thermal equilibrium, where energy inflow from the Sun equals energy re-radiated by Earth. Greenhouse gases like CO2 absorb infrared radiation, increasing thermal retention and shifting this balance.
Solar energy originates from the proton-proton chain in the Sun. This energy travels as electromagnetic waves, forming a spectrum where atmospheric interactions convert shorter wavelengths into near-infrared thermal energy.
Wien's Displacement Law states λmaxT = constant, while the Stefan-Boltzmann Law states Power = σAT^4. These describe the intensity of solar emission and the power density reaching planetary bodies.
Sea level rise is driven by ice on land melting into the ocean, increasing its mass via the density equation ρ = m/V. Archimedes' principle confirms that floating icebergs displace their own weight in water, so their melting does not raise sea levels.
Intensity I from the Sun follows the inverse square law I = P/A, where A = 4πr^2. Photovoltaic cells convert this intensity into electrical energy, with efficiency calculated as output electrical power divided by solar input power.
Wind power is extracted from fluid kinetic energy. The available power formula is P = 0.5 * ρ * A * v^3, where ρ is air density, A is swept area, and v is wind velocity.
Efficiency of wind turbines is limited by factors like blade design and wind speed variability. Betz's law provides the theoretical maximum efficiency for energy capture.
Numerical Example: A turbine with a 20m blade radius in air (ρ = 1.2 kg/m^3) at 10 m/s wind speed has power P = 0.5 * 1.2 * (π * 20^2) * 10^3 = 753,982 W or approximately 754 kW.
This teaching assumes ideal conditions where air flow is constant and turbine blades capture energy without friction losses, which are inherent limits in real-world application.
Compare UK and international deployment without inventing production statistics: UK solar output is variable with season, day length and cloud cover, while sunny lower-latitude regions generally offer higher annual solar yield. Rooftop PV supplies distributed electricity; large solar farms need land and grid capacity. Compare resource, capacity factor, cost, storage, land use and grid access using current sourced data if a question provides it. UK onshore/offshore wind benefits from suitable wind resources but faces siting, wildlife, grid and maintenance constraints; other countries may have stronger winds, larger available land or different infrastructure. Installed capacity is not annual delivered energy.
A photovoltaic efficiency calculation uses electrical output divided by incident solar power on the panel: η=Pout/(IA). At I=800 W m⁻², area 2.0 m² and output 320 W, η=320/(800×2.0)=0.20=20%. In the Sun’s main proton-proton chain, four protons ultimately form helium-4 with positrons, neutrinos and released energy; neutrinos carry away part of that energy. Incoming solar radiation heats Earth, which emits longer-wavelength infrared. Greenhouse gases absorb and re-emit parts of that outgoing radiation, changing the energy balance; this is not each incoming photon simply changing its wavelength in the atmosphere.
Use density and Archimedes’ principle for melting ice. Floating ice displaces a weight of water equal to its own weight. In the ideal same-density water model, its melted water occupies that already displaced volume, so the level does not rise; grounded land ice instead adds water that was not displacing the ocean before. Ocean warming also causes thermal expansion. Real freshwater/seawater density differences give a small correction to the floating-ice idealisation, not the main effect of land-ice loss.
What to do in an assessment
Sketch the Earth's incoming and outgoing radiation spectrum to visualise the greenhouse effect.
Practice rearranging the P = 0.5 * ρ * A * v^3 equation to solve for velocity or area.
Use density calculations to verify why land ice raises sea levels while sea ice does not.
Compare the efficiency of different renewable sources based on their energy conversion chains.
In plain language
This lesson covers the physics of global climate equilibrium and the quantitative mechanisms behind solar and wind energy conversion.
Self-check
A wind turbine has a sweep area of 500 m^2 and operates in air of density 1.25 kg/m^3 with a wind speed of 8 m/s. Calculate the available power.
Show the answer
Using P = 0.5 * ρ * A * v^3: P = 0.5 * 1.25 kg/m^3 * 500 m^2 * (8 m/s)^3 = 0.5 * 1.25 * 500 * 512 = 160,000 W or 160 kW.
Advanced Energy Systems and Thermal TransferCore
Scope: Core · A2 Unit 4 Section B option: any of Option D: Energy and the Environment · A2 Unit 4 Option D
Open revision guidance
What to know
Hydroelectric and tidal systems convert gravitational potential energy (Ep = mgh) into kinetic energy (Ek = 0.5mv²) as water descends or flows through turbines. Power is generated at a rate P = dE/dt, which depends on the mass flow rate.
Nuclear fission uses enrichment to increase U-235 concentrations, while breeding produces fissile fuel from fertile material. Sustained fusion remains challenging due to the fusion triple product requirement: plasma density, confinement time, and temperature must be simultaneously maintained to overcome electrostatic repulsion.
Fuel cells convert chemical energy directly into electrical energy through electrochemical reactions. For hydrogen fuel, water is the point-of-use product; greenhouse-gas benefits depend on how hydrogen and its processing energy are produced.
Thermal conduction is governed by ΔQ/Δt = -KA(Δθ/Δx). Here, K is thermal conductivity (W/m·K), A is cross-sectional area (m²), and Δθ/Δx is the temperature gradient. The negative sign denotes heat flow from hot to cold.
Heat flow through a building element is P=UAΔT, where U is its overall heat-transfer coefficient, A its area and ΔT the temperature difference. Combine thermal resistances for contacting layers, and add powers for separate parallel surfaces.
Example calculation: A hydroelectric dam releases 500 kg of water per second from a height of 20 m. Power = mgh/t = 500 * 9.81 * 20 = 98,100 W (98.1 kW).
Assumptions include steady state flow, no turbulence losses, and ideal energy conversion efficiency, which is rarely achieved in real-world scenarios.
Sustainable development relies on comparing the intermittency of renewables like wind against the high energy density of nuclear sources.
Environmental impacts vary by source: hydro alters local ecosystems, while nuclear management requires long-term radioactive waste containment.
Thermal insulation increases resistance to heat transfer and lowers the overall U-value, reducing heat loss for a given inside-outside temperature difference.
Global energy strategies now emphasise coupling renewable generation with high-efficiency transmission and storage technologies.
