📚 Common Misconceptions in A-Level AQA Physics | A-Level AQA 物理：常见误区
Misconceptions in physics are deeply rooted ideas that conflict with accepted scientific theory. They often arise from everyday language or incomplete understanding of fundamental principles. In the AQA A-Level Physics specification, certain topics repeatedly trap students who rely on intuition rather than rigorous physical laws. This article addresses the most common misconceptions, explaining why they are wrong and providing the correct conceptual frameworks. By tackling these errors head-on, you can strengthen your grasp of key ideas and improve exam performance.
1. Constant Force Means Constant Velocity | 恒力意味着恒定速度
Many students believe that a constant force acting on an object produces a constant velocity. This stems from the everyday experience that to keep something moving, you must keep pushing it. However, this ignores the effect of friction and contradicts Newton’s second law. A resultant force causes acceleration, not velocity. If the resultant force is constant, the acceleration is constant, which means the velocity changes at a steady rate. An object moving at constant velocity actually has zero resultant force acting upon it. This misconception leads to errors when analysing terminal velocity or motion in a gravitational field.
2. Action and Reaction Forces Cancel Out | 作用力与反作用力相互抵消
The third law pair of forces are often thought to act on the same object and thus cancel each other out. In reality, Newton’s third law states that if body A exerts a force on body B, then body B exerts an equal and opposite force on body A. These forces act on different bodies, so they can never cancel each other in the free-body diagram of a single object. For instance, the weight of a book on a table and the normal reaction force from the table are not a third law pair. The third law pair to the book’s weight is the gravitational pull of the book on the Earth. Similarly, the normal contact force between book and table has its third law counterpart as the force the book exerts downwards on the table. Recognising which forces act on which body is crucial for solving dynamics problems correctly.
学生常误以为牛顿第三定律中的一对力作用在同一物体上，因此会相互抵消。实际上，牛顿第三定律指出，如果物体 A 对物体 B 施加一个力，那么物体 B 也对物体 A 施加一个大小相等、方向相反的力。这两个力作用在不同的物体上，因此永远无法在单个物体的受力分析图中相互抵消。例如，放在桌子上的书所受的重力与桌子给予的支持力并不是一对第三定律力。书的重力的反作用力是书对地球的引力。类似地，桌子与书之间的正压力，其反作用力是书对桌子向下的压力。辨别哪些力作用在哪个物体上，对正确解决动力学问题至关重要。
3. Heavier Objects Fall Faster | 较重的物体下落得更快
The idea that heavy objects fall faster than light ones is one of the most persistent misconceptions, dating back to Aristotelian physics. In the absence of air resistance, all objects near the Earth’s surface fall with the same acceleration due to gravity, approximately 9.81 m s⁻². Galileo’s thought experiment and the Apollo 15 feather-and-hammer demonstration both confirm this. The confusion arises because in everyday life, air resistance dominates the motion of light objects like feathers, while it affects dense objects much less. In A-Level problems, unless air resistance is explicitly included, the acceleration due to gravity is independent of mass. This is a direct consequence of the equivalence principle, which also underpins general relativity.
认为重的物体比轻的物体下落得更快，是最顽固的误区之一，可以追溯到亚里士多德的物理学。在没有空气阻力的情况下，地球表面附近的所有物体都以相同的重力加速度下落，大约为 9.81 m s⁻²。伽利略的思想实验和阿波罗 15 号的羽毛-锤子实验都证实了这一点。产生混淆的原因是，在日常生活中，空气阻力对羽毛等轻质物体的运动影响很大，而对密度大的物体影响较小。在 A-Level 题目中，除非明确考虑空气阻力，否则重力加速度与质量无关。这是等效原理的直接结果，该原理也是广义相对论的基础。
4. Voltage is ‘Used Up’ in a Circuit | 电压在电路中被“用掉”
A common fallacy is to think of voltage as a substance that gets consumed as current flows through a circuit. In fact, voltage (potential difference) is a measure of energy transferred per unit charge between two points. When a charge moves through a resistor, electrical energy is converted into heat, but the charge itself is not used up, and charge carriers are conserved. The sum of the potential differences across components in a series circuit equals the supply voltage – this is often misinterpreted as voltage being ‘shared out’ and disappearing. Actually, the energy carried by the charges decreases, while the number of charges remains unchanged. Understanding voltage as energy per coulomb, rather than as a fluid-like quantity, prevents errors in circuit analysis.
5. Current is the Same as Speed of Electrons | 电流等于电子的速度
Students often imagine that when a switch is closed, electrons race around the circuit at nearly the speed of light. In reality, the drift velocity of electrons in a typical metal wire is on the order of millimetres per second. The electric field that drives them propagates at close to the speed of light, which is why lights turn on almost instantly. The current (measured in amperes) is the rate of flow of charge, given by I = nAve, where n is the number density of charge carriers, A is the cross-sectional area, v is the drift velocity, and e is the elementary charge. For a given current, a thicker wire has a smaller drift velocity because of its larger cross-sectional area. Confusing current with the speed of individual electrons can lead to misunderstandings about resistance and power transmission.
学生经常想象，当开关闭合时，电子以接近光速在电路中飞驰。实际上，在普通金属导线中，电子的漂移速度大约为每秒几毫米的量级。驱动它们的电场以接近光速传播，这就是为什么灯光几乎瞬间亮起的原因。电流（以安培为单位）是电荷流动的速率，由 I = nAve 给出，其中 n 是载流子数密度，A 是横截面积，v 是漂移速度，e 是基本电荷。对于给定的电流，较粗的导线因横截面积较大，漂移速度反而较小。将电流与单个电子的速度混淆，会导致对电阻和电力传输的误解。
6. Energy is ‘Used Up’ and Disappears | 能量被“用掉”并消失了
Everyday language says we ‘use energy’, which can create the impression that energy is destroyed. The first law of thermodynamics clearly states that energy cannot be created or destroyed, only converted from one form to another. In a mechanical system, work done against friction converts kinetic energy into thermal energy, warming the surfaces. In a light bulb, electrical energy is transformed into light and heat. The total energy of an isolated system remains constant. The concept of efficiency does not mean energy is destroyed; it simply indicates how much of the input energy is converted into useful output. A refrigerator does not ‘make cold’ by destroying heat – it pumps thermal energy from inside to outside, transferring energy rather than annihilating it.
7. Gases Must Heat Up When Compressed Quickly Because Friction | 气体被快速压缩时因摩擦而生热
In adiabatic compression, the temperature of a gas rises, but not primarily due to friction between molecules. When a gas is compressed rapidly without time for heat exchange with the surroundings, work is done on the gas. This work increases the internal energy, and since no heat leaves, the average kinetic energy of the particles increases, raising the temperature. This is described by the first law: ΔU = Q + W. If Q = 0 (adiabatic), then W done on the gas (positive) directly increases U. The temperature can also be understood in terms of the ideal gas law pV ∝ T: if volume decreases and pressure rises, temperature must rise. Molecular collisions are elastic, so friction is not the mechanism. Confusing adiabatic heating with frictional heating is a common oversimplification.
在绝热压缩过程中，气体的温度会升高，但这并非主要因为分子间的摩擦。当气体被快速压缩而来不及与周围环境进行热交换时，外界对气体做功。这些功增加了气体内能，由于没有热量散失，粒子的平均动能增大，温度因此升高。这可以用热力学第一定律描述：ΔU = Q + W。若 Q = 0（绝热），则对气体做的正功 W 直接增大内能 U。温度也可以从理想气体定律 pV ∝ T 来理解：如果体积减小且压强上升，温度必然升高。分子间的碰撞是弹性的，因此摩擦并非温度升高的机制。将绝热升温与摩擦生热混为一谈是一种常见的过分简化。
8. A Capacitor Stores Charge Like a Bucket | 电容器像水桶一样储存电荷
A common analogy treats a capacitor as a ‘charge bucket’ that fills up with electrons. In truth, a capacitor stores energy in the electric field between its plates, not net charge. When a capacitor is connected to a voltage source, charge is removed from one plate and an equal amount of charge is deposited on the other, so the net charge on the capacitor remains zero. The energy is stored by the separation of positive and negative charges. The misconception leads to errors such as expecting current to flow ‘through’ a capacitor in a DC circuit indefinitely. In reality, current stops when the potential difference across the capacitor equals the supply voltage, and the circuit reaches a steady state. Recognising the capacitor as an energy storage device, rather than a charge storage device, clarifies its behaviour in charging, discharging, and time-constant calculations.
9. The Photoelectric Effect Requires Intensity to Exceed a Threshold | 光电效应要求光强超过某个阈值
In the early 20th century, the classical wave model predicted that any frequency of light, if intense enough, would eventually eject electrons from a metal surface. This is false. The photoelectric effect demonstrates that electron emission occurs only if the photon energy (hf) exceeds the work function (Φ) of the metal, regardless of intensity. Intensity determines the number of photons per second, and hence the photocurrent, provided the frequency is above the threshold. A very bright red light will not cause emission from a metal with a high work function, yet a dim ultraviolet light will. This was one of the key phenomena that led to the acceptance of photon theory. Students often confuse the energy of individual photons with the total energy delivered, leading to incorrect predictions about emission.
In two-source interference, there are regions of destructive interference where the resultant amplitude is zero. A common misconception is that energy has been destroyed in these regions. According to the principle of conservation of energy, the energy is simply redistributed. The energy that ‘disappears’ from the dark fringes appears in the bright fringes, where the amplitude is double that of a single wave, giving four times the intensity. The overall energy delivered to the screen remains equal to the sum of the energies from the two sources. Similarly, in standing waves, nodes have zero displacement, but energy flows back and forth between kinetic and potential forms within the medium. The idea that interference ‘cancels’ energy overlooks the global energy balance.
11. Strong Nuclear Force Is Always Attractive Between Nucleons | 强核力在核子之间总是吸引力
The strong nuclear force is essential for binding protons and neutrons in the nucleus, overcoming the electrostatic repulsion between protons. A common simplification is that it is purely attractive at all separations. However, the strong force is actually repulsive at very short ranges (below about 0.5 fm). This repulsive core prevents nucleons from collapsing into each other and gives the nucleus its finite size. The force is strongly attractive at around 1 fm, the typical nucleon separation, then falls rapidly to zero beyond a few femtometres. Treating the strong force as always attractive fails to explain nuclear density and saturation. AQA questions often probe the graph of force versus separation, expecting an understanding that the net strong force can be repulsive at extremely small distances.
强核力对于将质子和中子束缚在原子核内、克服质子间的静电排斥至关重要。一种常见的简化是它在所有距离上都表现为吸引力。然而，强核力在极短距离内（约 0.5 fm 以下）实际上是排斥力。这个排斥芯阻止核子相互坍缩，并使原子核具有有限大小。该力在大约 1 fm 处——典型的核子间距——表现为强吸引力，然后在几飞米之外迅速降为零。将强核力视为始终为吸引力，便无法解释核密度和核饱和性。AQA 考题常会涉及力与距离的关系图，期望学生理解：在极近距离下，净强核力可以是排斥力。
12. For an Ideal Transformer, 100% Efficiency Means No Losses Anywhere | 理想变压器 100% 的效率意味着完全没有损耗
The statement that an ideal transformer has 100% efficiency is often interpreted as no energy being lost at all. In the ideal model, we assume no resistive heating in the windings (zero resistance), no magnetic flux leakage, and no hysteresis or eddy current losses in the core. Under these assumptions, the power input to the primary coil equals the power output from the secondary coil: Vₚ Iₚ = Vₛ Iₛ. However, even in an ideal transformer, which is merely a theoretical construct, the core experiences energy transfer in the form of alternating magnetisation and demagnetisation, but no net energy is dissipated as heat. In a real transformer, losses do occur, but the ideal case is a useful approximation. Students sometimes confuse the idealised equations with the behaviour of real devices and fail to account for the reasons why step-up transformers increase voltage at the expense of current, keeping power constant only when losses are negligible.
A capacitor is a device that stores electric charge and energy in an electric field, and it lies at the heart of everything from smoothing circuits to camera flashes. In both IB Physics and AQA A‑level Physics, capacitance appears as a conceptually rich topic that blends electric fields, circuit theory and exponential change. This article distills the key concepts, equations and common pitfalls you must master to excel in exam questions, whether you are sitting Paper 1 multiple‑choice or tackling longer structured problems.
Capacitance (C) is defined as the ratio of the charge (Q) stored on each plate of a capacitor to the potential difference (V) across its plates: C = Q/V. A capacitor of 1 farad stores 1 coulomb of charge when the potential difference across it is 1 volt. In practice, the charge Q always refers to the magnitude of charge on one plate, not the net charge of the whole device.
A farad (F) is an impractically large unit for everyday electronics. Most capacitors you encounter have values in microfarads (µF = 10⁻⁶ F), nanofarads (nF = 10⁻⁹ F) or picofarads (pF = 10⁻¹² F). Exam questions frequently require you to convert prefixes correctly before substituting into formulas, so always check the multiplier.
For an ideal parallel‑plate capacitor, the capacitance is given by: C = εA/d, where ε = ε₀εᵣ is the permittivity of the material between the plates, A is the overlapping plate area, and d is the separation. This relation shows that C increases with larger plate area and a smaller gap, and it explains why capacitors inevitably discharge when the insulation breaks down.
Here ε₀ ≈ 8.85 × 10⁻¹² F m⁻¹ is the permittivity of free space, an important constant supplied in IB and AQA data booklets.
此处 ε₀ ≈ 8.85 × 10⁻¹² F m⁻¹ 是真空电容率，这是一个IB和AQA数据手册中提供的重要常数。
4. Dielectric Materials | 电介质材料
A dielectric is an insulating material inserted between the plates to increase capacitance without altering the plate geometry. The dielectric constant (relative permittivity εᵣ) multiplies the capacitance by a factor εᵣ compared with vacuum. Polar molecules in the dielectric reduce the net electric field between the plates, allowing more charge to be stored for the same applied voltage. Exam questions may ask you to explain why the capacitance rises or to calculate the new C after inserting a dielectric.
The energy (U) stored in a charged capacitor is the work done to separate the charges. Three equivalent forms are commonly used:
电容器储存的能量（U）是分离电荷所做的功。常用的三种等价形式有：
U = ½QV = ½CV² = Q²/(2C)
Remember that the energy is not directly proportional to Q or V alone – the factor of ½ appears because the average potential difference during charging is V/2. When a capacitor discharges through a resistor, this stored energy is converted to internal energy in the resistor.
