WJEC物理 电路分析 光折射 核衰变 考点 | WJEC Physics: Circuit Analysis, Light Refraction & Nuclear Decay Exam Points

WJEC物理 电路分析 光折射 核衰变 考点

The WJEC A-Level Physics specification brings together three fascinating areas: electricity and circuits, the behavior of light (optics), and nuclear physics. This article breaks down the core concepts, formulas, and exam techniques you need to master. WJEC A-Level物理考纲涵盖三大核心板块：电路与电学、光学（光的折射与波动）、以及核物理。本文梳理核心概念、关键公式和应试技巧，助你高效备考。

Part 1: Electricity and Circuits 电路与电学

Current (I) is the rate of flow of charge. 电流(I)是电荷流动的速率。 I = Q / t。Unit: ampere (A)。In metals, current is carried by free electrons drifting slowly through the lattice -- this is the electron drift velocity model, where I = nAve。金属导体中，自由电子在晶格中缓慢漂移形成电流。注意区分 conventional current (正电荷方向) 和 electron flow (电子实际运动方向)。

Potential difference (V) is the energy transferred per unit charge. 电势差/电压(V)是单位电荷转移的能量。 V = W / Q。Unit: volt (V)。The emf (electromotive force, ε) of a source is the total energy supplied per unit charge when no current flows -- it includes energy lost to internal resistance (r)。电源电动势(ε)包含内阻(r)上的能量损耗，terminal pd = ε - Ir。

Ohm's law 欧姆定律: V = IR, where R is resistance in ohms (Ω)。电阻取决于材料、长度和截面积: R = ρL/A, where ρ is resistivity (电阻率)。WJEC常考 I-V characteristics: ohmic conductor (直线过原点), filament lamp (曲线, 电阻随温度升高), semiconductor diode (单向导通)。

🔌 Series Circuits 串联电路

Current: I = I₁ = I₂ = I₃ (same everywhere 处处相等)
Voltage: V = V₁ + V₂ + V₃
Resistance: R = R₁ + R₂ + R₃
The potential divider 分压器 is a key application: V_out = V_in × R₂/(R₁+R₂)

⚡ Parallel Circuits 并联电路

Current: I = I₁ + I₂ + I₃
Voltage: V = V₁ = V₂ = V₃ (same across each branch 各支路相同)
Resistance: 1/R = 1/R₁ + 1/R₂ + 1/R₃
Total resistance is always less than the smallest individual resistor

Electrical Power 电功率: P = IV = I²R = V²/R。Unit: watt (W)。WJEC喜欢考察 energy transfer 和 efficiency 的计算, 特别是在电路中含有 internal resistance 的场景。记住: total power supplied = εI, useful power = I²R (external load), wasted power = I²r (internal resistance)。

Resistivity experiment 电阻率实验考点: 使用 micrometer 测量 wire diameter, 用 metre rule 测 length, 用 voltmeter + ammeter (或 ohmmeter) 测 resistance。Plot R against L, gradient = ρ/A。常见误差来源: zero error on micrometer, heating effect (电流过大导致升温), contact resistance at crocodile clips。

Kirchhoff's laws 基尔霍夫定律: WJEC requires you to apply both laws to multi-loop circuits。Kirchhoff's 1st Law (current law / junction rule): the sum of currents entering a junction equals the sum leaving -- ΣI_in = ΣI_out。This is a consequence of conservation of charge。Kirchhoff's 2nd Law (voltage law / loop rule): around any closed loop, the sum of emfs equals the sum of p.d.s -- Σε = ΣIR。This is a consequence of conservation of energy。Worked example: a circuit with two batteries and three resistors -- set up simultaneous equations using both laws。

Superconductivity 超导性与临界温度: Some materials, when cooled below their critical temperature (临界温度 T_c), lose all electrical resistance (R = 0)。This was discovered by Heike Kamerlingh Onnes in 1911 with mercury at 4.2 K。Applications include: MRI scanners (强磁场), maglev trains (磁悬浮列车), and particle accelerators like the LHC。The challenge: most superconductors need liquid helium cooling, which is expensive。High-temperature superconductors (e.g., YBCO ceramics, T_c ~ 92 K) can use cheaper liquid nitrogen but are brittle ceramics。

Thermistors and LDRs 热敏电阻与光敏电阻: A thermistor (NTC 负温度系数) has resistance that decreases as temperature increases -- used in temperature sensors and fire alarms。A Light Dependent Resistor (LDR 光敏电阻) has resistance that decreases as light intensity increases -- used in automatic street lamps and camera light meters。Both are commonly featured in WJEC potential divider circuit questions: as the sensor resistance changes, V_out changes, triggering a switch or alarm。