In pumped storage, spare electrical energy pumps water uphill (electrical to gravitational potential); later downhill flow generates electricity. It stores energy rather than producing a new net supply and returns less than was used because of losses. Tidal barrages also use a height difference but follow predictable tides; hydro depends on available flow/head, while wind power varies approximately with v³ and output is weather-dependent. Compare energy over the same time interval, not just maximum power: 98.1 kW of ideal hydro for 2 h gives 196.2 kWh; 160 kW of available wind for 2 h gives 320 kWh before turbine efficiency and variation.
A hydrogen fuel cell’s useful output reaction produces water, but “only water at the point of use” does not guarantee zero life-cycle emissions: hydrogen manufacture and electricity sources matter. Fuel-cell chemical energy is converted electrochemically rather than through a heat engine. In enrichment, the proportion of fissile U-235 is increased; breeding converts fertile nuclei into fissile fuel using neutron capture and subsequent changes. Sustained fusion needs adequate temperature, particle density and confinement time (the fusion triple product), not just a very hot plasma.
U is an overall heat-transfer coefficient in W m⁻² K⁻¹, not a dimensionless efficiency. For layers in series across the same area, thermal resistances add: approximately 1/U=Σ(dᵢ/Kᵢ), adding surface resistances if specified. For separate parallel paths such as wall and window, add powers Ptotal=Σ(UᵢAᵢΔT), not the U-values alone. A 10 m² wall with U=0.30 and a 2 m² window with U=1.5 at ΔT=20 K lose 0.30×10×20+1.5×2×20=120 W. Insulation increases thermal resistance and reduces heat flow for a given temperature difference; it need not reduce that imposed temperature difference.
What to do in an assessment
Practice deriving the power output of a turbine using fluid mass flow rates.
Sketch the temperature profile across composite walls with different thermal conductivities.
Compare the energy density of fossil fuels versus nuclear fusion using representative data.
Solve problems involving parallel thermal resistances in building insulation.
In plain language
This lesson covers the physics of hydroelectric, nuclear, and chemical energy conversion alongside the mathematical modelling of steady-state thermal conduction and insulation.
Self-check
A window of area 2.0 m² has a thermal conductivity K of 0.8 W/m·K and thickness 0.005 m. Calculate the rate of heat loss if the internal temperature is 22°C and external is 2°C.
Show the answer
Using ΔQ/Δt = KAΔθ/Δx: P = 0.8 * 2.0 * (22 - 2) / 0.005 = 6400 W. Units: W. Substitution: 0.8 * 2.0 * 20 / 0.005 = 6400.

A2 Unit 5 Practical Examination: Assessment and Mathematical RigorCore
Scope: Core · Appendix A: mathematical requirements
Open revision guidance
What to know
The A2 Unit 5 Practical Examination constitutes 10% of the total qualification, split into two externally marked components: a 90-minute Experimental Task (25 marks) and a 60-minute Practical Analysis Task (25 marks). These are individual assessments under controlled conditions.
Success requires mastery of mathematical skills. You must recognise and correctly apply units (e.g., m s⁻¹ for velocity) and convert prefixes (e.g., cm³ to m³). Standard form is mandatory for physical constants like c = 3.00 × 10⁸ m s⁻¹. Always report final answers to the significant figures allowed by the least precise raw measurement.
Data handling involves calculating arithmetic means for repeated readings and identifying uncertainty. When combining data—such as calculating density ρ = m/V—you must manage uncertainty through addition, multiplication, or powers. Using appropriate symbols like ∝ for proportionality or Δ for differences is required for clear communication.
Calculations often involve trigonometric functions for vectors, power functions, and logs. For example, in an experimental task measuring a force vector, use sin θ or cos θ to resolve components. Ensure your calculator is in the correct mode (degrees or radians).
Practical apparatus mastery is assessed by your ability to interpolate between analogue scales or operate digital multimeters for voltage and current. Accuracy is improved by methods like timing multiple oscillations or using fiducial markers.
Working scientifically involves posing questions, risk management, and rigorous analysis. You must recognise correlations versus causal relationships and resolve conflicting evidence. Ethics and social implications are key to scientific decision-making.
Example: Calculating density of a metal block. Mass m = 0.50 kg ± 0.01 kg, Volume V = 2.0 × 10⁻⁵ m³ ± 0.1 × 10⁻⁵ m³. Density ρ = m/V = 0.50 / (2.0 × 10⁻⁵) = 25,000 kg m⁻³. Using fractional uncertainty: (Δρ/ρ) = (Δm/m) + (ΔV/V) = (0.01/0.50) + (0.1/2.0) = 0.02 + 0.05 = 0.07. Absolute uncertainty Δρ = 25,000 × 0.07 = 1,750. Result: (2.5 ± 0.2) × 10⁴ kg m⁻³.
Preparation focuses on official 'Instructions to Teachers/Exams Officers' received in early spring for specific topic areas. Do not rely on speculation for future themes.
Practical sessions require individual work without communication between cohorts. Teachers mark specific practical skills, but WJEC handles the external assessment of the tasks.
Evaluation requires comparing experimental design to scientific principles and justifying choices. Referencing printed and digital sources correctly is expected.
Apparatus usage, such as signal generators or radioactive detectors, must be safe and precise. Always record observations immediately and clearly.
Finally, differentiate between instantaneous rates of change (tangents on displacement-time graphs) and mean values. Use ICT for processing when appropriate.
Understanding order of magnitude helps check calculations; if you expect a force in Newtons and get 10⁸, verify your unit conversions.
Written Physics papers use paper-specific data booklets: official published 2026 requirements list them for AS Units 1–2 and A2 Units 3–4. Read the actual instructions and booklet supplied for your paper; do not assume every equation is provided, or that a previous year’s booklet is unchanged. Practise selecting equations, deriving required relationships, rearranging and using the supplied constants with their units. Ask your centre for the current 2027 arrangements.
What to do in an assessment
Verify your calculator mode is set to degrees or radians to match your geometry problem.
When performing calculations, track significant figures at each intermediate step to avoid rounding errors.
Review the WJEC list of prescribed topics released in spring for your specific exam cycle.
Always define variables and symbols clearly in your reports to ensure scientific communication standards.
Practice identifying the dependent and independent variables before beginning any experimental task.
In plain language
This unit evaluates experimental and analytical proficiency through a controlled practical examination requiring rigorous application of mathematical, scientific, and technical skills.