注意能量并不与 Q 或 V 单独成正比——系数 ½ 的出现是因为充电过程中的平均电势差为 V/2。当电容通过电阻放电时，这部分储能转化为电阻的内能。
6. Charging a Capacitor: RC Circuit | 电容器充电：RC电路
When a capacitor is connected in series with a resistor and a constant emf source, the charge and voltage grow exponentially towards their maximum values. The charge as a function of time is given by:
当电容器与电阻和恒压源串联时，电荷与电压按指数规律向其最大值增长。电荷随时间的函数为：
q(t) = Q₀(1 − e^(−t/RC))
The potential difference across the capacitor follows a similar law: v_c(t) = ε(1 − e^(−t/RC)), where ε is the source emf. The current decreases exponentially: i(t) = (ε/R)e^(−t/RC). A common exam task is to deduce the initial current or the capacitor voltage after a given time.
When the source is removed and the capacitor discharges through a resistor, the charge, voltage and current all decay exponentially from their initial values. The discharge equations are:
The negative sign in the current indicates that the direction of flow is opposite to that during charging. Note that I₀ = V₀/R. As with charging, the product RC governs the timescale.
The time constant τ = RC is the time taken for the charge (or voltage) to fall to 1/e ≈ 37% of its initial value during a discharge, or to rise to about 63% of its final value during charging. Dimensionally, τ has units of seconds (Ω × F = s). The time constant is a measure of how fast a capacitor charges or discharges; a larger R or C gives a slower response.
时间常数 τ = RC 是放电过程中电荷（或电压）降至初始值 1/e ≈ 37% 所需的时间，或是充电过程中升至终值约 63% 所需的时间。从量纲上看，τ 的单位是秒（Ω × F = s）。时间常数是衡量电容器充放电快慢的量；R 或 C 越大，响应越慢。
9. Graphical Analysis of Charge & Discharge | 充放电的图解分析
IB and AQA papers regularly test your ability to interpret Q–t, V–t and I–t graphs. For a discharging capacitor, the graph of ln(V) against t yields a straight line with gradient −1/RC, which is a classic method for determining an unknown capacitance or resistance. You may also be asked to sketch curves showing the effect of doubling R or C on the charging time. Always label key points: initial value, 37% level, and asymptotic maximum.
IB和AQA试题经常考查你对 Q–t、V–t 和 I–t 图像的解读。对放电电容，ln(V) 对 t 作图可得斜率为 −1/RC 的直线，这是测定未知电容或电阻的经典方法。你还可能被要求勾勒出 R 或 C 加倍对充电时间的影响。务必标注关键点：初值、37% 水平和渐近最大值。
10. Capacitor Combinations: Series & Parallel | 电容器的串并联
The rules for combining capacitors are the reverse of those for resistors. When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitances: C_parallel = C₁ + C₂ + … (same voltage across each). In series, the reciprocal rule applies: 1/C_series = 1/C₁ + 1/C₂ + … (same charge stored on each). This can be a source of confusion, so double‑check the context.
Pitfall 1: Forgetting to convert µF, nF, pF to farads before calculation. Always write the conversion explicitly.
陷阱1：忘记在计算前将 µF、nF、pF 转换为法拉。一定要显式写出换算过程。
Pitfall 2: Mixing up series and parallel rules for capacitors and resistors. Use the physical principle: “same charge in series, same voltage in parallel” to remind yourself.
陷阱2：混淆电容和电阻的串并联规则。利用物理原理：“串联同电荷，并联同电压”来提醒自己。
Pitfall 3: Misreading which quantity is plotted in exponential graphs. The “63%” and “37%” rules apply to voltage and charge, not to current during charging (which starts at a maximum and decays).
Pitfall 4: Using E = ½QV incorrectly when Q is not the value when the capacitor is fully charged. Always consider the instantaneous values.
陷阱4：在电容未完全充满时错误使用 E = ½QV。始终考虑瞬时值。
12. Real‑World Applications | 实际应用
Capacitors appear in smoothing circuits where they reduce ripple in rectified DC, in timing circuits (e.g., with a 555 timer where τ determines the oscillation period), as energy stores in camera flashes, and for power‑factor correction in AC systems. Linking these uses to the underlying theory shows the examiner you can apply physics, not just quote formulas.
📚 A-Level OCR Physics: Alternating Current Revision | 交流电考点精讲
Alternating current is central to OCR A Level Physics Module 6, appearing in electromagnetic induction, power transmission and rectification. Mastering peak, rms, transformer relationships and smoothing circuits is essential for exam success.
交流电是 OCR A Level 物理模块六的核心内容，涉及电磁感应、电力输送与整流。掌握峰值、有效值、变压器关系及滤波电路对考试至关重要。
1. Characteristics of AC | 交流电的特性
Alternating current (AC) periodically reverses direction. The voltage usually follows a sinusoidal form: V = V0 sin(ωt), where V0 is the peak voltage, ω = 2πf is the angular frequency, and f is the supply frequency in hertz (Hz). UK mains electricity has f = 50 Hz.
The period T is the time for one complete oscillation. It is linked to frequency by T = 1/f. An AC waveform is fully described by its peak value, period and shape.
周期 T 是一次完整振荡所需的时间，它与频率的关系为 T = 1/f。交流波形完全由其峰值、周期和形状描述。
2. Peak, Peak-to-Peak and RMS Values | 峰值、峰峰值与有效值
The peak voltage V0 is the maximum displacement from zero. The peak-to-peak voltage Vpp is twice the peak value: Vpp = 2V0. On an oscilloscope trace, Vpp is the vertical height from the positive to the negative peak.
The root mean square (rms) value of a sinusoidal AC is the equivalent DC value that delivers the same heating power. For voltage and current:
Vrms = V0 / √2 and Irms = I0 / √2
The mains 230 V rating in the UK is an rms value, so its peak is approximately 325 V.
正弦交流电的均方根（rms）值是能产生相同热效应的等效直流值。电压和电流满足：
Vrms = V0 / √2  ； Irms = I0 / √2
英国市电标称的 230 V 是 rms 值，因此峰值约为 325 V。
3. Using an Oscilloscope | 使用示波器
An oscilloscope displays voltage on the vertical axis and time on the horizontal axis. From the screen you can read the peak voltage (multiplied by the Y-gain setting) and the time period (multiplied by the time-base setting). For example, if the time-base is 5 ms/div and one complete cycle spans 4 divisions, T = 20 ms and f = 1/0.020 = 50 Hz.
示波器的垂直轴表示电压，水平轴表示时间。从屏幕上可以读出峰值电压（乘以 Y 增益设定）和周期（乘以扫描时基设定）。例如，若时基为 5 ms/div，一个完整周期占据 4 格，则 T = 20 ms，f = 1/0.020 = 50 Hz。
Many exam questions ask you to determine the rms value from an oscilloscope picture: read Vpp, calculate V0 = Vpp/2, then apply Vrms = V0/√2.
For a purely resistive load, the average AC power is calculated using rms values. The instantaneous power is p(t) = v(t)i(t), but the useful quantity is average power: Pavg = IrmsVrms. This can also be written as Pavg = Vrms2 / R = Irms2 R.
This relationship explains why appliances rated at 230 V, 2.0 A dissipate approximately 460 W in a resistive heater. The same rms current in a DC circuit would deliver identical heating, demonstrating the equivalence of rms quantities.
A simple AC generator consists of a coil rotating in a uniform magnetic field. According to Faraday’s law, the induced emf is ε = BANω sin(ωt), where B is the magnetic flux density, A is the coil area, N is the number of turns, and ω is the angular speed. The peak emf is ε0 = BANω.
Slip rings and carbon brushes connect the rotating coil to the external circuit, maintaining the sinusoidal output. Increasing the rotation speed or the magnetic field strength raises both the peak emf and the frequency.
滑环和碳刷将旋转线圈与外部电路相连，保证了正弦输出。提高转速或增强磁场均可增大峰值电动势和频率。
6. Transformers | 变压器
An ideal transformer operates on the principle of electromagnetic induction, changing the voltage and current while conserving power. For two coils on a common iron core, the turns ratio equation is:
Vs / Vp = Ns / Np
It is assumed 100% efficiency, so primary power equals secondary power: VpIp = VsIs.
理想变压器基于电磁感应原理，可改变电压和电流并保持功率守恒。对于共用铁芯的两个线圈，匝数比方程为：
Vs / Vp = Ns / Np
假设效率为 100%，则初级功率等于次级功率：VpIp = VsIs。
A step-up transformer has Ns > Np, increasing voltage and reducing current. A step-down transformer does the reverse. Real transformers experience energy losses due to eddy currents, hysteresis in the core, and resistance in the windings.
Electricity is transmitted over long distances at very high voltages (e.g. 400 kV) to minimise energy lost as heat in the cables. The power dissipated in a cable of resistance R is Ploss = I2R. By stepping up the voltage at the power station and stepping it down near consumers, the current in the transmission lines is greatly reduced, dramatically lowering Ploss.
电能通过高压（如 400 kV）远距离输送，以降低电缆热损耗。电阻为 R 的电缆耗散功率为 Ploss = I2R。在发电站升压、在用户附近降压，可大幅降低输电线中的电流，从而显著减少 Ploss。
For a given transmission power P = IV, doubling the voltage halves the current, and the I²R loss becomes one quarter. This is the fundamental reason for using AC grids with transformers.
对于给定的输送功率 P = IV，电压加倍则电流减半，I²R 损耗降为四分之一。这是交流电网结合变压器使用的根本原因。
8. Half-Wave Rectification | 半波整流
Half-wave rectification uses a single diode. During the positive half-cycle the diode is forward biased and conducts; during the negative half-cycle it is reverse biased and blocks current. The output voltage across the load is a series of positive half-sine pulses, with a mean DC value of Vdc = V0 / π.
Because half-wave rectification discards the negative half-cycles, the output waveform has large gaps and a high ripple content, making it unsuitable for sensitive electronic devices without further smoothing.
Full-wave rectification is typically achieved with a bridge rectifier consisting of four diodes. In both half-cycles, two diodes conduct so that the load current always flows in the same direction. The resulting output consists of overlapping positive humps, and the mean DC value is Vdc = 2V0 / π, exactly double that of half-wave rectification.
Importantly, the ripple frequency of the unfiltered full-wave output is twice the input AC frequency (e.g. 100 Hz for 50 Hz mains). This higher ripple frequency makes smoothing more effective.
Smoothing reduces the ripple in a rectified DC output. A capacitor placed across the load charges up to the peak voltage and then slowly discharges through the load resistance, filling the gaps between pulses. The time constant τ = CR governs the discharge rate: a larger capacitance or load resistance reduces the ripple.
In a full-wave rectified supply with smoothing, the output voltage has a small triangular ripple. The approximate ripple voltage is ΔV ≈ Iload / (frippleC), where Iload is the load current and fripple is twice the mains frequency. Choosing C sufficiently large maintains a nearly constant DC output.
在全波整流加滤波的电源中，
Published by TutorHao | A-Level Physics Revision Series | aleveler.com
📚 Oxford AQA International A-Level Physics: AS Unit 2 Concepts Explained | 牛津AQA国际A-Level物理：AS单元2概念解析
Unit 2 of the Oxford AQA International AS Physics specification covers the core topics of electricity, waves, and particles. This unit bridges classical electromagnetism with the early quantum ideas that reshaped modern physics. Understanding the behaviour of charges in circuits, the propagation and interference of waves, and the dual nature of light and matter is essential for A-Level success and forms the foundation for further study in fields ranging from engineering to quantum technology. The following article systematically breaks down each key concept, pairing clear English explanations with Chinese translations to support bilingual learning.
1. Overview of AS Unit 2: Electricity, Waves and Particles | AS单元2概述：电学、波动与粒子
Oxford AQA International AS Physics Unit 2 is assessed by a written examination lasting 1 hour 30 minutes. It contributes 50% of the AS qualification. The content is divided into three main sections: electricity, waves, and particles. In the electricity section, students explore current, potential difference, resistance, and DC circuit analysis. The waves section introduces mechanical and electromagnetic waves, with a strong focus on superposition, interference, and stationary waves. The particles section introduces the photon model, the photoelectric effect, energy levels in atoms, and wave–particle duality. A practical skills component is integrated throughout, often tested through questions on experimental methods and data analysis.
2. Current, Potential Difference and Resistance | 电流、电势差与电阻
Electric current is the rate of flow of charge. In a metallic conductor, current is carried by delocalised electrons. The unit of current is the ampere (A), defined as one coulomb per second. Charge (Q), current (I), and time (t) are related by the equation Q = It. Potential difference (V) between two points is the work done per unit charge to move a charge between those points. It is measured in volts (V), where 1 V = 1 J C⁻¹. Resistance is a measure of the opposition to current flow in a component. The resistance (R) is given by R = V/I, and the unit is the ohm (Ω).
电流是电荷流动的速率。在金属导体中，电流由自由电子承载。电流的单位是安培（A），定义为每秒一库仑。电荷（Q）、电流（I）和时间（t）的关系为 Q = It。两点间的电势差（V）是单位电荷在两点间移动时所做的功，单位为伏特（V），1 V = 1 J C⁻¹。电阻是衡量元件对电流阻碍作用的物理量。电阻（R）由 R = V/I 给出，单位是欧姆（Ω）。
3. Ohm’s Law and I–V Characteristics | 欧姆定律与I–V特性曲线
For an ohmic conductor at constant temperature, the current through it is directly proportional to the potential difference across it. This is Ohm’s law, expressed as V = IR. The I–V graph for an ohmic component is a straight line through the origin. In contrast, a filament lamp does not obey Ohm’s law because its temperature increases with current. Its I–V curve is a curved line that flattens at higher voltages, showing increasing resistance. A diode allows current to flow in one direction only; its I–V characteristic shows a very low current in reverse bias and a steep rise once the threshold voltage (about 0.6 V for silicon) is exceeded in forward bias.
4. Resistivity and Temperature Dependence | 电阻率与温度依赖性
The resistance of a wire depends on its length L, cross-sectional area A, and the material’s resistivity ρ. The relationship is R = ρL/A. Resistivity is a property of the material, measured in ohm metres (Ω m). For a metal, resistivity increases with temperature because lattice vibrations scatter electrons more. For a semiconductor such as a thermistor, resistivity typically decreases as temperature rises, because more charge carriers become available. Superconductors have zero resistivity below a critical temperature. This concept is frequently examined via practical questions on measuring resistivity using a micrometer, metre rule, and ohmmeter or voltmeter–ammeter method.