Part 2: Light and Optics 光学与光的折射

Light is an electromagnetic wave 电磁波 that exhibits both wave-like and particle-like behavior (wave-particle duality 波粒二象性)。In the WJEC optics section, we focus on the wave model: reflection, refraction, diffraction, interference, and polarisation。

Refraction 折射与 Snell's law: When light crosses a boundary between two media, its speed and direction change。n₁ sin θ₁ = n₂ sin θ₂, where n is the refractive index 折射率 of the medium。n = c / v (真空中光速 / 介质中光速)。Light bends towards the normal 向法线偏折 when entering a denser medium (n₂ > n₁); bends away from the normal 远离法线 when entering a less dense medium。

Total Internal Reflection (TIR) 全反射: Occurs when light travels from a denser medium to a less dense one at an angle greater than the critical angle (临界角 C)。sin C = n₂/n₁ = 1/n (when n₂ = 1, i.e., going into air)。TIR is the principle behind optical fibres 光纤: the core has a higher refractive index than the cladding, so light stays trapped inside via multiple TIRs。Applications: telecommunications, endoscopy (内窥镜)。

Diffraction 衍射: The spreading of waves when they pass through a gap or around an obstacle。Maximum diffraction occurs when the gap width ≈ wavelength (缝宽约等于波长时衍射最显著)。Single-slit diffraction produces a central bright fringe twice as wide as the side fringes。对于 diffraction grating 衍射光栅: d sin θ = nλ, where d is slit spacing, n is order number (级数)。Grating produces sharper, brighter maxima than double slits -- perfect for measuring wavelength precisely。

Young's double-slit experiment 杨氏双缝实验: Proved light is a wave via interference patterns。λ = ay/D, where a = slit separation (双缝间距), y = fringe spacing (条纹间距), D = distance to screen (缝到屏距离)。Coherence 相干性 is essential: the two sources must have constant phase difference。WJEC exam tip: describe how fringe spacing changes if (a) slit separation decreases (fringe spacing increases), (b) wavelength increases / switch to red light (fringe spacing increases), (c) screen moved further away (fringe spacing increases)。

Stationary waves on strings 弦上的驻波: 虽然严格说不属于光学, 但WJEC常将波动概念连在一起考。Fundamental frequency f = (1/2L)√(T/μ), where L = string length, T = tension (张力), μ = mass per unit length (线密度)。Harmonics: f_n = n × f₀。Nodes (波节) = zero displacement; antinodes (波腹) = maximum displacement。

Polarisation 偏振: Polarisation is evidence that light is a transverse wave (横波) -- longitudinal waves (like sound) cannot be polarised。Unpolarised light vibrates in all directions perpendicular to propagation。A polarising filter (偏振片) only allows vibrations in one plane to pass。Malus's law: I = I₀ cos²θ, where θ is the angle between the transmission axes of two polarisers。Applications: polaroid sunglasses reduce glare (reflected light from water/roads is partially horizontally polarised), LCD screens, stress analysis in materials (photoelasticity)。

Photoelectric effect 光电效应: When light of sufficient frequency shines on a metal surface, electrons are emitted。Key observations that classical wave theory could NOT explain: (1) threshold frequency f₀ exists -- below f₀, no electrons emitted regardless of intensity; (2) kinetic energy of emitted electrons depends on frequency, not intensity; (3) emission is instantaneous (no time delay)。Einstein's explanation (Nobel Prize 1921): light consists of photons (光子), each with energy E = hf。The work function (逸出功 Φ) is the minimum energy to remove an electron: hf = Φ + KE_max。The stopping potential V_s relates to KE_max: eV_s = KE_max = hf - Φ。

Wave-particle duality 波粒二象性: Light behaves as a wave (diffraction, interference, polarisation) AND as a particle (photoelectric effect)。De Broglie extended this to matter: all particles have an associated wavelength λ = h/p = h/(mv)。Electron diffraction (Davisson-Germer experiment) confirmed matter waves -- electrons passing through a graphite crystal produce a diffraction pattern identical to X-rays。The wave nature of matter is only observable for very small particles (electrons, neutrons); macroscopic objects have wavelengths too tiny to detect。