Self-check
If an experimental measurement of current is 0.12 A (±0.01 A) and voltage is 6.0 V (±0.1 V), calculate the resistance R = V/I and its percentage uncertainty.
Show the answer
R = 6.0 / 0.12 = 50 Ω. Percentage uncertainty in V = (0.1/6.0) × 100 ≈ 1.67%. Percentage uncertainty in I = (0.01/0.12) × 100 ≈ 8.33%. Total percentage uncertainty = 1.67% + 8.33% = 10%.
A2 Unit 5 Practical Examination and Quantitative PhysicsCore
Scope: Core · Appendix A: mathematical requirements
Open revision guidance
What to know
Unit 5 constitutes 10% of the A-level qualification, consisting of an Experimental Task (90 min, 25 marks) and a Practical Analysis Task (60 min, 25 marks). These assessments are conducted individually under controlled conditions, with prescribed topic areas communicated early in the spring term via 'Instructions to Teachers/Exams Officers'.
Mathematical rigor is foundational to Physics. Students must be able to change the subject of equations, including non-linear ones, and substitute physical quantities with correct SI units. For instance, in kinematics, if v² = u² + 2as, one must be proficient in rearranging for 'a' and solving algebraic or quadratic forms when parameters are unknown.
Graphical analysis requires translating between numerical, algebraic, and graphical forms. When plotting variables, the linear relationship y = mx + c serves as the primary model. For linear data, the slope (m) represents a rate of change, and the intercept (c) indicates the base value of a physical property.
Calculating rates of change from linear graphs is straightforward, but non-linear relationships require drawing a tangent to a curve. The slope of this tangent provides the instantaneous rate of change, which is physically distinct from a mean rate of change over a broader interval.
Integrating under a curve also carries physical significance. The area under a velocity-time graph represents displacement. This can be calculated geometrically or estimated using grids for irregular curves. Logarithmic plots are similarly essential for handling data that spans several orders of magnitude, such as radioactive decay (N = N0e⁻λt) or capacitor discharging.
Data evaluation involves understanding measurement uncertainty. Students must ensure that all calculations and recorded observations reflect the appropriate number of significant figures, constrained by the least accurate measurement in the set.
Practical execution involves independent thinking, safely using apparatus, and recording data accurately. Evaluation of experimental design and identification of variables are crucial, as is understanding the difference between random errors and systematic uncertainties.
Consider this worked numerical example: A capacitor discharges such that V = V0e⁻(t/RC). To linearize this, take natural logs: ln(V) = ln(V0) - (1/RC)t. If you plot ln(V) against t, the slope of the resulting straight line is -1/RC. If the slope is -0.5 s⁻¹, and R = 1000 Ω, then C = 1 / (0.5 * 1000) = 0.002 F.
To succeed, prioritise disciplined record keeping and rigorous application of scientific terminology. Always verify that apparatus usage aligns with the safety requirements specified in your practical instructions.
The scientific process demands more than just measurement; it requires evaluating causal relationships and reproducibility. Conflicting evidence must be analysed to justify the validity of conclusions, ensuring that findings align with established models.
Ethics and social decisions are key dimensions of modern Physics. Students should consider the implications of scientific applications, such as the environmental impact of energy storage or radiation use, and how these inform societal decision-making.
Final performance is validated through external WJEC marking. Reading about a technique cannot replace the practice of setting up circuits, using signal generators, or interpreting oscilloscope time-base settings personally.
The scientific community's role is to ensure integrity through peer scrutiny and standard-setting, which underscores why all reported findings must be properly cited and theoretically justified.
The area under a velocity-time graph is signed displacement, even when acceleration varies. Use rectangles or trapezia to estimate the area; for successive readings vi and vi+1 separated by Δt, a trapezium contributes (vi+vi+1)Δt/2. Negative velocity contributes negative displacement. Similar area reasoning gives impulse under force-time, work under force-displacement and charge under current-time, with units checked in each case.
What to do in an assessment
Always define variables and identify the independent and control variables before commencing an experiment.
Perform at least three repeats for each data point to calculate a reliable arithmetic mean.
Use a fiducial marker or plumb line to minimise parallax error when taking analogue measurements.
State all final answers with consistent significant figures based on the least precise input data.
Check circuit diagrams for polarity and component orientation before connecting power supplies.
In plain language
This lesson covers the structure of the Unit 5 practical examination and the rigorous mathematical and experimental skills required to analyse physical data effectively.
Self-check
A student measures the extension x of a spring as force F is applied. They obtain a linear graph passing through the origin. If F = 20 N results in x = 0.05 m, calculate the spring constant k in N m⁻¹ using F = kx.
Show the answer
Using F = kx, rearrange for k: k = F / x. Substituting values: k = 20 N / 0.05 m = 400 N m⁻¹.
A2 Unit 5 Practical Examination Techniques and Mathematical RequirementsCore
Scope: Core · Appendix A: mathematical requirements
Open revision guidance
What to know
A2 Unit 5 constitutes 10% of the A-level qualification, consisting of two distinct sessions: a 90-minute Experimental Task (25 marks) and a 60-minute Practical Analysis Task (25 marks). These are externally marked by WJEC, though teachers conduct direct assessment of specific practical skills.
The Experimental Task involves solving a specific problem with provided apparatus. Centres receive official Instructions to Teachers/Exams Officers in the early spring, detailing prescribed topic areas. It is vital to note these are specific themes, not generic guesses for 2027.
Mathematical competency is essential for success. For rate-of-change problems like radioactive decay (delta x / delta t = -lambda x), you must use graphical methods or software modelling rather than formal calculus. This requires interpreting data points correctly to determine rates.
Logarithmic plots are crucial for testing exponential relationships. If a variable y changes with x according to y = A e^(-lambda t), taking natural logs (ln y = ln A - lambda t) transforms this into a linear relationship, where the gradient equals -lambda.
You must be proficient in sketching relationships including 1/x, 1/x squared, trigonometric functions like sin(theta) and cos squared(theta), and exponential decays. These models represent physical laws like inverse-square laws for radiation intensity.