导线的电阻取决于其长度 L、横截面积 A 以及材料的电阻率 ρ，关系式为 R = ρL/A。电阻率是材料的固有属性，单位为欧姆米（Ω m）。金属的电阻率随温度升高而增大，因为晶格振动增强，对电子的散射加剧。对于半导体比如热敏电阻，随温度升高电阻率通常下降，因为可用的载流子增多。超导体在临界温度以下电阻率为零。这个概念常通过测量电阻率的实验题考查，涉及千分尺、米尺与欧姆表或伏安法等。
5. Kirchhoff’s Laws and Circuit Analysis | 基尔霍夫定律与电路分析
Kirchhoff’s first law states that the total current entering a junction is equal to the total current leaving it. This is a consequence of charge conservation. Kirchhoff’s second law states that in any closed loop of a circuit, the sum of the electromotive forces (e.m.f.) is equal to the sum of the potential differences across the components. This is a result of energy conservation. These laws are used to analyse series and parallel circuits. For resistors in series, the total resistance Rₜ = R₁ + R₂ + … . For resistors in parallel, the total resistance is given by 1/Rₜ = 1/R₁ + 1/R₂ + … . Internal resistance r of a power source causes the terminal p.d. to fall below the e.m.f.: V = ε − Ir.
A wave is a transfer of energy without net transfer of matter. Mechanical waves require a medium; electromagnetic waves do not. Key parameters include amplitude (A) – the maximum displacement from equilibrium; frequency (f) – the number of complete oscillations per second, measured in hertz (Hz); wavelength (λ) – the distance between two consecutive points in phase; and period (T) – the time for one complete oscillation, where T = 1/f. Displacement–time and displacement–distance graphs are essential tools for describing wave behaviour. Transverse waves have oscillations perpendicular to the direction of energy transfer (e.g. light, water waves). In longitudinal waves, oscillations are parallel to the direction of energy transfer (e.g. sound).
7. The Wave Equation and Superposition | 波动方程与叠加原理
The wave equation relates wave speed v, frequency f, and wavelength λ: v = fλ. This applies to all waves. Wave speed depends on the medium; for electromagnetic waves in a vacuum, v = c = 3.00 × 10⁸ m s⁻¹. When two or more waves meet at a point, they superpose. The principle of superposition states that the resultant displacement is the vector sum of the individual displacements. This leads to constructive interference (amplitudes add) when waves are in phase, and destructive interference (amplitudes subtract) when they are in antiphase. Coherence – a constant phase relationship between sources – is essential for observable interference patterns.
波动方程将波速 v、频率 f 和波长 λ 联系起来：v = fλ。这适用于所有波。波速取决于介质；对于真空中的电磁波，v = c = 3.00 × 10⁸ m s⁻¹。当两列或更多波在某点相遇时，它们会叠加。叠加原理指出，合位移是各波引起位移的矢量和。这导致了当波同相时出现相长干涉（振幅相加），反相时出现相消干涉（振幅相减）。相干性——波源之间保持恒定的相位差——是产生可观测干涉图样的必要条件。
8. Interference, Diffraction and Standing Waves | 干涉、衍射和驻波
Young’s double-slit experiment demonstrates interference of light. Bright fringes correspond to path difference nλ (constructive), and dark fringes to (n + ½)λ (destructive). Fringe spacing w is given by w = λD/s, where s is slit separation and D is the distance to the screen. Diffraction is the spreading of waves around obstacles or through apertures; it is most noticeable when the aperture size is comparable to the wavelength. A diffraction grating produces sharper, more widely spaced maxima, used to measure wavelength precisely. Standing (stationary) waves form when two identical progressive waves travel in opposite directions. Nodes (zero displacement) and antinodes (maximum displacement) are formed at fixed positions. This is exploited in musical instruments and microwave ovens.
杨氏双缝实验演示了光的干涉。亮条纹对应光程差为 nλ（相长），暗条纹对应 (n + ½)λ（相消）。条纹间距 w 由 w = λD/s 给出，其中 s 是缝距，D 是到屏幕的距离。衍射是波绕过障碍物或穿过小孔扩散的现象；当孔尺寸与波长相近时最为显著。衍射光栅能产生更尖锐、间距更大的明纹，用于精确测量波长。当两列相同的行波相向传播时会形成驻波。节点（位移为零）和腹点（位移最大）在固定位置形成。这被用于乐器和微波炉中。
9. Photons and the Photoelectric Effect | 光子与光电效应
The photoelectric effect is the emission of electrons from a metal surface when electromagnetic radiation of sufficiently high frequency shines on it. Classical wave theory could not explain the threshold frequency or the instantaneous emission. Einstein proposed that light consists of photons, each with energy E = hf, where h is Planck’s constant. Electrons are emitted if the photon energy exceeds the work function φ of the metal. The kinetic energy of emitted electrons is given by Eₖ = hf − φ. This equation shows that intensity affects the number of photoelectrons, not their kinetic energy. The concept of the photon as a particle of light is central to quantum physics.
Atoms have discrete energy levels. Electrons can move between levels by absorbing or emitting photons of energy equal to the difference between the levels: ΔE = E₂ − E₁ = hf. This explains atomic line spectra. An emission spectrum consists of bright lines on a dark background, produced when excited electrons drop to lower levels. An absorption spectrum shows dark lines on a continuous background, caused by electrons absorbing specific frequencies and moving to higher levels. The hydrogen spectrum is well described by the Balmer series, which lies partly in the visible region. Fluorescent lighting and lasers operate on these principles of stimulated emission and energy level transitions.
Light exhibits both wave and particle behaviour. Interference and diffraction demonstrate wave nature, while the photoelectric effect shows particle behaviour. De Broglie proposed that matter also has wave properties, with a wavelength λ = h/p, where p is momentum. This was confirmed by electron diffraction experiments. Wave–particle duality means that whether a quantum object behaves like a wave or a particle depends on the experiment performed. Electron microscopes exploit the short de Broglie wavelength of electrons to achieve much higher resolution than optical microscopes. An understanding of duality is essential for modern physics, including quantum mechanics and semiconductor theory.
Mastering the mathematical relationships in Unit 2 is vital for problem solving. The table below summarises the most important equations. Students should be able to apply them in unfamiliar contexts, rearrange terms, and combine them with principles like conservation of energy. The practical skills involved, such as measuring current–voltage data, using oscilloscopes, and setting up ripple tanks, are equally important and are often assessed in the written paper. Regular practice with past examination questions helps consolidate these concepts and build the analytical thinking required to achieve top grades.
Writing extended responses in GCSE WJEC Physics requires more than just recalling facts — it demands structured explanations, application of knowledge, and critical thinking. This article provides a complete essay writing template, guiding you through planning, paragraph structure, scientific vocabulary, and evaluation techniques. Whether you are tackling questions on motion, circuits, or waves, this template will help you craft clear, high-mark answers under timed conditions.
Begin by carefully reading the question and identifying the command words, such as ‘describe’, ‘explain’, ‘compare’, or ‘evaluate’. Each requires a different response style. Underline key scientific terms and note the number of marks — this indicates the depth expected. For WJEC, a 6-mark question typically needs a detailed, multi-step answer with clear reasoning.
Spend 2–3 minutes jotting down a quick bullet-point plan. This prevents you from going off-topic. Arrange your points in a logical sequence: start with the basic scientific principle, then apply it to the context, and finally link to any data or examples given. Leave space to add evaluation or comparison if the question demands it.
Use the PEEL framework for each main paragraph: Point – state the scientific idea. Evidence – provide data, equations, or observations to support it. Explanation – explain the science behind the evidence. Link – connect back to the question or to the next paragraph. This structure keeps your answer focused and ensures you address mark scheme criteria.
Accurate vocabulary is essential. Use words like ‘acceleration’, ‘potential difference’, and ‘refraction’ precisely. Demonstrate your understanding by defining terms briefly in the context of your answer. For example, say “The acceleration is the rate of change of velocity” rather than just “it speeds up”. Avoid vague words like ‘thing’ or ‘stuff’.
准确的词汇必不可少。精确使用诸如 “acceleration”、”potential difference” 和 “refraction” 等词汇。在答案上下文中简要定义术语，以展示你的理解。例如，说 “The acceleration is the rate of change of velocity” 而不仅仅是 “it speeds up”。避免使用如 “thing” 或 “stuff” 这类模糊词语。
5. Incorporating Equations and Calculations | 纳入方程式和计算
When applicable, write down the relevant equation, substitute values with correct units, and show each calculation step clearly. For WJEC, you may need to rearrange equations. Use the triangle method or algebraic manipulation. Always state the final answer with appropriate significant figures and units. For example:
Even if a calculation is not the main focus, including one can strengthen your evidence.
即使计算不是重点，加入一个计算也能增强你的证据。
6. Describing Graphs and Data | 描述图表和数据
When a question provides a graph, table or diagram, refer to it explicitly. Describe the pattern: mention any proportionality (direct/inverse), linearity, plateaus, or anomalies. Use comparative phrases like ‘as X increases, Y increases linearly until…’. Extract numerical values to support your description. State what the gradient or area under the graph represents in physics terms.
当题目提供图表、表格或示意图时，要明确提及它。描述模式：提到任何比例关系（正比/反比）、线性、平台或异常值。使用比较性短语，如 “as X increases, Y increases linearly until…”。提取数值来支持你的描述。用物理语言说明梯度或曲线下面积代表什么。
7. Making Comparisons and Evaluations | 进行比较和评估
For ‘compare’ questions, set up a balanced discussion. Use sentences like “Both materials conduct electricity, but metal A has a lower resistivity than metal B.” For ‘evaluate’ tasks, you must weigh advantages and disadvantages, consider reliability of methods, and conclude with a justified opinion. Mention sources of error and limitations of the data if relevant.
对于 “compare” 类问题，建立一个平衡的讨论。使用诸如 “Both materials conduct electricity, but metal A has a lower resistivity than metal B.” 这类句子。对于 “evaluate” 类任务，你必须权衡优点和缺点，考虑方法的可靠性，并以有依据的观点作总结。如果相关，提及误差来源和数据的局限性。
8. Linking Ideas with Connectives | 使用连接词串联观点
Coherent answers flow logically. Use appropriate connectives to sequence your explanation:
连贯的答案具有逻辑流动性。使用合适的连接词来串联你的解释：
Function | 功能
Connectives | 连接词
Cause and effect | 因果关系
Therefore, as a result, this leads to | 因此，结果，这导致
Contrast | 对比
However, whereas, on the other hand | 然而，而，另一方面
Addition | 递进
Furthermore, moreover, additionally | 此外，而且，另外
Sequence | 顺序
Initially, subsequently, finally | 最初，随后，最后
Overusing simple ‘and then’ will reduce the quality of your writing. Practise varying your sentence openers.
过度使用简单的 “and then” 会降低你写作的质量。练习变换句子开头。
9. Example Essay Question and Model Answer | 示例问题与范文
Question: Explain why the terminal velocity of a skydiver changes during the fall. Include references to forces and use Newton’s laws. (6 marks)
题目：解释为什么跳伞者在下降过程中终端速度会改变。引用力并运用牛顿定律。（6 分）
Model answer: Initially, the skydiver accelerates downwards due to the force of weight (gravity) which is greater than the air resistance. According to Newton’s second law, resultant force causes acceleration (F = ma). As speed increases, air resistance increases. Eventually air resistance balances the weight, so the resultant force becomes zero. From Newton’s first law, when forces are balanced, the skydiver travels at a constant speed — this is terminal velocity. When the parachute opens, the surface area increases dramatically, so air resistance becomes much larger than weight. The resultant force is now upwards, causing deceleration. The skydiver slows down until air resistance again equals weight, reaching a new, lower terminal velocity.
Read the mark scheme clues: Look at the number of marks and answer in sufficient detail.
读懂评分标准线索： 看分值并以足够的细节作答。
Time management: Allocate about 1 minute per mark on extended writing.
时间管理： 长篇写作中每 1 分大约分配 1 分钟。
Stay within the context: Don’t write everything you know; only answer what is asked.
紧扣情境： 不要写出你知道的所有内容；只回答题目所问。
Use diagrams: If it helps, sketch a quick labelled force diagram — but always refer to it in the text.
使用示意图： 如果有帮助，快速画一个带标注的受力图——但一定要在文中提及其。
Proofread: Reserve the last minute to check for unit errors, missing connectives, or unclear statements.
检查： 预留最后一分钟检查单位错误、遗漏的连接词或不清晰的陈述。
11. Common Pitfalls to Avoid | 需要避免的常见错误
Do not merely list facts without linking them to the question. Avoid contradictions in your logic — for example, stating that air resistance decreases when speed increases. Never ignore the command word: a ‘describe’ answer should not become an ‘explain’ essay. Finally, don’t forget to use the data or context provided; it is there for a reason.
Regularly practise past WJEC extended-response questions under timed conditions. After writing, compare your answer with the mark scheme and identify what you missed — whether it is a key term, a linked equation, or an evaluation point. Keep a log of improvements. Over time, your ability to write structured, scientific essays will become second nature.
Gravitation is the universal force of attraction acting between all matter. From Newton’s law to satellite orbits, mastering gravitational concepts is essential for IB and OCR A-level Physics. In this revision guide, we break down every key point, formula and exam tip to help you excel.
万有引力是作用于所有物质之间的基本吸引力。从牛顿定律到卫星轨道，掌握引力概念对 IB 和 OCR A Level 物理至关重要。本文梳理每一个考点、公式和考试技巧，助你高效备考。
1. Newton’s Law of Universal Gravitation | 牛顿万有引力定律
Newton’s law states that every point mass attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. The magnitude is given by:
where G = 6.67 × 10⁻¹¹ N m² kg⁻² is the universal gravitational constant. The force acts along the line joining the centres of the two masses and is always attractive.
式中 G = 6.67 × 10⁻¹¹ N m² kg⁻² 为万有引力常量。力沿两质点连线方向，且始终为引力。
Note that the law applies strictly to point masses, but it can be applied to spherical objects with uniform density as if their mass were concentrated at the centre. The force on each mass is equal in magnitude and opposite in direction (Newton’s third law).
A gravitational field is a region of space where a mass experiences a force. The gravitational field strength g at a point is the gravitational force per unit mass acting on a small test mass placed at that point:
引力场是空间中任何具有质量的物体都会受到力的作用的区域。某点的引力场强度 g 定义为作用在该点单位质量测试物体上的引力：
g = F / m
For a point mass M (or a spherical body), the field strength at a distance r from its centre is:
对于点质量 M（或球体），距其中心 r 处的引力场强为：
g = G M / r²
On the Earth’s surface, g ≈ 9.81 N kg⁻¹ (m s⁻²). The direction of g is towards the centre of the mass causing the field. g is a vector quantity, and for a uniform spherical shell, the field inside the shell is zero.