EM spectrum overview 电磁波谱: WJEC expects you to know the full spectrum from longest to shortest wavelength: Radio → Microwave → Infrared → Visible (ROYGBIV 红橙黄绿蓝靛紫) → Ultraviolet → X-ray → Gamma。Key relationships: c = fλ (all EM waves travel at c = 3×10⁸ m/s in a vacuum)。Higher frequency = shorter wavelength = higher photon energy (E = hf)。UV causes skin cancer and fluorescence; X-rays penetrate soft tissue for medical imaging; gamma rays are used in radiotherapy and sterilisation。Infrared is associated with thermal radiation -- all objects above 0 K emit IR。

Part 3: Nuclear Physics 核物理与放射性衰变

Atomic structure 原子结构: The nucleus contains protons (质子) and neutrons (中子), collectively called nucleons (核子)。Atomic number Z = number of protons (defines the element); mass number A = protons + neutrons。Isotopes (同位素) are atoms of the same element with different numbers of neutrons。The strong nuclear force (强核力) holds the nucleus together, overcoming electrostatic repulsion between protons。It has a very short range (~3-4 fm) and is attractive at ~1 fm。

Radioactive decay 放射性衰变: Unstable nuclei emit radiation to become more stable。Three types:

α Alpha decay α衰变

Helium nucleus: ⁴₂He
A decreases by 4, Z decreases by 2
Highly ionising, low penetration
Stopped by paper or skin
高电离能力, 穿透力弱

β⁻ Beta minus decay β⁻衰变

Neutron → proton + electron + antineutrino
A unchanged, Z increases by 1
Moderate ionisation and penetration
Stopped by ~3mm aluminium
n → p + e⁻ + ν̄ₑ

γ Gamma decay γ衰变

EM radiation only, no particle
A and Z unchanged
Low ionisation, very high penetration
Reduced by thick lead or concrete
仅释放电磁波, 穿透力极强

Half-life (半衰期 T₁/₂): The time taken for half the radioactive nuclei in a sample to decay, or for the activity to halve。Decay follows an exponential law: N = N₀ e^{-λt}, where λ = decay constant (衰变常数)。Activity A = λN = A₀ e^{-λt}。Key relationship: λ = ln 2 / T₁/₂。WJEC exam style: given a graph of activity vs time, determine half-life; calculate remaining mass after n half-lives: m = m₀ / 2^n。

Carbon dating 碳-14测年法: ¹⁴C has T₁/₂ ≈ 5730 years。Living organisms maintain a constant ¹⁴C/¹²C ratio by exchanging carbon with the environment。After death, ¹⁴C decays without replenishment。By measuring the remaining ¹⁴C activity, archaeologists estimate the age of organic materials。Limitations: only works for samples up to ~50000 years; contamination can skew results; assumes constant atmospheric ¹⁴C levels。

Mass-energy equivalence 质能方程: E = mc²。In nuclear reactions, the total mass of products is slightly less than the total mass of reactants -- this mass defect (质量亏损) is converted into energy。Binding energy (结合能) = mass defect × c²。The binding energy per nucleon 平均结合能 peaks at iron-56 (⁵⁶Fe), the most stable nucleus。Nuclei lighter than iron release energy via fusion (聚变); nuclei heavier than iron release energy via fission (裂变)。

Nuclear fission 核裂变: A heavy nucleus (e.g., ²³⁵U) absorbs a neutron, becomes unstable, and splits into two lighter nuclei plus 2-3 neutrons + energy (~200 MeV per fission)。These neutrons can trigger further fissions -- a chain reaction (链式反应)。In a nuclear reactor, control rods (控制棒) absorb excess neutrons to maintain a steady rate; moderator (慢化剂) slows neutrons so they are more likely to cause fission。

Nuclear fusion 核聚变: Two light nuclei combine to form a heavier nucleus + energy。The Sun fuses hydrogen into helium via the proton-proton chain。Fusion requires extremely high temperatures (~10⁷ K) to overcome Coulomb repulsion -- this is why fusion reactors (like tokamaks) are so challenging。Advantage over fission: abundant fuel (hydrogen isotopes from water), less radioactive waste, no risk of meltdown。Disadvantage: we haven't achieved sustained net energy output yet。

Particle physics 粒子物理基础: WJEC introduces the idea that protons and neutrons are made of quarks (夸克)。Proton = uud (up up down), neutron = udd (up down down)。Up quark charge = +2/3 e, down quark charge = -1/3 e。In β⁻ decay, a down quark changes into an up quark: d → u + e⁻ + ν̄ₑ, mediated by the weak nuclear force (弱核力)。The neutrino (中微子) was originally hypothesised to conserve energy and momentum in beta decay。