Geometry and trigonometry skills involve resolving vectors in 2D and 3D. When using Pythagoras’ theorem for a resultant force or resolving forces using sin and cos, ensure your calculator mode matches your input—degrees or radians. Conversion (180 degrees = pi radians) is frequently tested.
Small angle approximations (sin(theta) approx theta) simplify calculations for interference patterns or diffraction. Use these only when theta is small; otherwise, precise trigonometric functions are required for accurate analysis.
Numerical examples: Calculate the fringe separation using the double-slit equation w = lambda D / s. If lambda = 600 nm, D = 2.0 m, and s = 0.5 mm, convert to SI units: w = (600 x 10^-9 m * 2.0 m) / (0.5 x 10^-3 m) = 2.4 x 10^-3 m, or 2.4 mm.
For experimental reliability, always define independent, dependent, and control variables. Equipment resolution must be justified; for instance, using a micrometer (0.01 mm) is superior to a ruler (1 mm) for wire diameter.
Uncertainty analysis is mandatory. For an added length l1 + l2, absolute uncertainties add. For products like V = IR, percentage uncertainties add. Always evaluate reproducibility and consider conflicting data points.
Ethics and social decision-making are components of 'How Science Works'. Reflect on the safety risks of your equipment and the implications of using ionizing radiation or high-voltage circuits in your experimental design.
The practical exam is individual work; communication between sessions is prohibited. Always keep a clear, organised record of your experimental activity, as this informs your final evaluation of methodology and evidence.
Remember, reading instructions is not practising. Hands-on experience with apparatus—multimeters, oscilloscopes, and data loggers—is the only way to demonstrate the required performance standard.
Geometry supports real measurements: triangle area=½bh; circle circumference=2πr and area=πr²; cuboid surface area=2(ab+bc+ca) and volume=abc; closed cylinder surface area=2πr²+2πrh and volume=πr²h; sphere area=4πr² and volume=4πr³/3. For a cylinder with r=0.010 m and h=0.050 m, V=π×0.010²×0.050=1.57×10⁻⁵ m³. Square or cube the unit conversion too: 1 cm³=10⁻⁶ m³.
For positive k, y=k/x decreases towards zero for x>0 and has an asymptote at x=0; y=k/x² also decreases but more steeply. y=kx is a straight line through the origin and y=kx² a parabola. Sine and cosine are periodic and can be negative; sin²x and cos²x are non-negative, have half the period, and sum to one. eˣ grows and e⁻ˣ decays; both equal one at x=0 and never cross zero. Recognise these shapes before fitting a physical model, and label the axes with its actual quantities and units.
What to do in an assessment
Convert all prefixes (e.g., cm, mm, nm) to base SI units before beginning calculations.
Check your calculator mode (degrees or radians) before resolving vector components.
When plotting, always use a line of best fit and determine the gradient for linear relationships.
Include units in every step of your calculation to verify physical consistency.
In plain language
This unit requires individual mastery of experimental procedures and mathematical analysis, focusing on graphical interpretation, exponential modelling, and geometric problem-solving within a strictly controlled 10% weighted examination context.
Self-check
How would you determine the time constant RC of a discharging capacitor using a logarithmic plot?
Show the answer
Plot ln(V) on the y-axis against time (t) on the x-axis. Using the equation ln(V) = ln(V0) - (1/RC)t, the graph will be a straight line with a gradient of -1/RC. The time constant RC is the negative reciprocal of the gradient.
View diagrams
Mathematical models
Use the labelled model alongside the explanation. Idealised curves are not measured data.
Planning investigationsCore
Scope: Core · Appendix C: Working Scientifically
Open revision guidance
What to know
Plan an investigation by applying a relevant physical model to an experimental question. Predict a testable relationship, choose the independent and dependent quantities, identify controls and a suitable range, select instruments and repeats, and assess hazards before collecting data. Adapt the method thoughtfully to practical difficulties rather than changing observations to match a prediction.
Reading about these techniques does not certify performance; you must practise using equipment to gain confidence. You must be able to use analogue apparatus, such as vernier calipers for length or thermometers for temperature, and interpolate between scale markings correctly.
Digital instruments like electrical multimeters must be used accurately for measuring voltage, current, and resistance. When designing circuits, ensure correct component polarity and verify your wiring against diagrams before powering on.
For timing experiments, use methods to increase accuracy, such as taking the average of multiple oscillations using a fiducial marker to define the start and end of a cycle. Use light gates or stopwatches where appropriate.
Data collection should be recorded clearly with appropriate units. Use ICT and software to process findings and present data scientifically, adhering to significant figure conventions.
Always evaluate experimental design and results by considering measurement uncertainties. If you measure a length of 12.5 cm with a ruler of 1 mm resolution, your uncertainty is ±0.05 cm per reading.
Mathematical analysis is used throughout experimental Physics. You must plot graphs, calculate slopes, and find intercepts to represent linear relationships. For a displacement-time graph, the tangent gradient gives instantaneous velocity.
Consider a worked example: If a student calculates velocity (v = s/t) where distance s = 5.00 m ± 0.01 m and time t = 2.00 s ± 0.02 s, the percentage uncertainty in velocity is the sum of percentage uncertainties: (0.01/5.00 + 0.02/2.00) * 100% = 1.2%.
Finally, understand that science involves peer scrutiny, social decision-making, and addressing conflicting data. Your lab work is a bridge between theoretical models and real-world evidence.
What to do in an assessment
Practice using analogue scales and digital multimeters regularly to ensure you can interpolate measurements correctly.
Refine your graph plotting skills, ensuring you can calculate the slope and intercept of linear plots to determine physical constants.
Ensure all numerical results reflect the precision of your raw data using correct significant figures.
Review the WJEC Instructions to Teachers document provided in the spring term to understand the specific topic scope for your exam year.
In plain language
These are shared Physics skills used in written practical-context questions and supervised investigations. They support preparation; reading is not evidence of assessed practical performance.
Self-check
A student measures the period of a pendulum as 1.50 s ± 0.05 s. Calculate the percentage uncertainty.
Show the answer
The percentage uncertainty is (0.05 / 1.50) * 100% = 3.33%, which should be rounded to 3% given the significant figures.
Measuring and evaluating evidenceCore
Scope: Core · Appendix C: Working Scientifically
Open revision guidance
What to know
Use a written experimental method accurately and record observations as they occur. Choose a justified range and repeats, identify random scatter separately from systematic offsets, estimate uncertainties from the actual apparatus and method, then interpret the results against the proposed physical relationship. Evaluate limitations and propose specific, justified improvements.