在地球表面，g ≈ 9.81 N kg⁻¹（m s⁻²）。g 的方向指向引力源质量中心。g 是矢量，对于均匀球壳，球壳内部引力场强为零。
3. Gravitational Potential & Potential Energy | 引力势与引力势能
Gravitational potential V at a point is defined as the work done per unit mass to bring
Published by TutorHao | IB Physics Revision Series | aleveler.com
📚 Capacitors in IGCSE OCR Physics | IGCSE OCR 物理：电容考点精讲
A capacitor is a passive electronic component that stores electrical energy in an electric field. In the OCR IGCSE Physics syllabus, understanding capacitors, their behaviour in circuits, and the key equations C = Q / V and E = ½QV are essential for answering both calculation and explanation questions. This article breaks down every major concept, typical exam pitfalls, and how to approach capacitor problems with confidence.
电容器是一种能够以电场形式储存电能的被动电子元件。在 OCR IGCSE 物理大纲中，掌握电容器的原理、在电路中的行为、以及核心公式 C = Q / V 和 E = ½QV，是解答计算题和说理题的关键。本文逐一拆解重要概念、常见失分点和应对电容器题目的思路，帮助你从容备考。
1. What Is a Capacitor? | 什么是电容器？
A capacitor consists of two conducting plates separated by an insulating material called a dielectric. When connected to a voltage source, opposite charges accumulate on the two plates, creating an electric field that stores energy.
The ability to store charge is called capacitance. In the IGCSE context, the capacitor is usually depicted as two parallel metal plates, and you need to understand that current does not flow through the dielectric — the capacitor stores charge, it does not let steady current pass.
Capacitance (C) is defined as the charge stored per unit potential difference across the capacitor. The defining equation is:
电容（C）定义为电容器两端每单位电势差所储存的电荷量。定义公式为：
C = Q / V
where C is capacitance in farads (F), Q is the magnitude of charge on one plate in coulombs (C), and V is the potential difference in volts (V).
其中 C 是电容，单位法拉（F）；Q 是一块极板上所带电荷的绝对值，单位库仑（C）；V 是电势差，单位伏特（V）。
1 farad is a very large unit. In most IGCSE circuits, capacitors are measured in microfarads (µF), nanofarads (nF) or picofarads (pF). You must be comfortable with unit conversions: 1 µF = 10⁻⁶ F, 1 nF = 10⁻⁹ F, 1 pF = 10⁻¹² F.
For a given capacitor, the charge stored (Q) is directly proportional to the potential difference (V) across it. This linear relationship means that a graph of Q against V is a straight line through the origin, and the gradient equals the capacitance C.
对同一个电容器而言，储存的电荷量 Q 与两端的电势差 V 成正比。这种线性关系意味着 Q–V 图是一条过原点的直线，斜率等于电容 C。
If a question provides a Q–V graph, you can determine C from the gradient. Similarly, given any two quantities, you can calculate the third using C = Q / V. Remember that the charge Q always refers to the magnitude of the charge on one plate — the other plate carries an equal but opposite charge.
如果题目给出 Q–V 图像，你可以通过斜率求出 C。同样，已知任意两个物理量，就能用 C = Q / V 计算第三个量。要记住，式中的 Q 始终指一块极板所带的电荷量——另一块极板带等量异号电荷。
4. Charging a Capacitor | 电容器的充电过程
When an uncharged capacitor is connected to a d.c. supply through a resistor, charge gradually builds up on the plates. The charging current is initially large but decreases with time because the growing potential difference across the capacitor opposes the supply voltage.
Charge (Q) or voltage (V) across the capacitor rises exponentially to a maximum value.
Charging current (I) starts high and falls exponentially to zero.
充电过程中需要识别的主要图像有：
电容器两端的电荷量 Q 或电压 V 按指数规律上升，趋近最大值。
充电电流 I 起始很大，随后按指数规律衰减至零。
Although the IGCSE course does not require you to use the exponential equations, you must be able to sketch and interpret these curves, and explain why the current decreases as the capacitor charges.
When a charged capacitor is disconnected from the supply and connected across a resistor, it discharges. Electrons flow from the negative plate to the positive plate through the external circuit, neutralising the charge.
当已充电的电容器脱离电源并接到电阻两端时，它开始放电。电子通过外电路从负极板流向正极板，中和电荷。
During discharge:
The potential difference (V) across the capacitor and the charge (Q) both fall exponentially to zero.
The discharge current is initially large but decays to zero as the voltage driving it decreases.
放电过程中：
电容器两端的电势差 V 和电荷量 Q 都按指数规律下降到零。
放电电流起初很大，但随着驱动电压降低，逐渐衰减至零。
The time taken for the voltage to halve is constant for a given RC combination (the time constant), though time constant calculations are not usually examined; you only need qualitative understanding.
A charged capacitor stores electrical potential energy. This energy can be released quickly — for example, in a camera flash or a defibrillator. The energy stored (E) is given by:
已充电的电容器储存了电势能。这种能量可以快速释放——例如相机闪光灯或除颤器。储存的能量 E 由以下公式计算：
E = ½ Q V
Using C = Q / V, this can also be written as:
E = ½ C V² or E = Q² / (2C)
The factor ½ arises because the average potential difference during charging is half the final voltage. Make sure you can use these forms flexibly, especially when only two quantities are given.
公式中的 ½ 因子来源于充电过程中平均电势差是最终电压的一半。确保你能够灵活运用这些等效形式，尤其在只给出两个物理量时。
In an exam, if you are asked to calculate the energy stored, always check the units: V in volts, Q in coulombs, C in farads, and energy in joules (J).
Dielectric material: A material with a higher permittivity increases the capacitance.
对于平行板电容器，电容大小取决于三个物理因素：
极板面积 A：面积越大，电容越大。
极板间距 d：间距越小，电容越大。
电介质材料：介电常数越大的材料，电容越大。
While the formula C = εA / d is not always required by OCR IGCSE, understanding these qualitative dependencies helps in explaining the construction of variable capacitors and practical applications.
虽然公式 C = εA / d 在 OCR IGCSE 中不一定要求，但理解这些定性关系有助于解释可变电容器的构造和实际应用。
8. Capacitors in Series and Parallel (Extended) | 电容器的串联与并联（拓展）
Although the IGCSE core syllabus may limit calculations to single capacitors, knowing the patterns for combined capacitors is useful:
In parallel: The total capacitance is the sum of individual capacitances: Ctotal = C₁ + C₂ + …
In series: The total capacitance is given by 1 / Ctotal = 1/C₁ + 1/C₂ + …
尽管 IGCSE 核心大纲的计算题可能仅限于单个电容器，但了解电容器组合的规律很有用：
并联：总电容等于各个电容之和：C总 = C₁ + C₂ + …
串联：总电容满足 1 / C总 = 1/C₁ + 1/C₂ + …
These rules are the opposite of those for resistors. In series, the total capacitance is smaller than any individual capacitor, whereas in parallel, it is larger. Some extension questions may probe this, so it is worth remembering.
Capacitors appear in many real-world contexts mentioned in IGCSE Physics:
Camera flash units: A capacitor charges slowly from a battery, then discharges rapidly through a flash tube to produce a bright burst of light.
Smoothing circuits: In rectifier circuits, a capacitor smooths out voltage fluctuations by charging when the input rises and discharging when it falls.
Timing circuits: The time taken for a capacitor to charge or discharge through a resistor can be used to create time delays (e.g., in electronic timers).
Defibrillators: Capacitors store energy that is delivered in a controlled shock to restore a normal heartbeat.
IGCSE 物理中提到的电容器实际应用有：
相机闪光灯：电容器从电池缓慢充电，然后通过闪光管快速放电，产生强烈闪光。
滤波电路：在整流电路中，电容器在输入电压升高时充电、降低时放电，从而平滑电压波动。
定时电路：电容器通过电阻充放电所需的时间可用于实现延时（如电子定时器）。
除颤器：电容器储存能量，并以控制电击的形式释放，以恢复正常心跳。
For each application, you should be able to link the behaviour back to the charge/discharge curves and the energy equation E = ½CV².
对于每一个应用，你应该能够把原理和充放电曲线以及能量公式 E = ½CV² 联系起来。
10. Common Misconceptions and Exam Tips | 常见误区与应试技巧
Misconception 1: Thinking that a capacitor stores charge permanently. In reality, a capacitor stores energy, and the net charge on the whole capacitor is zero — it separates charge.
Misconception 2: Confusing C = Q/V with Ohm’s law. Capacitance is not resistance; the relation is linear but does not imply energy dissipation.
误区 2：混淆 C = Q/V 与欧姆定律。电容不是电阻；这一关系是线性的，但并不涉及能量耗散。
Exam tips:
Always write down the formula you use, show substitution, and give the unit.
When asked to sketch a charging curve, label the axes (Voltage/Time or Current/Time) and show the characteristic exponential shape levelling off at maximum.
In energy calculations, check whether you are given V, Q, or C to decide which form of the energy equation is quickest. If you have Q and V, use E = ½QV directly.
In explanation questions, use the terms ‘build-up of charge’, ‘potential difference opposes supply’, and ‘rate of charge flow decreases’ to gain full marks.
12. Linking Capacitors to the Wider Circuit Context | 电容器与整体电路的关联
In the OCR IGCSE exam, a capacitor question often appears as part of a circuit analysis problem, perhaps alongside resistors, LDRs, or diodes. You might be asked to explain how a capacitor in parallel with a component affects the voltage across it over time, or to interpret a circuit in a camera flash.
Practise sketching the charge and discharge graphs for both V and I, and be ready to describe the energy transfers: during charging, electrical energy from the battery is transferred to energy stored in the electric field of the capacitor; during discharging, this stored energy is transferred to the resistor, where it is dissipated as thermal energy.
要多练习画出 V 和 I 的充放电图像，并准备好描述能量转移过程：充电时，电池的电能转换为电容器电场中储存的能量；放电时，这些储存的能量转移到电阻上，并以热能形式耗散。
Understanding these fundamental ideas will not only help you with capacitor-specific questions but will also strengthen your overall circuit analysis skills for the IGCSE Physics exam.
Circuit analysis is a cornerstone of Edexcel Physics, demanding a firm grasp of fundamental laws and the ability to apply them to both simple and complex networks. This article breaks down essential concepts—from Ohm’s law and Kirchhoff’s rules to potential dividers and internal resistance—into clear, exam-focused revision notes. Master these principles to confidently tackle multiple-choice questions, structured problems, and practical-based exam items.
1. Charge, Current and Potential Difference | 电荷、电流与电势差
Electric current is the rate of flow of charge. For a conductor, current I = ΔQ / Δt, where ΔQ is the charge passing a point in time Δt. The unit of current is the ampere (A), equivalent to coulomb per second.
Potential difference (p.d.) between two points is the energy transferred per unit charge. One volt is one joule per coulomb. The p.d. across a component drives the current through it; without a p.d., there is no net flow of charge in a circuit.
Resistance R is defined as R = V / I, where V is the p.d. across a component and I is the current through it. The unit of resistance is the ohm (Ω). A component obeys Ohm’s law if the ratio V/I remains constant at constant temperature; such a component is an ohmic conductor, like a metal wire under steady conditions.
电阻 R 定义为 R = V / I，其中 V 是元件两端的电压，I 是通过它的电流。电阻的单位是欧姆 (Ω)。如果温度恒定时 V/I 比值保持不变，则该元件遵循欧姆定律；这种元件称为欧姆导体，例如恒温下的金属导线。
Resistance depends on the material’s resistivity ρ, length L and cross-sectional area A: R = ρL/A. Resistivity is a property of the material and increases with temperature for most metals. In an I–V graph, an ohmic conductor shows a straight line through the origin, while a filament lamp curves as temperature rises, and a diode allows current in one direction only.
电阻取决于材料的电阻率 ρ、长度 L 和横截面积 A：R = ρL/A。电阻率是材料的固有性质，对大多数金属而言随温度升高而增大。在 I–V 图中，欧姆导体显示过原点的直线，而灯丝灯泡随温度升高曲线弯曲，二极管仅允许单向电流。
3. I–V Characteristics | 电流-电压特性曲线
The current–voltage characteristic of a component is a crucial identification tool. For a fixed resistor, the I–V graph is a straight line through the origin, indicating constant resistance. For a filament lamp, the graph is a curve that flattens at higher voltages because increased temperature raises resistance. A diode shows negligible current for reverse bias and a sharp rise in forward bias once the threshold voltage (≈0.6 V for silicon) is exceeded.
Thermistors and LDRs are resistive components whose resistance changes with temperature and light intensity respectively. A negative temperature coefficient (NTC) thermistor’s resistance decreases as temperature rises; an LDR’s resistance drops when light intensity increases. Their characteristic curves are non-linear and essential for sensor circuits.
Resistivity ρ is an intrinsic property quantifying how strongly a material opposes current. Conductivity σ is the reciprocal of resistivity: σ = 1/ρ. The resistance formula R = ρL/A shows that longer conductors have higher resistance, and thicker conductors (larger A) have lower resistance. Typical metals have low resistivity, semiconductors are intermediate, and insulators have extremely high resistivity.
In Edexcel exam questions, you may need to calculate the resistivity from a graph of resistance against length, or combine resistivity with the temperature coefficient of resistance. Pay attention to units: resistivity is quoted in Ω m.
在 Edexcel 考题中，你可能需要从电阻-长度图计算电阻率，或结合电阻温度系数进行运算。注意单位：电阻率用 Ω m 表示。
5. Series and Parallel Circuits | 串联与并联电路
In a series circuit, components are connected end-to-end. The current is the same at all points: I_total = I₁ = I₂ = … The total p.d. is shared: V_total = V₁ + V₂ + … The total resistance is the sum: R_total = R₁ + R₂ + …
In a parallel circuit, components are connected across the same two points. The p.d. across each branch is identical: V_total = V₁ = V₂ = … The total current is the sum of branch currents: I_total = I₁ + I₂ + … The combined resistance is found from 1/R_total = 1/R₁ + 1/R₂ + … For two resistors in parallel, the product-over-sum formula R_total = (R₁R₂)/(R₁ + R₂) is a convenient shortcut.
Mixed circuits combine series and parallel sections. To solve them, simplify step by step: first reduce parallel groups to equivalent series resistors, then sum those series contributions.