Nuclear reactor design 核反应堆设计: WJEC may ask you to describe the key components。The fuel rods (燃料棒) contain enriched uranium (²³⁵U, typically 3-5%)。The moderator (慢化剂), often water or graphite, slows fast neutrons to thermal energies (~0.025 eV) where they are more likely to cause fission。The control rods (控制棒), made of boron or cadmium, absorb neutrons -- inserting them deeper reduces the reaction rate。The coolant (冷却剂), often pressurised water or CO₂ gas, transfers heat from the core to a heat exchanger where steam is produced to drive turbines。The entire core is surrounded by thick concrete shielding (屏蔽层) to absorb radiation。

Radioactive safety and background radiation 辐射安全与背景辐射: The three principles of radiation protection are: time (minimise exposure time), distance (intensity follows inverse square law I ∝ 1/r², so double distance = quarter intensity), and shielding (use appropriate materials: paper for α, aluminium for β, lead/concrete for γ)。Background radiation comes from: cosmic rays (宇宙射线), radon gas from rocks (岩石中的氡气), medical X-rays, and nuclear weapons testing fallout。In the UK, average background radiation is ~2.7 mSv/year, with radon contributing about half。

Medical applications of radiation 辐射的医学应用: Radiotherapy (放射治疗) uses gamma rays or X-rays to kill cancer cells -- the beam is rotated around the patient so healthy tissue receives less dose while the tumour receives a concentrated dose。Radioactive tracers (示踪剂) like technetium-99m (T₁/₂ = 6 hours) are injected into the body to image organs -- the short half-life minimises patient exposure。PET scans (正电子发射断层扫描) use positron-emitting isotopes (e.g., ¹⁸F-FDG) which produce gamma ray pairs that are detected to create 3D metabolic images。Sterilisation of medical equipment uses high doses of gamma radiation to kill bacteria without heat (cold sterilisation)。

Nuclear waste management 核废料处理: High-level waste (spent fuel rods) is initially stored in cooling ponds to allow short-lived isotopes to decay。Long-term storage involves vitrification (玻璃固化) -- mixing waste with molten glass and sealing it in stainless steel containers。These are stored in deep geological repositories (深层地质储存库), typically in stable rock formations 500-1000m underground。The challenge: some fission products have half-lives of thousands of years, requiring isolation for geological timescales。

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Exam Tips and Common Pitfalls 考试技巧与常见失分点

1. Units and prefixes 单位与数量级: WJEC examiners are strict about units。Always include units in calculations, and know your prefixes: nano (n, 10⁻⁹), micro (μ, 10⁻⁶), milli (m, 10⁻³), kilo (k, 10³), mega (M, 10⁶), giga (G, 10⁹)。A common mistake: confusing resistivity ρ (Ω·m) with resistance R (Ω)。

2. Significant figures 有效数字: Give answers to the same number of significant figures as the least precise data given in the question。If in doubt, 3 significant figures is usually safe for A-Level。

3. Graph questions 图像题: WJEC loves asking you to (a) describe the relationship shown, (b) determine gradient/area under graph, (c) relate gradient to a physical quantity。For I-V graphs, don't just say "it's a curve" -- describe what happens to resistance: "the gradient decreases, so resistance increases"。For radioactive decay graphs: use tangents to find rate of decay at a specific time。

4. Practical / experiment questions 实验题: WJEC Unit 2 and Unit 4 include practical assessments。Be ready to: describe how to reduce uncertainty (重复测量, use instruments with higher resolution, reduce parallax error), identify sources of systematic vs random error, and suggest improvements to an experimental setup。

5. Definitions to memorise 必背定义: (a) The ampere: current which, flowing in two infinitely long parallel wires 1m apart in a vacuum, produces a force of 2×10⁻⁷ N per metre。 (b) The volt: 1 joule per coulomb。 (c) The ohm: 1 volt per ampere。 (d) Activity (becquerel, Bq): 1 decay per second。These are in the WJEC spec so learn them word-for-word。

6. Nuclear equations must balance 核方程必须守恒: Total A (mass number) must be the same on both sides; total Z (atomic number) must be the same on both sides。For β⁻ decay, remember the antineutrino ν̄ₑ carries zero mass and zero charge, but it must be shown for full marks in WJEC。

7. Link concepts across topics 跨章节串联: WJEC synoptic questions may combine electricity with mechanics (e.g., a motor lifting a mass -- calculate current from power and emf), or optics with quantum physics (photon energy = hf = hc/λ, photoelectric effect)。Practice connecting ideas from different units。

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