When collecting data, students must follow written instructions precisely, keeping clear records of all observations. Records should include units, appropriate significant figures based on instrument resolution, and estimates of uncertainty. For instance, if using a meter rule, one must interpolate between scale markings to reduce uncertainty, perhaps using fiducial markers for timing oscillations to ensure reproducibility.
Mathematical analysis is used throughout experimental Physics. For linear relationships following y = mx + c, students must extract the slope and intercept, understanding their physical significance. For example, if plotting v against t for constant acceleration, the slope represents acceleration (m s-2) and the intercept represents initial velocity (m s-1). Students must correctly handle standard form, prefixes, and unit conversions.
Consider a worked example: A student measures a force F = 5.0 +/- 0.1 N acting over a displacement s = 2.0 +/- 0.1 m. The work done W = Fs = 10.0 J. The percentage uncertainty in F is (0.1/5.0)*100 = 2%, and in s is (0.1/2.0)*100 = 5%. The total percentage uncertainty is 2% + 5% = 7%. Thus, W = 10.0 +/- 0.7 J. This demonstrates how to combine uncertainties when multiplying quantities.
Evaluation requires critical thinking about design. One must discuss if the chosen range of the independent variable was sufficient and if controls were adequate. If an experiment on gas laws shows conflicting data, the student must assess whether this is due to measurement error or a limitation of the model, such as failing to maintain a constant temperature.
Scientific evidence is built on models, reproducibility, and peer scrutiny. Students must demonstrate the ability to present data in a scientific way, perhaps by plotting graphs of extension versus force, and using these to calculate constants like the Young modulus. The analysis must be rigorous, recognising that causal relationships require evidence beyond simple correlation.
Ethical considerations and social decisions are key components of scientific work. When evaluating applications, students should discuss benefits and risks, acknowledging that data may be used to inform public or industrial decision-making. Integrity is maintained by documenting research citations and acknowledging the role of the scientific community in validating new knowledge.
Finally, students must use ICT for data processing and modelling. Whether using data loggers to capture high-frequency oscillations or software to perform non-linear regressions, the tool must serve the objective of interpreting physical phenomena. Proficiency in these techniques is demonstrated through the external exam, which tests the application of these skills in new contexts.
What to do in an assessment
Review official Instructions to Teachers/Exams Officers released in early spring to understand the specific topic areas for the current cycle.
Practice converting units and applying significant figures to every calculation, ensuring the final result respects the precision of the raw data.
Use fiducial markers and repeated measurements to minimise uncertainty in all experimental timing tasks.
Practise the specific apparatus techniques listed in the specification, such as using an oscilloscope's time-base or a multimeter's settings.
Always define the uncertainty of a combined value using the sum of percentage uncertainties for multiplication/division.
In plain language
These are shared Physics skills used in written practical-context questions and supervised investigations. They support preparation; reading is not evidence of assessed practical performance.
Self-check
A student measures current I = 0.50 +/- 0.02 A and voltage V = 12.0 +/- 0.3 V. Calculate the power P = IV and the absolute uncertainty in the power.
Show the answer
P = IV = 0.50 * 12.0 = 6.0 W. Percentage uncertainty in I = (0.02/0.50)*100 = 4%. Percentage uncertainty in V = (0.3/12.0)*100 = 2.5%. Total % uncertainty = 4% + 2.5% = 6.5%. Absolute uncertainty = 6.0 * 0.065 = 0.39 W. Result: 6.0 +/- 0.4 W.
Practical calculations and graphsCore
Scope: Core · Appendix C: Working Scientifically
Open revision guidance
What to know
Numeracy in a practical context requires absolute rigor. When reporting physical quantities, you must use standard form for large or small numbers and ensure your results reflect the correct number of significant figures, determined by the least accurate measurement taken. Never report a calculated value with more precision than your raw data provides, as this falsely implies experimental accuracy.
Plotting and interpreting graphs is a foundational skill. For a linear relationship following y = mx + c, you must identify the gradient (m) and intercept (c) correctly. For instance, when plotting velocity-time data to find acceleration, the slope represents the rate of change. Ensure units are consistent throughout, and recognise when to use logarithmic plots to linearize exponential decay data.
Consider margins of error, accuracy, and precision. Accuracy is how close your result is to the true value; precision is the consistency of your repeats. You must account for measurement uncertainties by calculating percentage errors using (uncertainty/reading) * 100. When combining data through multiplication or division, add percentage uncertainties; when adding or subtracting, add absolute uncertainties.
Scientific evidence requires identifying causal relationships versus mere correlations. You must evaluate your methodology—considering range, repeats, and equipment resolution—to minimise systematic and random errors. Always justify your choice of equipment based on its resolution and consider whether your sample size is sufficient for reproducibility.
Peer scrutiny and the scientific community play vital roles in validating knowledge. Your work must be ethically sound, particularly when dealing with radioactive sources or human subjects. When conflicting data appears, analyse why: is it a calibration issue, an uncontrolled variable, or a limitation of the current model?
Consider a worked example: If you measure a distance d = 10.0 ± 0.1 cm and time t = 2.0 ± 0.1 s, the speed v = d/t = 5.0 m/s. The percentage uncertainty in d is 1%, and in t is 5%. Adding these (as they are being divided), total uncertainty is 6%. Thus, v = 5.0 ± 0.3 m/s.
Always evaluate the social and environmental implications of your findings. When reporting, use appropriate terminology and cite sources correctly. Evidence is not just data; it is the synthesis of experimental results evaluated against established physical models.
Avoid using generic advice. Ensure your records are neat and reflect all activities performed during your laboratory sessions. Even if equipment is provided, you are responsible for checking its operation before starting.
Finally, realise that your practical work must be reproducible. If an experiment yields data that contradicts the predicted model, investigate the apparatus and technique thoroughly before evaluating the validity of the model itself.
The external assessment verifies that you can execute these tasks under pressure. Focus on your planning, your ability to control variables, and your critical evaluation of the resulting data.
What to do in an assessment
Calibrate all digital and analogue equipment before starting every experiment.