Kirchhoff’s current law (KCL) states that the total current entering a junction equals the total current leaving it. This is a consequence of charge conservation. In equation form: Σ I_in = Σ I_out.
Kirchhoff’s voltage law (KVL) states that the sum of electromotive forces (emfs) around any closed loop equals the sum of potential differences (products of IR) around that loop. This reflects energy conservation: Σ ε = Σ IR. When applying KVL, follow a consistent loop direction and assign signs carefully.
These laws are indispensable for analysing circuits with multiple batteries or complex resistor networks. Practice setting up simultaneous equations to solve for unknown currents in two or three loops.
A potential divider produces a fraction of the input voltage. For two resistors R₁ and R₂ in series across a supply voltage V_in, the output voltage across R₂ is V_out = V_in × [R₂/(R₁ + R₂)]. This is derived from the equal current through both resistors.
Potential dividers are not limited to fixed resistors. Replacing one resistor with a thermistor, LDR, or variable resistor creates a sensing circuit. For example, an LDR in the R₁ position with a fixed R₂ yields a voltage that rises when light decreases—ideal for automatic lighting circuits.
A potentiometer uses a sliding contact on a single resistive track, acting as an adjustable potential divider. It can provide any output between zero and the supply voltage.
8. Electromotive Force and Internal Resistance | 电动势与内阻
The electromotive force (emf) ε of a source is the energy transferred per unit charge when no current flows. It is measured in volts. A real power source has internal resistance r, which causes the terminal p.d. V to drop when a current I is drawn: V = ε − Ir. The “lost volts” inside the source equal Ir.
电源的电动势 (emf) ε 是无电流流动时每单位电荷转移的能量，单位为伏特。实际电源具有内阻 r，当有电流 I 流过时，端电压 V 会降低：V = ε − Ir。内电路消耗的电压称为 “失落电压”，等于 Ir。
To determine emf and internal resistance experimentally, a variable resistor is used to alter circuit current. A graph of terminal p.d. V against current I yields a straight line with gradient −r and y-intercept ε. A parallel experiment uses a graph of R versus 1/I, but the standard V–I method is most common in Edexcel practicals.
通过实验测定电动势和内阻时，使用可变电阻改变电路电流。画出端电压 V 对电流 I 的图像，得到一条斜率为 −r、y 截距为 ε 的直线。也可采用 R 对 1/I 的图像，但 Edexcel 实验中最常用的是标准 V–I 法。
9. Electrical Energy and Power | 电能与电功率
Electrical power P is the rate at which energy is transferred. For any component, P = IV. Using V = IR, this can be expressed as P = I²R = V²/R for resistive components. The unit is the watt (W), where 1 W = 1 J s⁻¹.
电功率 P 是能量转移的速率。对任何元件，P = IV。利用 V = IR，对于电阻元件可表示为 P = I²R = V²/R。单位为瓦特 (W)，1 W = 1 J s⁻¹。
Energy E transferred in time t is E = Pt = IVt = I²Rt = V²t/R. This energy is dissipated as heat in resistive components. In exam problems, be careful to distinguish between total power supplied by a source (εI) and power delivered to the external circuit (VI). The difference, I²r, is wasted internally.
时间 t 内转移的能量 E 为 E = Pt = IVt = I²Rt = V²t/R。电阻元件将这部分能量耗散为热量。解题时注意区分电源提供的总功率 (εI) 与输出到外电路的功率 (VI)。差值 I²r 消耗在内阻上。
Efficiency of a power source is the ratio of useful power output to total power input: efficiency = (VI)/(εI) = V/ε. Maximising efficiency requires minimising internal resistance.
10. Combining Circuit Rules in Problem Solving | 综合运用电路规则解题
Edexcel exam questions often integrate multiple concepts. A common scenario: a cell with internal resistance r connected to two parallel resistors. Steps: (1) Find the equivalent external resistance R_ext from the parallel combination. (2) Determine total circuit current using I = ε / (R_ext + r). (3) Use KVL and current division to find branch currents and voltages.
Edexcel 考题常综合多个概念。常见情景：内阻为 r 的电池连接两个并联电阻。解题步骤：(1) 先求并联组合的等效外电阻 R_ext。(2) 用 I = ε / (R_ext + r) 求出总电流。(3) 利用 KVL 和分流原理求出各支路电流和电压。
Always label your circuit diagram with currents and voltages, indicating assumed directions. Apply KVL consistently: if your assumed direction gives a negative current, it simply means the real direction is opposite. Neat working and clear algebraic manipulation often earn method marks even if a numerical slip occurs.
For multiple-choice questions, use quick checks: units, expected behaviour (e.g., adding a parallel resistor always reduces total resistance), and symmetrical simplifications to save time.
对于选择题，采用快速检查：单位、预期行为（例如并联电阻总是减小总电阻）以及对称性化简来节省时间。
Published by TutorHao | Physics Revision Series | aleveler.com
📚 AS Physics: Measurements and Errors – Deriving Uncertainty Formulas | AS物理：测量与误差 – 不确定度公式推导
In AS Physics, the topic of Measurements and Their Errors is fundamental because no experimental result is meaningful without a quantified uncertainty. This article focuses on the step-by-step derivations of the key uncertainty propagation formulas that are required for OxfordAQA International AS Physics. We will build up from basic definitions to combination rules for sums, differences, products, quotients, and powers, and finally discuss a worked example using a pendulum to determine g.
1. Absolute, Relative, and Percentage Uncertainties | 绝对不确定度、相对不确定度与百分比不确定度
Any measured quantity x is reported as x ± Δx, where Δx is the absolute uncertainty representing the range within which the true value is expected to lie. The absolute uncertainty has the same units as the quantity itself.
任何测量量x都表示为 x ± Δx，其中 Δx 是绝对不确定度，表示真值预期所在的范围。绝对不确定度与测量量具有相同的单位。
The fractional uncertainty (or relative uncertainty) is the ratio Δx/x, a dimensionless number. The percentage uncertainty is simply the fractional uncertainty multiplied by 100%. These relative forms are essential when combining uncertainties through multiplication or division.
2. Uncertainty in Direct Measurements | 直接测量中的不确定度
For a single reading taken from a digital instrument, the absolute uncertainty is taken as the smallest division of the display. For an analogue scale, it is half of the smallest scale division. When repeated readings are taken, the absolute uncertainty can be estimated by half the range (the spread) of the values, or by using the standard deviation where appropriate.
If a length L is measured five times giving readings of 1.23 m, 1.25 m, 1.24 m, 1.23 m, 1.25 m, the range is 0.02 m, so ΔL ≈ 0.01 m. The result is expressed as L = 1.24 ± 0.01 m.
3. Derivation for Sums and Differences | 和与差的误差公式推导
Consider two measured quantities A = a ± Δa and B = b ± Δb. Let Z = A + B. The maximum possible value of Z is Zmax = (a + Δa) + (b + Δb) = (a + b) + (Δa + Δb). The minimum possible value is Zmin = (a − Δa) + (b − Δb) = (a + b) − (Δa + Δb). Thus the absolute uncertainty in Z is ΔZ = Δa + Δb.
考虑两个测量量 A = a ± Δa 和 B = b ± Δb。设 Z = A + B。Z 的最大可能值为 Zmax = (a + Δa) + (b + Δb) = (a + b) + (Δa + Δb)，最小可能值为 Zmin = (a − Δa) + (b − Δb) = (a + b) − (Δa + Δb)。因此，Z 的绝对不确定度为 ΔZ = Δa + Δb。
For the difference Z = A − B, we apply the worst-case method. The maximum of Z occurs when A is as large as possible and B is as small as possible: Zmax = (a + Δa) − (b − Δb) = (a − b) + (Δa + Δb). The minimum is (a − Δa) − (b + Δb) = (a − b) − (Δa + Δb). Hence, once again ΔZ = Δa + Δb.
对于差 Z = A − B，我们采用最坏情况法。当 A 尽可能大而 B 尽可能小时，Z 取最大值：Zmax = (a + Δa) − (b − Δb) = (a − b) + (Δa + Δb)。最小值为 (a − Δa) − (b + Δb) = (a − b) − (Δa + Δb)。因此，同样 ΔZ = Δa + Δb。
Rule: For Z = A ± B, ΔZ = Δa + Δb.
规则：对于 Z = A ± B，ΔZ = Δa + Δb。
This simple additive rule tells us that uncertainties always add in absolute terms for addition and subtraction, making the overall uncertainty at most the sum of individual absolute uncertainties.
Let Z = A B. Using the measured values a and b and their uncertainties, we can compute the maximum expected value of Z: Zmax = (a + Δa)(b + Δb) = ab + aΔb + bΔa + ΔaΔb.
设 Z = A B。利用测量值 a 和 b 及其不确定度，可以计算 Z 的最大预期值：Zmax = (a + Δa)(b + Δb) = ab + aΔb + bΔa + ΔaΔb。
The term ΔaΔb is a product of two small uncertainties and is much smaller than the other terms; it can be neglected. Hence the absolute uncertainty in Z is approximately ΔZ ≈ aΔb + bΔa.
Dividing by the central value Z = ab, we obtain the fractional uncertainty:
除以中心值 Z = ab，得到相对不确定度：
ΔZ/Z ≈ (aΔb + bΔa) / ab = Δb/b + Δa/a.
ΔZ/Z ≈ (aΔb + bΔa) / ab = Δb/b + Δa/a。
Thus for multiplication, the fractional uncertainties add. The same result can be obtained by considering the natural logarithm: ln Z = ln A + ln B, leading to dZ/Z = dA/A + dB/B, and converting differentials to finite uncertainties gives the same additive combination. In terms of percentage uncertainties, the percentage uncertainty in Z is the sum of the percentage uncertainties in A and B.
因此，对于乘法，相对不确定度相加。通过考虑自然对数也可得到相同结果：ln Z = ln A + ln B，导出 dZ/Z = dA/A + dB/B，并将微分转换为有限不确定度，得到相同的加和组合。就百分比不确定度而言，Z 的百分比不确定度等于 A 和 B 的百分比不确定度之和。
5. Derivation for Quotients | 商的误差公式推导
For division, Z = A/B. Again we apply the worst-case scenario. The maximum value of Z occurs with the largest numerator and smallest denominator: Zmax = (a + Δa)/(b − Δb).
对于除法，Z = A/B。再次应用最坏情况。当分子最大而分母最小时，Z 取得最大值：Zmax = (a + Δa)/(b − Δb)。
We can rewrite the fraction using series expansion or algebraic manipulation: Zmax = (a(1+Δa/a))/(b(1−Δb/b)) ≈ (a/b) (1+Δa/a)(1+Δb/b + (Δb/b)² + …). Ignoring second-order terms, we get Zmax ≈ (a/b)(1 + Δa/a + Δb/b). Similarly, Zmin ≈ (a/b)(1 − Δa/a − Δb/b).
Therefore the fractional uncertainty is ΔZ/Z ≈ Δa/a + Δb/b, exactly the same as for a product. The rule for multiplication and division is unified: fractional uncertainties add when quantities are multiplied or divided.
Let Z = An, where n is a constant (may be positive, negative, or fractional). Using the binomial expansion for a small uncertainty Δa:
设 Z = An，其中 n 为常数（可以是正数、负数或分数）。利用微小不确定度 Δa 的二项式展开：
(a + Δa)ⁿ = aⁿ (1 + Δa/a)ⁿ ≈ aⁿ [1 + n (Δa/a) + …].
(a + Δa)ⁿ = aⁿ (1 + Δa/a)ⁿ ≈ aⁿ [1 + n (Δa/a) + …]。
The first-order approximation gives the change in Z: ΔZ ≈ n an−1 Δa. Dividing by Z = an, we get:
一阶近似给出 Z 的变化：ΔZ ≈ n an−1 Δa。除以 Z = an，得出：
ΔZ/Z ≈ |n| (Δa/a).
ΔZ/Z ≈ |n| (Δa/a)。
The absolute value is used because an uncertainty in A contributes a proportional change irrespective of the sign of n. For example, if n = −1 (reciprocal), the relative uncertainty is the same as that in A. For n = ½ (square root), the fractional uncertainty is half that of A.
使用绝对值是因为无论 n 的符号如何，A 的不确定度都会贡献一个成比例的变化。例如，若 n = −1（倒数），相对不确定度与 A 的相对不确定度相同。若 n = ½（平方根），相对不确定度是 A 的一半。
7. General Approach Using Partial Derivatives | 使用偏导数的一般方法
When a quantity is a function of several variables, Z = f(A, B, …), the worst-case absolute uncertainty can be derived from the total differential. Treating uncertainties as small changes:
Here, the partial derivatives are evaluated at the measured values, and the absolute values ensure all contributions add constructively (worst-case). This general formula reduces to our earlier rules:
For Z = A + B, ∂f/∂A = 1, ∂f/∂B = 1 ⇒ ΔZ = Δa + Δb.
对于 Z = A + B，∂f/∂A = 1，∂f/∂B = 1 ⇒ ΔZ = Δa + Δb。
For Z = A B, ∂f/∂A = B, ∂f/∂B = A ⇒ ΔZ = b Δa + a Δb, which divided by ab gives the fractional form.
对于 Z = A B，∂f/∂A = B，∂f/∂B = A ⇒ ΔZ = b Δa + a Δb，除以 ab 即得相对形式。
For Z = An, ∂f/∂A = n An−1 ⇒ ΔZ = n an−1 Δa ⇒ ΔZ/Z = n Δa/a (absolute value taken).
对于 Z = An，∂f/∂A = n An−1 ⇒ ΔZ = n an−1 Δa ⇒ ΔZ/Z = n Δa/a（取绝对值）。
This approach is extremely powerful and can be used for any formula, including trigonometric or logarithmic functions, although at AS level the focus is on algebraic combinations.
这种方法非常强大，可用于任何公式，包括三角函数或对数函数，尽管在AS阶段重点还是代数组合。
8. Combining Rules: Density of a Sphere | 组合规则实例：球体密度
Imagine measuring the mass m and radius r of a solid sphere to find its density ρ = m / ((4/3)πr³). The constant factor 4/3 π does not affect the fractional uncertainty. Treat ρ ∝ m r−3. Using the product and power rules:
假设测量一个实心球的质量m 和半径r 以求其密度 ρ = m / ((4/3)πr³)。常数因子 4/3 π 不影响相对不确定度。视 ρ ∝ m r−3。应用乘积和幂规则：
Δρ/ρ = Δm/m + 3 (Δr/r).
Δρ/ρ = Δm/m + 3 (Δr/r)。
Suppose m = 1.20 ± 0.01 kg and r = 0.050 ± 0.001 m. The fractional uncertainty in mass is 0.01/1.20 = 0.00833 (0.833%), and in radius it is 0.001/0.050 = 0.020 (2.0%). The fractional uncertainty in density is 0.00833 + 3 × 0.020 = 0.06833, or 6.8%. This direct addition illustrates how the cube on r amplifies the uncertainty.
📚 Key Derivations for AQA 9630 PH03 International A-Level Physics | AQA 9630 PH03 国际 A-Level 物理关键推导
The AQA 9630 PH03 unit, ‘Fields and their consequences’, demands a solid grasp of how fundamental equations arise. According to the v4.2 mark scheme, examiners reward structured derivations that clearly show the logical flow from first principles. This article revisits the core mathematical journeys behind gravitational, electric, and magnetic field formulas, capacitor behaviour, and electromagnetic induction — exactly the steps that secure full marks on ‘show that’ and long-answer questions.
1. Deriving Gravitational Field Strength g from Newton’s Law | 由牛顿定律推导引力场强度 g
Start with Newton’s law of gravitation: the force between two point masses M and m separated by distance r is F = GMm / r².
从牛顿万有引力定律出发：两个质点 M 和 m 相距 r 时，它们之间的引力为 F = GMm / r²。
The gravitational field strength at a point is defined as the force per unit mass: g = F / m.
引力场强度定义为作用在单位质量上的力：g = F / m。
Substituting the force expression gives g = (GMm / r²) / m = GM / r². This is the magnitude of the field due to a point mass M at distance r.
代入力的表达式，得到 g = (GMm / r²) / m = GM / r²。这就是一个质点 M 在距离 r 处产生的引力场大小。
In radial fields, the direction is always towards the centre of mass M. The mark scheme often expects the step of cancelling m.
在径向场中，方向始终指向质点 M 的中心。评分方案通常要求写出约去 m 的步骤。
2. Derivation of Gravitational Potential V = –GM/r | 引力势 V = –GM/r 的推导
Gravitational potential at a point is the work done per unit mass to bring a small test mass from infinity to that point.
引力势指的是将单位质量从无穷远处移到该点所做的功。
The force on the test mass m at a distance x is F = GMm / x², opposing the displacement. Work done by an external agent against the field is dW = –F dx = –(GMm / x²) dx.
在距离 x 处，测试质量 m 受到的引力为 F = GMm / x²，与位移方向相反。外力反抗引力场做的元功为 dW = –F dx = –(GMm / x²) dx。
Integrate from infinity to r: W = ∫∞ʳ (–GMm / x²) dx = [GMm / x]∞ʳ = GMm / r. The per-unit-mass potential is V = W / m = GM / r. By convention, potential at infinity is zero, and work is done by the field, so the potential is negative: V = –GM / r.
从无穷远积分到 r：W = ∫∞ʳ (–GMm / x²) dx = [GMm / x]∞ʳ = GMm / r。除以质量得到势 V = W / m = GM / r。按约定，无穷远处势为零，实际因引力做正功，势取负值：V = –GM / r。
V = –GM / r
Examiners look for the negative sign and the limits of integration in the mark scheme.
评分者会注意负号以及积分上下限。
3. Deriving Orbital Velocity v = √(GM/r) | 轨道速度 v = √(GM/r) 的推导
For a satellite in a circular orbit, the centripetal force is provided entirely by gravitational attraction.
对于做圆周运动的卫星，向心力完全由万有引力提供。
Equate the two forces: GMm / r² = mv² / r, where m is the satellite mass and r the orbital radius.
令二力相等：GMm / r² = mv² / r，其中 m 为卫星质量，r 为轨道半径。
Cancel m and one power of r to obtain v² = GM / r. Hence v = √(GM / r).
约去 m 并消去一个 r，得 v² = GM / r，因此 v = √(GM / r)。
The derivation highlights that orbital speed depends only on the central mass and radius, not on the satellite’s mass. The mark scheme rewards explicit mention of the cancellation step.
推导凸显轨道速度仅取决于中心天体的质量和轨道半径，与卫星质量无关。评分方案要求明确展示约分步骤。
4. Electric Field Strength of a Point Charge E = Q/(4πε₀r²) | 点电荷的电场强度
Coulomb’s law gives the force between two point charges: F = (1/(4πε₀)) Qq / r².
库仑定律给出两点电荷间的作用力：F = (1/(4πε₀)) Qq / r²。
Electric field strength is force per unit positive charge: E = F / q.
电场强度定义为每单位正电荷所受的力：E = F / q。
Substituting and cancelling q yields E = (1/(4πε₀)) Q / r². The direction is radially outward from a positive Q.
代入并约去 q，得到 E = (1/(4πε₀)) Q / r²。若是正电荷 Q，方向沿径向向外。
E = Q / (4πε₀ r²)
When combined with F = qE, this forms the basis for many PH03 questions on charged particle motion.
该式与 F = qE 结合，是 PH03 中带电粒子运动许多问题的基础。
5. Electric Potential due to a Point Charge V = Q/(4πε₀r) | 点电荷的电势
Analogous to gravitational potential, electric potential is the work done per unit charge to bring a test charge from infinity to a point distance r from Q.
类比引力势，电势是把单位正电荷从无穷远移到距离 Q 为 r 的点所做的功。
Force on test charge q at distance x is F = (1/(4πε₀)) Qq / x². External agent works against the field: dW = –F dx = –(1/(4πε₀)) Qq/x² dx.
测试电荷 q 在距离 x 处受力 F = (1/(4πε₀)) Qq / x²。外力反抗电场做功：dW = –F dx = –(1/(4πε₀)) Qq/x² dx。
Integrate from ∞ to r: W = ∫∞ʳ –(1/(4πε₀)) Qq/x² dx = (1/(4πε₀)) Qq / r. Dividing by q gives V = W / q = (1/(4πε₀)) Q / r.
These relationships often appear in PH03 questions linking time constants to graphical analysis of exponential decay.
上述关系常在 PH03 试题中结合指数衰减图像分析出现。
9. Faraday’s Law and Induced emf ε = –N dΦ/dt | 法拉第定律与感应电动势推导
Faraday discovered that an emf is induced when the magnetic flux Φ through a coil changes. The magnitude is proportional to the rate of change of flux.
法拉第发现当穿过线圈的磁通量 Φ 发生变化时，会感应出电动势。其大小与磁通量变化率成正比。
For a coil of N turns, flux linkage is NΦ. The induced emf is ε = – d(NΦ)/dt = –N dΦ/dt. The negative sign reflects Lenz’s law.
This empirical law can be derived from energy conservation: moving a magnet in a coil requires work against the induced magnetic forces, converting mechanical energy to electrical energy.
这条经验定律可从能量守恒导出：移动磁铁进出线圈需抵抗感应磁场力做功，机械能转化为电能。
In a uniform magnetic field, flux Φ = BA cos θ, so a change in B, A, or θ induces an emf. The mark scheme rewards stating both the law and the linking of minus sign to Lenz’s law.
在匀强磁场中，Φ = BA cos θ，因此 B、A 或 θ 的变化都会感应出电动势。评分方案要求既陈述定律，也把负号与楞次定律关联。
10. emf Induced in a Rotating Coil ε = BANω sin(ωt) | 旋转线圈中的感应电动势
Consider a rectangular coil of area A, N turns, rotating with angular speed ω in a uniform magnetic field B.
考虑面积为 A、N 匝的矩形线圈在匀强磁场 B 中以角速度 ω 旋转。
At time t, the angle between the field and the normal to the coil is θ = ωt. The flux through the coil is Φ = BA cos(ωt).
在 t 时刻，磁场方向与线圈法线夹角 θ = ωt。穿过线圈的磁通量 Φ = BA cos(ωt)。
Examiners expect the chain rule differentiation of cos(ωt) and recognition that the induced emf varies sinusoidally.
考官期望对 cos(ωt) 使用链式法则求导，并识别感应电动势呈正弦变化。
11. Force on a Moving Charge F = BQv (Derivation from F = BIl) | 运动电荷受力 F = BQv 的推导
A current-carrying conductor experiences a force F = BIl sin θ in a magnetic field. Current is due to moving charges.
载流导体在磁场中受力 F = BIl sin θ。电流源自电荷的运动。
For a conductor of length l, drift velocity v, with n charges per unit volume of charge q, current I = nAvq. Substituting into F = BIl gives F = B (nAvq) l = BQ_total v, where Q_total is the total moving charge.
对于长度为 l 的导体，漂移速度为 v，每单位体积有 n 个电荷 q，电流 I = nAvq。代入 F = BIl 得 F = B (nAvq) l = BQ_total v，其中 Q_total 为总移动电荷。
For a single charge Q moving at velocity v perpendicular to B, the magnetic force is simply F = BQv. This derivation clarifies the link between macroscopic and microscopic force.
对于以速度 v 垂直于 B 运动的单个电荷 Q，磁场力即为 F = BQv。该推导理清了宏观力与微观力间的联系。
F = BQv (with v ⟂ B)
12. Radius of Curvature for a Charged Particle in a Magnetic Field | 带电粒子在磁场中的回转半径
A charge Q moving with speed v perpendicular to a uniform B experiences a force F = BQv, which provides the centripetal force.
电荷 Q 以速度 v 垂直射入匀强磁场 B 中时，受到力 F = BQv，此力充当向心力。
Set BQv = mv² / r, where m is the mass and r the radius of the circular path.
令 BQv = mv² / r，其中 m 为质量，r 为圆周轨道半径。
Cancel one power of v and rearrange: r = mv / (BQ). This equation is fundamental for mass spectrometers and cyclotrons.
约去一个 v 并整理得：r = mv / (BQ)。此公式是质谱仪和回旋加速器的基本原理。
r = mv / (BQ)
The derivation must show the force balance and justify that the velocity stays perpendicular to B for uniform circular motion.
推导过程需展示力平衡，并说明因速度始终垂直于 B 而维持匀速圆周运动。
Published by TutorHao | Physics Revision Series | aleveler.com
Electromagnetic induction is the process of generating an electromotive force (EMF) across a conductor when it is exposed to a changing magnetic field. This phenomenon, discovered by Michael Faraday, forms the foundation of modern electrical power generation, transformers, and countless everyday devices. In the IGCSE OCR Physics syllabus, you are expected to understand the principles, apply Faraday’s law and Lenz’s law, and explain how generators and transformers work.
Electromagnetic induction occurs whenever a conductor cuts through magnetic field lines or experiences a change in magnetic flux. No physical contact is needed – the effect relies entirely on relative motion between the conductor and the magnetic field. If a straight wire is moved downwards through a horizontal magnetic field, an EMF is induced across its ends. If the wire is part of a closed circuit, a current flows.
Magnetic flux (Φ) is a measure of the total magnetic field passing through a given area. For a uniform field B perpendicular to an area A, Φ = B A. Flux linkage through a coil of N turns is NΦ. Although flux itself is not always required for IGCSE calculations, the concept helps explain why moving a magnet faster or using a stronger magnet alters the induced EMF.
磁通量 (Φ) 是穿过某一面积的总磁场的量度。对于垂直于面积 A 的匀强磁场 B，Φ = B A。通过 N 匝线圈的磁链为 NΦ。虽然 IGCSE 不一定直接计算磁通量，但这一概念有助于解释为什么加快磁铁运动速度或使用更强的磁铁会改变感应电动势。
3. Faraday’s Law of Induction | 法拉第电磁感应定律
Faraday’s law states that the magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux linkage. The equation is often written as:
法拉第定律指出，感应电动势的大小与磁链的变化率成正比。公式常写作：
ε = − N (ΔΦ / Δt)
where ε is the induced EMF, N is the number of coil turns, and ΔΦ/Δt is the rate of change of flux. The negative sign represents Lenz’s law, which we will discuss next. In an exam, if a coil of 100 turns experiences a flux change of 0.02 Wb in 0.5 s, the average induced EMF is ε = 100 × (0.02 / 0.5) = 4 V.
Lenz’s law gives the direction of the induced current: the induced current always flows in such a direction as to oppose the change in magnetic flux that produced it. This is why the negative sign appears in Faraday’s law. For example, if a north pole is pushed into a coil, the induced current creates a north pole at the end facing the magnet, repelling it and opposing the motion.
This principle is a consequence of the conservation of energy. If the induced current aided the change, energy would be created from nothing, which is impossible.
这一原理是能量守恒的必然结果。如果感应电流助长了原本的变化，能量就会无中生有，这是不可能的。
5. Factors Affecting Induced EMF | 影响感应电动势的因素
Several factors determine how large an induced EMF will be. Understanding these helps in designing generators and in predicting experimental outcomes.
有几个因素决定了感应电动势的大小。理解这些因素有助于设计发电机和预测实验结果。
Rate of flux change: Faster movement of magnet or conductor → larger ΔΦ/Δt → larger EMF.
Number of turns (N): More turns in the coil increase the flux linkage change.
Magnetic field strength (B): Stronger magnets produce larger flux changes for the same motion.
Orientation: Maximum EMF occurs when the motion is perpendicular to the field lines; zero when parallel.
磁通量变化率：磁铁或导体移动越快 → ΔΦ/Δt 越大 → 感应电动势越大。
匝数 (N)：线圈匝数越多，磁链变化量越大。
磁感应强度 (B)：相同运动下，磁铁越强，磁通量变化越大。
取向：运动方向与磁感线垂直时电动势最大；平行时为零。
6. The Simple AC Generator (Alternator) | 简单交流发电机
An AC generator converts mechanical energy into alternating current. It consists of a rectangular coil that rotates between the poles of a permanent magnet. The ends of the coil are connected to two separate slip rings, which rotate with the coil. Carbon brushes press against the slip rings to collect the current without reversing the connections.
As the coil rotates, the sides cut through the magnetic field, inducing an EMF. The direction of the induced current reverses every half turn because each side of the coil moves alternately up and down through the field. This produces a sinusoidal alternating voltage. The peak EMF occurs when the coil is horizontal (maximum flux cutting), and zero EMF when vertical (no flux cutting).
A DC dynamo works on the same principle but uses a split-ring commutator instead of two slip rings. The commutator reverses the connections to the external circuit every half turn. This ensures that the current in the external circuit always flows in the same direction, producing a direct current (DC). The induced EMF in the coil is still alternating, but the commutator rectifies it.
The output voltage from a DC dynamo is not perfectly steady; it varies from zero to a peak value in each half-cycle, creating a pulsating DC waveform. In practice, more coils and commutator segments are used to smooth the output.