Record raw data in tables with consistent significant figures and clearly labelled units.
Perform at least three repeats for each variable set to identify and exclude anomalies.
Always sketch a graph during the experiment to detect non-linear trends early.
Calculate and quote the percentage uncertainty for every primary measurement.
In plain language
These are shared Physics skills used in written practical-context questions and supervised investigations. They support preparation; reading is not evidence of assessed practical performance.
Self-check
If a resistor has a measured potential difference of 5.0 ± 0.1 V and a current of 0.25 ± 0.02 A, what is the value of the resistance and its absolute uncertainty?
Show the answer
R = V/I = 20 Ω. Percentage uncertainty in V = (0.1/5.0)*100 = 2%. Percentage uncertainty in I = (0.02/0.25)*100 = 8%. Total uncertainty = 2% + 8% = 10%. 10% of 20 Ω = 2 Ω. Result: 20 ± 2 Ω.
Research and referencingCore
Scope: Core · Appendix C: Working Scientifically
Open revision guidance
What to know
Effective experimental planning involves identifying independent variables, controlled variables, and appropriate ranges. Accuracy must be enhanced using techniques like fiducial markers for timing oscillations, or utilising set squares and plumb lines for alignment. Equipment resolution should be justified based on the precision of the instrument.
When performing measurements, learners must apply correct units (e.g., m s⁻¹ for velocity) and standard form for constants. If measuring Young modulus, the area of cross-section must be calculated accurately. Precision is limited by the least accurate instrument; therefore, final calculations must use appropriate significant figures.
Mathematical analysis often requires rearranging equations like v = u + at or using logarithms for decay laws, such as N = N₀e⁻ᵀt. When plotting graphs, the slope and intercept provide physical evidence, such as the initial velocity from a velocity-time graph. Uncertainties must be considered when combining readings.
Scientific evidence requires recognising correlations versus causal relationships. Evaluation involves assessing methodology, resolving conflicting evidence, and acknowledging how scientific understanding evolves through peer scrutiny and social ethical decisions.
Research and referencing skills are essential for sound practice. Learners must use reliable online and offline sources, including textbooks and scientific websites, to support their investigative approaches. Information must be cited correctly to demonstrate academic integrity in any submitted reports.
Example: If measuring resistance R from V and I, where V = (2.00 ± 0.05) V and I = (0.50 ± 0.02) A, the value is R = 4.00 Ω. The percentage uncertainty is (0.05/2.00) + (0.02/0.50) = 2.5% + 4.0% = 6.5%. The uncertainty is ± 0.26 Ω, so report as 4.0 ± 0.3 Ω.
For a specific research task, compare your measured g from a pendulum or falling-body experiment with an appropriate reference value. Consult a reliable physics textbook and an identified scientific or standards website, noting whether the reference is standard gravity (9.80665 m s⁻²) or local gravitational acceleration, which varies with location. Do not claim every measured local g must equal standard gravity exactly. Record author/organisation, title, edition or date, page for a book, and exact URL plus access date for a website. A usable model citation is: Organisation/Author, Title, publication year, page or URL, accessed date; fill it with the actual source rather than inventing a textbook or citation.
What to do in an assessment
Consult the 'Instructions to Teachers' document in early spring to identify the specific focus of the Unit 5 tasks.
Practice combining uncertainties during arithmetic calculations to ensure you can handle multiplication and division of measurements accurately.
Develop a habit of citing every scientific source used during investigations to build robust research habits.
Master the use of both digital and analogue instruments by ensuring you can interpolate between scale markings correctly.
In plain language
These are shared Physics skills used in written practical-context questions and supervised investigations. They support preparation; reading is not evidence of assessed practical performance.
Self-check
Your measured gravitational acceleration differs from 9.80665 m s⁻². What should you check about a reference source before declaring your result incorrect, and what details should you record?
Show the answer
Check whether the source gives conventional standard gravity or a local measured value: local g varies, so standard gravity is not an exact prediction for every site. Compare your uncertainty and method as well. Record author/organisation, title, publication or edition date, relevant page for print sources, or exact URL and access date for online sources. Use the actual source, not an invented citation.
Using apparatus safelyCore
Scope: Core · Appendix C: Working Scientifically
Open revision guidance
What to know
Experimental proficiency involves correctly using analogue apparatus to record physical quantities like length, temperature, pressure, force, angles, and volume, while mastering scale interpolation. For smaller dimensions, you must use micrometers or calipers with vernier scales. Accuracy should be improved through methods such as using fiducial markers for oscillations or set squares for perpendicularity.
Digital measurement is equally vital. You must be comfortable with electrical multimeters to measure current, voltage, and resistance, as well as digital stopwatches or light gates for timing. When dealing with circuits, you must verify polarity before energizing systems. Design and construct your circuits systematically, checking components against circuit diagrams to ensure validity.
Your waveform analysis skills must extend to operating signal generators and oscilloscopes. You need to adjust volts/division and time-base settings to capture clear traces. You should also be prepared to generate and measure waves using equipment like vibration transducers or microwave sources. Light-based investigations require using lasers to analyse interference and diffraction patterns.
ICT integration is essential. This includes using data loggers with various sensors or software for processing experimental results. For nuclear topics, you must know how to handle ionising radiation sources safely while using appropriate detectors. These techniques demand rigorous adherence to safety protocols and logical record-keeping.
Scientific evidence requires linking models to experimental results. You must identify independent, dependent, and control variables to ensure causality. Peer scrutiny is inherent in scientific validation; hence, you must evaluate conflicting data by assessing measurement uncertainties and systematic errors. Ethical considerations regarding human or environmental impacts must inform your experimental design.
Numerical work requires reporting results to appropriate significant figures, governed by the least accurate measurement. Use standard form for physical constants like the speed of light. When analysing data, you must calculate arithmetic means of repeats to improve precision and be ready to perform error analysis by calculating percentage uncertainties.
Mathematical modelling involves graphing experimental variables. For a linear relationship, use the form y=mx+c to determine the slope and intercept. For example, in a velocity-time graph, the slope represents acceleration, and the intercept represents initial velocity. For non-linear decay, use logarithmic plots to linearize the data and determine constants like decay factors.