A transformer is a device that changes the voltage of an alternating current supply. It consists of two coils of insulated wire wound on a common soft iron core. The primary coil is connected to the AC input, and the secondary coil provides the output. The soft iron core concentrates and guides the magnetic flux from the primary to the secondary coil.
An alternating current in the primary coil produces a changing magnetic field in the core. This changing flux links the secondary coil and, by Faraday’s law, induces an alternating EMF across its terminals. Transformers only work with AC; a steady DC current does not produce a changing flux and therefore cannot induce an EMF in the secondary.
For an ideal transformer with no energy losses, the relationship between primary and secondary voltages and the number of turns is given by:
对于无能量损失的理想变压器，初级与次级电压以及匝数之间的关系为：
Vₚ / Vₛ = Nₚ / Nₛ
where Vₚ and Vₛ are the primary and secondary voltages, Nₚ and Nₛ are the numbers of turns on the primary and secondary coils. A step-up transformer has Nₛ > Nₚ, so Vₛ > Vₚ. A step-down transformer has Nₛ < Nₚ, so Vₛ < Vₚ.
For 100% efficiency, the input power equals the output power: Pₚ = Pₛ, or Vₚ Iₚ = Vₛ Iₛ. Combining this with the voltage ratio gives the current ratio:
Thus, a step-up transformer increases voltage but decreases current, and vice versa.
因此，升压变压器提高电压但减小电流，反之亦然。
10. Power Transmission and Energy Loss | 电力传输与能量损失
Electricity is transmitted over long distances at very high voltages to minimise energy loss. When current flows through a cable of resistance R, the power lost as heat is I²R. For a given power P = V I, increasing the voltage V reduces the current I, thereby dramatically reducing the I²R losses.
电力通过高压进行远距离传输，以最大程度地减少能量损耗。当电流流过电阻为 R 的电缆时，发热损耗功率为 I²R。对于一定功率 P = V I，提高电压 V 会降低电流 I，从而显著减少 I²R 损耗。
Real transformers are not ideal. Energy is lost due to eddy currents induced in the iron core, hysteresis in the magnetic material, and resistive heating in the copper windings. Laminated cores and soft magnetic materials are used to reduce these losses.
11. Applications of Electromagnetic Induction | 电磁感应的应用
Beyond generators and transformers, electromagnetic induction is used in many everyday technologies. Inductive charging for smartphones uses a primary coil in the charger to induce current in a secondary coil inside the phone. Induction cooktops create a rapidly changing magnetic field that induces eddy currents directly in the metal pan, heating it efficiently. Dynamic microphones use a diaphragm attached to a coil moving in a magnetic field to convert sound waves into electrical signals.
Other examples include metal detectors, induction welding, and magnetic braking in vehicles. All rely on the fundamental principle of a changing magnetic flux inducing an EMF or current.
12. Common Misconceptions and Exam Tips | 常见误解与应试技巧
A common mistake is to think that a transformer can increase power. A transformer only changes voltage and current; power output is always less than or equal to power input (in practice, less due to losses). Another error is confusing the direction of motion with magnetic field direction when using Fleming’s right-hand rule (for generators): thumb – motion, first finger – field, second finger – induced current. Remember – generator = right hand, motor = left hand.
When describing a generator, never say the coil ‘cuts flux’ when it is rotating parallel to the field lines – this is the position of zero induced EMF. Also, in transformer questions, always check whether the question assumes an ideal transformer; if not, mention energy losses. Practise using the transformer equations together with P = V I to solve quantitative problems.
描述发电机时，切勿在线圈平面平行于磁感线旋转时称其“切割磁通量”——这是感应电动势为零的位置。另外，在变压器题中，务必先确认题目是否假设理想变压器；若未假设，则需提及能量损耗。练习综合利用变压器公式和 P = V I 解决定量问题。
Finally, ensure you can sketch and label the voltage–time graph for an AC generator and a DC dynamo, showing the positions of the coil at key points.
最后，要确保能画出并标注交流发电机和直流发电机的电压–时间图，并标出关键点对应的线圈位置。
Published by TutorHao | Physics Revision Series | aleveler.com
This comprehensive handbook brings together every essential formula you need for GCSE OCR Physics. Understanding these equations is the key to solving numerical problems and explaining scientific phenomena in your exams.
Average speed is the total distance travelled divided by the time taken.
平均速度是总路程除以所用时间。
v = s / t
Acceleration measures how quickly velocity changes. It is the change in velocity over time.
加速度衡量速度变化的快慢，等于速度变化量除以时间。
a = (v − u) / t
For uniform acceleration, the final velocity squared is related to initial velocity, acceleration and displacement.
对于匀加速运动，末速度的平方与初速度、加速度和位移有关。
v2 = u2 + 2 a s
2. Forces and Motion | 力与运动
Newton’s second law states that the resultant force on an object equals its mass multiplied by its acceleration.
牛顿第二定律指出，物体所受的合力等于质量乘以加速度。
F = m a
Weight is the force of gravity acting on a mass.
重量是作用在质量上的重力。
W = m g
Hooke’s law describes the extension of a spring as directly proportional to the applied force, up to the limit of proportionality.
胡克定律指出，在弹性限度内，弹簧的伸长量与施加的力成正比。
F = k x
3. Energy, Work and Power | 能量、功与功率
Work done is the energy transferred when a force moves an object over a distance.
功是力使物体移动一段距离时所传递的能量。
W = F d
Kinetic energy depends on mass and speed squared.
动能取决于质量和速度的平方。
Ek = ½ m v2
Gravitational potential energy increases with height in a gravitational field.
重力势能随高度增加而增大。
Ep = m g h
Elastic potential energy is stored in a stretched or compressed spring.
弹性势能储存在被拉伸或压缩的弹簧中。
Ee = ½ k x2
Power is the rate of energy transfer or work done.
功率是能量传递或做功的速率。
P = E / t
Efficiency is the ratio of useful output energy to total input energy.
效率是有用输出能量与总输入能量之比。
Efficiency = Useful energy output / Total energy input
4. Electricity and Circuits | 电学与电路
Electric charge transferred is the product of current and time.
转移的电荷量等于电流与时间的乘积。
Q = I t
Ohm’s law relates potential difference, current and resistance.
欧姆定律描述了电势差、电流和电阻之间的关系。
V = I R
When resistors are joined in series, the total resistance is the sum of individual resistances.
电阻串联时，总电阻等于各电阻之和。
Rtotal = R1 + R2
For resistors in parallel, the total resistance is found using the reciprocal formula.
电阻并联时，总电阻由倒数公式计算。
1 / Rtotal = 1 / R1 + 1 / R2
5. Electrical Power and Energy | 电功率与电能
Electrical power in a component can be calculated using potential difference and current.
元件的电功率可用电势差和电流计算。
P = I V
Power can also be expressed using current and resistance.
功率也可用电流和电阻表示。
P = I2 R
Using voltage and resistance gives another useful form.
用电压和电阻得到另一种形式。
P = V2 / R
Energy transferred by electricity is power multiplied by time.
电能传递量等于功率乘以时间。
E = P t
6. Waves | 波
Wave speed is the product of frequency and wavelength.
波速等于频率乘以波长。
v = f λ
The period of a wave is the reciprocal of the frequency.
波的周期是频率的倒数。
T = 1 / f
7. Density and Pressure | 密度与压强
Density is mass per unit volume.
密度是单位体积的质量。
ρ = m / V
Pressure is the force applied perpendicular to a surface per unit area.
压强是垂直作用于单位面积上的力。
p = F / A
Pressure exerted by a liquid column depends on depth, density and gravitational field strength.
液体柱产生的压强取决于深度、密度和重力场强。
p = h ρ g
8. Thermal Physics | 热物理
The energy needed to change the temperature of a substance is proportional to its mass, specific heat capacity and temperature change.
改变物体温度所需的能量与其质量、比热容和温度变化成正比。
ΔE = m c Δθ
Energy required for a change of state without temperature change is given by the latent heat.
没有温度变化的状态改变所需能量由潜热给出。
E = m L
9. Radioactivity | 放射性
Activity is the number of decays per second and is measured in becquerels.
活度是每秒衰变次数，单位为贝克勒尔。
A = ΔN / Δt
Half-life is the time for half the radioactive nuclei in a sample to decay; no single formula, but the count rate halves each half-life period.
半衰期是样本中一半放射性原子核衰变所需的时间；没有单一公式，但计数率在每个半衰期内减半。
10. Magnetism and Electromagnetism | 磁学与电磁学
For an ideal transformer, the ratio of voltages is equal to the ratio of turns in the coils.
对于理想变压器，电压比等于线圈匝数比。
Vp / Vs = Np / Ns
Assuming 100% efficiency, the electrical power in the primary coil equals the power in the secondary coil, which leads to the current-turns relationship.
假设效率100%，原线圈的电功率等于副线圈的电功率，由此得出电流与匝数的关系。
Ip Vp = Is Vs
Published by TutorHao | Physics Revision Series | aleveler.com
📚 A-Level Physics Application Question Skills: Insights from the June 2018 Examiner Report | A-Level物理应用题技巧：2018年6月考官报告解析
Every year, examiner reports for A-Level Physics provide invaluable feedback on where students gain and lose marks, particularly in application-based questions. The June 2018 examiner report highlighted several recurring issues in how students approach problem-solving, design experiments, and handle data. This article distills those insights into a practical guide to help you refine your technique and tackle application questions with confidence.
Many marks are lost because students fail to respond to the exact command word used in the question. The June 2018 report noted that candidates often ‘describe’ when asked to ‘explain’, or give a formula when asked to ‘state’ a principle. Command words such as ‘state’, ‘describe’, ‘explain’, ‘calculate’, ‘determine’, ‘suggest’, and ‘evaluate’ require different levels of detail.
For example, ‘state’ simply asks for a brief answer, often a definition or law; ‘explain’ requires a logical scientific argument, linking cause and effect; ‘evaluate’ demands a judgment based on evidence, with both strengths and limitations discussed.
Examiner tip: Underline the command word in every question and tailor your response accordingly.
考官建议：在每个问题中标出指令词，并据此作答。
2. Breaking Down the Problem | 分解问题
Application questions often present a novel scenario or a multi-step problem. The examiner report praised students who systematically broke the problem into smaller parts, identifying known quantities, unknown variables, and the relevant physics principles before jumping into calculations.
A common mistake was to start substituting numbers immediately without considering which equation is appropriate or whether unit conversions are needed. The June 2018 paper saw many errors from missing unit prefixes (e.g., cm to m, mA to A).
Check the answer for sense and significant figures
采用结构化方法：
阅读并想象问题情景
列出正确单位的已知数据
确定物理概念
选择合适方程
先符号求解，再代入数值
检查答案的合理性和有效数字
3. Applying Physics Principles, Not Just Formulas | 应用物理原理，而非仅仅公式
The examiner report stressed that many candidates treat physics as a collection of formulas to be memorised. In application questions, you are often required to reason from fundamental principles, such as conservation of energy, Newton’s laws, or the meaning of terms in an equation.
For instance, when a question asks why doubling the velocity quadruples the kinetic energy, simply quoting Eₖ = ½mv² is not enough – you must explain that the velocity term is squared, so the dependence is quadratic. Similarly, when analyzing a circuit change, refer to Ohm’s law and the concept of potential divider rather than just plugging numbers.
A significant part of the June 2018 application questions involved designing or critiquing experiments. Common weaknesses included vague descriptions of procedure, lack of controls, and failure to mention how variables would be measured or kept constant.
Examiners expect you to identify independent, dependent, and control variables explicitly. For example, in an investigation of how the period of a pendulum depends on length, you must state that mass and amplitude are controlled, length is measured with a metre rule, and period is timed for multiple oscillations to reduce uncertainty.
Also, always discuss safety precautions where relevant, and suggest improvements to reduce errors – such as using a set square to ensure vertical alignment, or repeating measurements and taking averages.
Capacitance is a key topic in the CCEA IGCSE Physics specification, linking electric fields, energy storage, and circuit behaviour. This bilingual revision guide dissects every essential concept — from defining the farad to analysing charge-discharge curves — ensuring you master both the qualitative understanding and the numerical skills required for top marks. Let’s build your confidence step by step.
Capacitance is a measure of a component’s ability to store electric charge. It is defined as the amount of charge stored per unit potential difference across the component. In equation form, this is written as:
电容是衡量元件储存电荷能力的物理量。它被定义为元件两端每单位电势差所储存的电荷量。用公式表示为：
C = Q / V
where Q is the charge in coulombs (C), V is the potential difference in volts (V), and C is the capacitance in farads (F). One farad is a very large unit; in practical circuits, capacitances are usually expressed in microfarads (µF, 10⁻⁶ F) or picofarads (pF, 10⁻¹² F).
A capacitor with a larger capacitance can store more charge for the same applied voltage. It is crucial not to confuse capacitance with the charge itself: capacitance is a property of the capacitor, while the stored charge depends on the voltage applied.
A capacitor is a passive electrical component consisting of two conducting plates separated by an insulating material called a dielectric. The plates store equal and opposite charges when a potential difference is applied: one plate gains a surplus of electrons (negative charge), while the other loses electrons (positive charge).
The dielectric serves two important purposes: it prevents direct electrical contact between the plates while allowing the electric field to be established, and it increases the capacitor’s ability to store charge by reducing the effective electric field, thereby allowing more charge to accumulate for the same voltage.
Common dielectric materials include air, paper, ceramic, and electrolytic substances. Changing the dielectric or the plate geometry directly alters the capacitance value, as we will explore.
The basic formula C = Q / V can be rearranged to suit different calculations: Q = C × V, and V = Q / C. This relationship is linear, meaning a graph of Q against V for a fixed capacitor yields a straight line through the origin, with gradient equal to the capacitance C.
基本公式 C = Q / V 可以变形以满足不同计算需求：Q = C × V，V = Q / C。这一关系是线性的，因此对于固定电容，电荷量 Q 对电压 V 的图像是一条通过原点的直线，其斜率等于电容 C。
The SI unit of capacitance is the farad (F). Because 1 F is inconveniently large, submultiples are routinely used:
1 µF = 1 × 10⁻⁶ F
1 nF = 1 × 10⁻⁹ F
1 pF = 1 × 10⁻¹² F
电容的国际单位是法拉 (F)。由于 1 F 大得不便使用，常用分数单位：
1 µF = 1 × 10⁻⁶ F
1 nF = 1 × 10⁻⁹ F
1 pF = 1 × 10⁻¹² F
Exam questions in CCEA IGCSE Physics often ask you to convert between these units or to read capacitor markings, so practise using prefixes confidently.