Worked Numerical Example: To determine the density of a cube of side 2.50 cm and mass 45.5 g. First, convert units: length = 0.0250 m, volume = (0.0250)^3 = 1.5625 x 10^-5 m^3. Mass = 0.0455 kg. Density = mass/volume = 0.0455 / 1.5625 x 10^-5 = 2912 kg m^-3. Reported to three significant figures, this is 2.91 x 10^3 kg m^-3.
For assessment preparation, focus on planning ranges for independent variables and identifying controls. Evaluate your method post-experiment; comment on whether your equipment resolution limited your precision. Reproducibility is the hallmark of scientific inquiry; ensure your procedure is documented clearly enough that another student could replicate your findings.
Finally, distinguish between instantaneous and mean rates of change. A tangent to a curve on a displacement-time graph provides the instantaneous velocity. Use trigonometry for resolving vectors in force diagrams and apply small-angle approximations for interference patterns where necessary.
An analogue pressure gauge, such as a calibrated Bourdon gauge, can measure pressure in a gas-law apparatus: check the zero/reference and units, distinguish gauge pressure from absolute pressure, read without parallax and interpolate between divisions only within justified resolution. For a manometer, a level difference h corresponds to pressure difference ρgh; that is not automatically the gas’s absolute pressure.
With a teacher-approved Geiger-Müller detector, first record background counts for a known time, repeat and calculate background count rate. In a supervised sealed-source absorption experiment, keep source-detector geometry fixed, record counts for equal times with different absorbers, then subtract the mean background rate. Follow the school’s radiation procedure, use source holders/tongs and time-distance-shielding controls; do not handle sources directly or perform radioactive-source work unsupervised. Counts fluctuate randomly, so repeated/longer counts improve reliability without removing systematic errors.
What to do in an assessment
Create a checklist of the 12 listed practical techniques and perform each at least once before the spring term.
Practice converting all physical units to SI base units before performing calculations to avoid order-of-magnitude errors.
Use graphs to identify systematic errors by looking for non-zero intercepts in experiments where the intercept should be zero.
Perform dummy 90-minute experimental tasks to condition your speed and accuracy in data collection.
In plain language
These are shared Physics skills used in written practical-context questions and supervised investigations. They support preparation; reading is not evidence of assessed practical performance.
Self-check
A supervised radiation experiment records 90 counts in 60 s with no source and 330 counts in 60 s with the source at a fixed distance. Calculate the background-corrected count rate and name two controls.
Show the answer
Background rate=90/60=1.5 s⁻¹; measured rate with source=330/60=5.5 s⁻¹. Corrected rate=5.5−1.5=4.0 s⁻¹. Keep source-detector distance and counting interval fixed, and follow the teacher-approved sealed-source procedure. Use repeat counts to assess random fluctuations; corrected count rate is not automatically the source’s activity because detector efficiency and geometry matter.
A2 Unit 5 Practical Examination and Scientific EvidenceCore
Scope: Core · How Science Works: skills 1–12
Open revision guidance
What to know
A2 Unit 5 is a mandatory, externally marked practical examination worth 10% of the total A Level qualification. It consists of two components: a 90-minute Experimental Task and a 60-minute Practical Analysis Task, both conducted individually under controlled conditions during the spring term of the second year. This is not an internal NEA or coursework endorsement; performance is evaluated based on task execution and analysis, not merely attendance or ticking records.
The Experimental Task requires students to manage equipment, identify variables, and record data accurately using techniques such as timing multiple oscillations or setting up D.C. circuits. Safety and risk management are inherent requirements. When measuring, students must justify their choice of instruments based on resolution, such as using micrometers for small distances.
Mathematical rigor is essential. Analysis involves plotting data to determine slopes and intercepts, where a linear relationship follows the y=mx+c format. For example, in a velocity-time graph, the gradient represents acceleration, and the intercept represents initial velocity. Calculations must reflect the limits of the least accurate measurement through appropriate significant figure usage.
Consider this worked numerical example: If a student measures the force F on a spring as 5.0 ± 0.1 N and its extension x as 0.20 ± 0.01 m, the spring constant k=F/x is 25 N m⁻¹. The percentage uncertainty in k is the sum of percentage uncertainties in F (0.1/5.0 = 2%) and x (0.01/0.20 = 5%), totaling 7%. The final result is 25 ± 2 N m⁻¹.
Scientific evidence requires using models to explain physical phenomena and evaluating methodology to resolve conflicting data. Reproducibility and the role of peer scrutiny are foundational to the development of scientific knowledge over time.
Ethical considerations, such as the impact of radiation experiments on the environment or biological organisms, must be evaluated alongside the benefits of scientific applications.
The scientific community validates knowledge through rigorous evaluation, ensuring integrity in findings. This process informs societal decision-making, where students must distinguish between correlation and causation in the data collected.
Official prescribed topic areas are communicated via the 'Instructions to Teachers/Exams Officers' in early spring; students must focus on these rather than speculative themes for 2027.
Clear record keeping, using ICT to process findings, and citing sources correctly are vital for demonstrating scientific competence throughout the assessment.
An explanation must link evidence to a specific model: kinetic theory connects random molecular collisions with gas pressure, while diffraction supports a wave description and photoelectric observations require photon energy. State assumptions, identify which observations a model explains, and distinguish a model’s limits from a measurement mistake. Before a practical, identify hazards, who could be harmed, severity/likelihood and controls; for heated gas-law apparatus consider hot surfaces and pressure, and for circuits use appropriate low-voltage supplies and discharge capacitors. Follow teacher-approved controls rather than assuming a reading checklist establishes safe practical competence.
What to do in an assessment
Ensure all final numerical answers are reported to the appropriate number of significant figures, determined by the raw data precision.
Justify equipment selection in your planning based on the resolution needed to minimise measurement error.
Always express uncertainties as percentages when combining variables through multiplication or division.
Practice rearranging complex physical equations like N=N₀e⁻λt to isolate variables for graphical interpretation.
Review the provided 'Instructions to Teachers' immediately upon receipt to align your preparation with prescribed topics.
In plain language
Unit 5 is an externally assessed 10% practical exam evaluating your ability to conduct experiments and perform rigorous data analysis under controlled conditions.
Self-check
Repeated measurements agree closely but all differ from an accepted value beyond their stated uncertainty. How should you evaluate this evidence and your model?
Show the answer
Close agreement indicates repeatability, not guaranteed accuracy. Check calibration, zero errors, controls, the reference conditions and whether the uncertainty estimate includes relevant effects. Compare independent methods and examine the model’s assumptions before accepting or rejecting it. Report evidence and limitations honestly, including results that do not support the original prediction; consider safety and broader consequences rather than changing the observations to fit the theory.

Practical exam preparationPractical exam preparation
Core
Scope: Core · Printed page 64: Unit 5 practical examination and annual topic notices
Reading this guidance does not complete or grade Unit 5. Practical performance is assessed separately and is not counted as written-exam progress.
Open revision guidance
What to know
The A2 Unit 5 Practical Examination is an externally assessed component constituting 10% of the total GCE A Level Physics qualification. This assessment requires students to demonstrate individual competence in practical investigation, data analysis, and evaluation under controlled, individual conditions. It is neither coursework nor an endorsement, and actual performance under the specified examination conditions is mandatory to earn marks.
The assessment comprises two distinct, time-bound tasks administered in the spring term of the second year of study. First, the Experimental Task is a 90-minute session worth 25 marks, where students are provided with specific apparatus to solve a practical physics problem. Second, the Practical Analysis Task is a 60-minute session, also worth 25 marks, where students analyse provided experimental data.
Administration follows strict confidentiality protocols to maintain test security. Centres may use multiple sessions if necessary, but must ensure no communication occurs between candidates who have taken the test and those yet to take it. While WJEC provides external marking, teachers are required to award specific marks for the direct observation of practical skills during the Experimental Task.
Topic areas for both tasks are officially communicated via the 'Instructions to Teachers/Exams Officers' document dispatched to centres early in the spring term and concurrently published on the WJEC website. These official notices are the sole source for exam preparation; speculation regarding future themes is ineffective and discouraged.
Mathematical proficiency is essential. For instance, in data analysis, you must consistently handle significant figures, ensuring results match the precision of the least accurate measurement. For example, if measuring a length of 12.4 cm (3 s.f.) and a time of 2.1 s (2 s.f.), a calculated velocity (v = s/t) must be reported to 2 s.f. to maintain validity.
Graphing skills involve plotting independent variables on the x-axis and dependent variables on the y-axis, applying y = mx + c to identify physical constants. In a Young Modulus experiment, the gradient of the linear elastic stress-strain graph is Young’s modulus, in pascals. Uncertainties must be identified, calculated, and propagated through additions or powers.
Consider a worked example: a student determines the spring constant k from a graph of force (F) against extension (x). With an intercept of 0.00 N and a slope of 15.2 N m⁻¹, the equation F = kx mirrors y = mx. If the gradient uncertainty is ±0.4 N m⁻¹, the result is reported as k = (15.2 ± 0.4) N m⁻¹.
Practical apparatus mastery requires more than theoretical familiarity. When measuring lengths with a micrometer, one must check the zero error before recording. If a zero error of +0.02 mm exists, it must be subtracted from all subsequent readings to ensure accuracy.
Safety and variable control are critical. In electrical experiments, circuits must be verified against diagrams before connecting power. For resistance-temperature investigations, students must identify control variables, such as maintaining constant current or ensuring the wire does not overheat, which could introduce systematic errors.
The scientific method in this unit involves evaluating methodology and identifying potential systematic or random errors. A systematic error, like a miscalibrated thermometer, shifts all results, whereas random errors, like human reaction time in timing oscillations, can be reduced by taking multiple repeats and calculating a mean.
Finally, ensure all citations and units are correct. Every physical quantity must be accompanied by its SI unit, such as N for force or kg m⁻³ for density. Adherence to these formal procedures is the foundation of achieving marks in the Unit 5 examination.
Your centre may arrange additional sessions on day 1 and/or day 2. Learners who have already taken the task must not communicate its content to those still due to sit it, including later sessions on the same day. Centres may use the two task versions for different groups; each learner takes only one Experimental Task. Both the Experimental Task and Practical Analysis Task are externally marked by WJEC, with teachers making the specified direct observations of practical skills during the experimental task. Reading this guide is preparation, not evidence that the assessed performance has been completed.
What to do in an assessment
Review the WJEC spring term official instructions immediately upon release to confirm assessed topics.
Practice graph construction by determining slopes and intercepts to calculate physical constants.
Use digital sensors or multimeters with correct units and account for resolution limits in your error analysis.
Maintain clear, accurate records of all experimental observations to support your evaluation of data.
In plain language
The A2 Unit 5 Practical Examination is a formal, two-task individual assessment requiring students to solve experimental problems and analyse data under controlled conditions.
Self-check
A force-extension graph has gradient (15.2 ± 0.4) N m⁻¹. State the spring constant and its percentage uncertainty. Does reading this guide certify assessed Unit 5 performance?
Show the answer
For a linear Hooke’s-law F-x graph, gradient is k=(15.2 ± 0.4) N m⁻¹. Percentage uncertainty is (0.4/15.2)×100≈2.6%. A reading tick records preparation only: the individual Experimental Task and Practical Analysis Task are assessed separately by WJEC.

Previous revision ticks

These are your ticks from the earlier guide. They do not count towards the new lessons, and the old content is not current teaching.

Use the equations of uniformly accelerated motion
Use motion graphs and constant-acceleration equations
Track energy, power and efficiency
Relate stress, strain and elastic behaviour
Use black-body spectra to infer star temperature
Analyse resistance and direct-current circuits
Apply wave interference and refraction
Use photon energy in the photoelectric effect
Calculate circular motion quantities
Use molecular energy and thermal laws
Interpret nuclear decay and half-life
Compare field strength, potential and orbital motion
Analyse phase and impedance in AC circuits
Use physics in diagnostic imaging
Apply mechanics and materials to sport
Evaluate energy systems and environmental impacts
Plan, perform and analyse the two practical-exam tasks

Earlier topic checklist

These earlier topic ticks are separate from the reviewed points above and do not count towards that progress.

Physics topic list

Tick each item off as you revise. Ticks are saved on this device only.

These ticks keep your earlier topic checklist. They do not count towards the new reviewed requirements above. Its numbering may be internal; use the linked references above for the exact reviewed source requirements.

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A2 Unit 4 Section B option

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