The capacitance of a parallel‑plate capacitor is determined by three physical factors:
平行板电容器的电容由三个物理因素决定：
The overlapping area of the plates, A: larger area allows more charge accumulation, so C ∝ A.
极板的重叠面积 A：面积越大，能积聚的电荷越多，因此 C 与 A 成正比。
The separation between the plates, d: smaller separation produces a stronger electric field for the same voltage, so C ∝ 1/d.
极板间距 d：间距越小，相同电压下的电场越强，因此 C 与 d 成反比。
The permittivity of the dielectric material, ε: materials with higher permittivity increase capacitance, so C ∝ ε.
电介质的介电常数 ε：介电常数越大的材料，越能提高电容，因此 C 与 ε 成正比。
The full relationship can be expressed as:
完整的关系可表达为：
C = ε × A / d
While you are not required to memorise the permittivity constant for IGCSE, you should be able to explain qualitatively how changing A, d, or the dielectric material affects the capacitance.
虽然 IGCSE 不要求记忆介电常数，但你应该能定性解释改变 A、d 或电介质材料如何影响电容。
5. Energy Stored in a Capacitor | 电容器储存的能量
When a capacitor is charged, it stores electrical potential energy in the electric field between its plates. The energy is derived from the work done by the power supply to move charge onto the plates against the growing potential difference.
Three equivalent formulas are used to calculate the stored energy, E:
用于计算储存能量 E 的等价公式有三个：
E = ½ Q V E = ½ C V² E = ½ Q² / C
Where E is measured in joules (J). The factor of ½ appears because the average potential difference during charging is half the final voltage. You must be able to select the most convenient form depending on the given variables.
其中 E 的单位是焦耳 (J)。出现 ½ 系数是因为充电过程中的平均电势差为最终电压的一半。你必须能够根据已知量选择最方便的公式形式。
This energy can be released very rapidly during discharge, which makes capacitors useful for applications like camera flash units and defibrillators.
这些能量在放电时可以极快地释放出来，这使得电容器在相机闪光灯和心脏除颤器等应用中极具价值。
6. Charging a Capacitor | 电容器的充电过程
When an uncharged capacitor is connected to a d.c. supply through a resistor, charge does not build up instantly. The charging process is exponential: initially the current is large because the potential difference across the capacitor is zero, and as charge accumulates, the voltage across the capacitor rises, reducing the potential difference across the resistor and thus the current.
For a simple RC series charging circuit, the voltage across the capacitor, V, follows:
对简单的 RC 串联充电电路，电容器两端电压 V 的变化规律为：
V = V₀ (1 − e^(−t / RC))
where V₀ is the supply voltage, R is the resistance, C is the capacitance, and t is the time elapsed. The product RC is called the time constant. After one time constant, the capacitor voltage reaches approximately 63% of V₀.
In the CCEA syllabus, you are expected to describe this behaviour qualitatively and to recognise the exponential shape of the voltage‑time graph, as well as perform simple calculations using the time constant.
If a charged capacitor is disconnected from the supply and connected across a resistor, it discharges through the resistor. The stored charge flows from one plate to the other, neutralising the capacitor. Again, the process is exponential.
The voltage V across the capacitor during discharge is given by:
放电过程中电容器两端的电压 V 由下式给出：
V = V₀ e^(−t / RC)
where V₀ is the initial voltage. After one time constant, the voltage drops to about 37% of its initial value. The current and charge follow similar exponential decays.
It is important to note that the discharging current flows in the opposite direction to the charging current. A common exam question involves reading values from an exponential decay graph or sketching it for given circuit parameters.
The time constant, usually represented by the Greek letter τ (tau), characterises how quickly a capacitor charges or discharges. For an RC circuit:
时间常数通常用希腊字母 τ 表示，它表征电容器充放电的快慢。对于 RC 电路：
τ = R × C
The unit of τ is seconds (s), provided R is in ohms (Ω) and C is in farads (F). A larger resistance or a larger capacitance gives a longer time constant, meaning the capacitor takes more time to charge or discharge to a given fraction.
时间常数的单位是秒 (s)，前提是 R 的单位为欧姆 (Ω)，C 的单位为法拉 (F)。电阻或电容越大，时间常数越大，意味着电容器充放电到某一比例所需的时间越长。
The time constant has practical significance:
After 1τ, charging reaches 63% of the final value, discharging falls to 37%.
After 5τ, the capacitor is considered fully charged or fully discharged (over 99% of the final state).
Many past paper questions ask you to determine the time constant from a graph by finding the time taken for the voltage to fall to 37% of its initial value in a discharge curve.
许多历年试题要求你通过找出放电曲线中电压降至初始值 37% 所用的时间，从图上判定时间常数。
9. Graphical Analysis | 图形分析
CCEA IGCSE Physics candidates must interpret and sketch voltage‑time (V‑t) and current‑time (I‑t) graphs for both charging and discharging. Here are the key features:
Charging V‑t: starts at 0, rises steeply at first then gradually flattens, approaching V₀ asymptotically.
充电 V‑t 图：从 0 开始，起初陡升然后逐渐变平，渐近趋向 V₀。
Discharging V‑t: starts at V₀, decays steeply then flattens, approaching zero asymptotically.
放电 V‑t 图：从 V₀ 开始，陡降后变平，渐近趋向零。
Charging I‑t: starts at maximum (I₀ = V₀ / R), decays exponentially to zero.
充电 I‑t 图：起始电流最大 (I₀ = V₀ / R)，指数衰减至零。
Discharging I‑t: starts at maximum negative value (if direction convention is held), decays to zero in magnitude.
放电 I‑t 图：若按方向惯例，从最大负值开始，绝对值衰减到零。
Always label axes with quantities and units, and indicate the time constant on the graph where possible. The exponential shape can be tested by showing that the time taken for the voltage to halve is constant (a property of exponential decay).
When capacitors are combined in a circuit, the total or equivalent capacitance depends on the arrangement. The rules are opposite to those for resistors.
电容器在电路中组合时，总电容（等效电容）取决于连接方式。其规则与电阻器的规则相反。
For capacitors in parallel:
对于并联电容器：
Ctotal = C₁ + C₂ + C₃ + …
The total capacitance increases because the effective plate area is increased. All capacitors share the same voltage.
总电容增大，这是因为等效极板面积增加了。所有电容器承受相同的电压。
For capacitors in series:
对于串联电容器：
1 / Ctotal = 1 / C₁ + 1 / C₂ + 1 / C₃ + …
The total capacitance is always smaller than the smallest individual capacitance. This is because the effective plate separation is increased and the same charge resides on each capacitor.
总电容总是小于其中最小的单个电容，这是因为等效极板间距增大，且每个电容器都带有相同的电荷。
Worked examples frequently ask you to calculate the combined capacitance and then find the total stored charge or energy. Always check whether the capacitors are in series or parallel before applying the formulas.
常见题型会要求你计算组合电容，再求储存的总电荷或能量。务必先判明串并联关系再套用公式。
11. Applications of Capacitors | 电容器的应用
Capacitors are found in a vast range of electronic and electrical devices. For CCEA IGCSE Physics, three applications are particularly relevant:
电容器广泛存在于各类电子和电气设备中。CCEA IGCSE 物理尤为关注以下三种应用：
Camera flash: a capacitor is slowly charged from a battery and then rapidly discharged through a flash lamp, delivering a bright burst of light.
相机闪光灯：电容器由电池缓慢充电，然后通过闪光灯快速放电，产生明亮的瞬间闪光。
Smoothing circuits: after rectification, a capacitor is used to reduce the ripple in the d.c. output by storing energy when the voltage rises and releasing it when it falls.
平滑电路：整流之后，用电容器在电压上升时储存能量、下降时释放能量，从而减小直流输出中的纹波。
Timing circuits: the predictable charging and discharging curve of an RC circuit is used to create precise time delays, for example in traffic light sequencers or electronic timers.
定时电路：RC 电路可预测的充放电曲线用于产生精确的时间延迟，例如用于交通灯顺序控制或电子定时器。
In each case, the capacitor’s ability to store and release energy controllably is the key principle. Understanding these real‑world connections helps you tackle context‑based exam questions with confidence.
In IGCSE Edexcel Physics, the particle physics topic focuses on the structure of atoms, radioactivity, nuclear processes, and their real-world applications. Understanding these concepts is essential for explaining natural phenomena and modern technology, from medical imaging to nuclear power. This revision guide breaks down every key point you need to master for the exam.
1. Atomic Structure and Subatomic Particles | 原子结构与亚原子粒子
All matter is made of atoms. Each atom consists of a tiny, dense, positively charged nucleus surrounded by negatively charged electrons moving in orbits or shells. The nucleus contains protons and neutrons, collectively called nucleons. A proton carries a charge of +1.6×10⁻¹⁹ C, an electron carries -1.6×10⁻¹⁹ C, and a neutron has no charge. The relative masses of proton, neutron, and electron are approximately 1, 1, and 1/1840 respectively. The atomic number (Z) is the number of protons in the nucleus and defines the element. The mass number (A) is the total number of protons plus neutrons.
所有物质都由原子组成。每个原子由一个极小的、致密的、带正电的原子核以及在其周围轨道或壳层中运动的带负电电子构成。原子核包含质子和中子，合称核子。一个质子带 +1.6×10⁻¹⁹ C 的电荷，电子带 -1.6×10⁻¹⁹ C，中子不带电。质子、中子和电子的相对质量分别约为 1、1 和 1/1840。原子序数（Z）是原子核中的质子数，决定了元素种类。质量数（A）是质子与中子的总数。
2. Isotopes | 同位素
Isotopes are atoms of the same element that have the same number of protons (same atomic number) but different numbers of neutrons (different mass numbers). For example, carbon-12 (¹²₆C) has 6 protons and 6 neutrons, while carbon-14 (¹⁴₆C) has 6 protons and 8 neutrons. Isotopes exhibit identical chemical properties because chemical behavior is determined by the electron configuration, which depends only on the number of protons. However, some isotopes are unstable and undergo radioactive decay, making them radioisotopes. Stability depends on the neutron-to-proton ratio.
Unstable nuclei emit radiation to become more stable. There are three main types: alpha (α) decay, beta (β) decay, and gamma (γ) emission. In α decay, the nucleus emits an alpha particle, which is a helium nucleus (⁴₂He). The mass number decreases by 4 and the atomic number by 2. In β decay, a neutron turns into a proton and emits an electron (β⁻ particle, ⁰₋₁e); the mass number stays the same but the atomic number increases by 1. Gamma rays are high-energy electromagnetic waves emitted by a nucleus after α or β decay to release excess energy; they have no mass and no charge, so the mass and atomic numbers remain unchanged.
Alpha particles are heavy, slow-moving, and strongly ionising. They can be stopped by a sheet of paper or a few centimetres of air. Beta particles are lighter, faster, and moderately ionising; they can penetrate paper but are stopped by a few millimetres of aluminium. Gamma rays are weakly ionising, extremely penetrating, and require several centimetres of lead or thick concrete to reduce intensity significantly. Ionising ability and penetration power are inversely related: the more ionising the radiation, the less penetrating it is. All three types are deflected by electric and magnetic fields, but α and β are deflected in opposite directions, while γ passes straight through unaffected.
Nuclear equations show the changes in mass and atomic numbers during radioactive decay. The sum of mass numbers (top) and the sum of atomic numbers (bottom) must balance on both sides of the equation. For example, alpha decay of uranium-238: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. Beta decay of carbon-14: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e. In beta decay, an antineutrino is also emitted but is often omitted in IGCSE equations. Gamma emission does not affect the nuclear equation because it has no mass or charge; it is often written simply as adding a γ symbol next to the daughter nucleus.
The half-life of a radioactive isotope is the time taken for half of the unstable nuclei in a sample to decay, or for the count rate (activity) to fall to half its initial value. Half-life is constant for a given isotope and is not affected by temperature, pressure, or chemical state. It is measured by monitoring the count rate over time using a Geiger-Müller tube and counter, with the background count subtracted. The decay pattern is exponential. Calculations often involve finding the number of half-lives elapsed and then dividing the initial quantity by 2 raised to that number. For example, if we have 80 g of a substance with a half-life of 2 hours, after 6 hours (3 half-lives) the mass remaining is 80 g ÷ 2³ = 10 g.
Background radiation is the low-level radiation present in our environment from natural and artificial sources. Natural sources include cosmic rays from space, radon gas from rocks, and radioactive materials in the ground and food. Artificial sources include medical X-rays, nuclear weapons testing, and nuclear power stations. The level of background radiation varies with location. When measuring the activity of a sample in the laboratory, you must always subtract the background count rate to obtain the corrected count rate. This ensures accurate half-life and activity measurements.
背景辐射是环境中来自天然和人为来源的低水平辐射。天然来源包括来自太空的宇宙射线、岩石释放的氡气以及土壤和食物中的放射性物质。人工来源包括医疗 X 射线、核武器试验和核电站。背景辐射水平因地区而异。在实验室测量样品活度时，必须始终减去本底计数率，以获得校正后的计数率，确保半衰期和活度测量准确。
8. Uses of Radioactivity | 放射性的应用
Radioactive isotopes have many practical applications. In medicine, gamma-emitting isotopes like technetium-99m are used as tracers to diagnose organ function, while cobalt-60 emits gamma rays for radiotherapy to kill cancer cells. In industry, beta sources are used to monitor the thickness of paper or metal sheets; if the count rate suddenly changes, the thickness has deviated. Alpha sources like americium-241 are used in domestic smoke detectors; smoke particles absorb alpha particles, reducing the ionisation current and triggering the alarm. Carbon-14 dating relies on measuring the remaining ¹⁴C in once-living material to estimate its age. Sterilisation of medical equipment uses high-intensity gamma rays to kill bacteria without the need for heat.
Ionising radiation can damage living cells, potentially causing mutations, cancer, or radiation sickness at high doses. Alpha particles are most dangerous if ingested or inhaled because they cause intense local ionisation inside the body. Safety precautions include: using sources for the shortest possible time, keeping as far away as possible (inverse square law applies to gamma intensity), using shielding (lead for gamma, aluminium for beta), wearing protective clothing, and handling sources with long-handled tongs. Radioactive materials must be stored in labelled, shielded containers and disposed of carefully according to regulations. Never point a source directly at anyone.
Nuclear fission is the splitting of a large, unstable nucleus into two smaller, more stable nuclei, along with the release of two or three neutrons and a large amount of energy. It occurs naturally or can be induced by neutron capture. Uranium-235 and plutonium-239 are common fissile fuels. In a nuclear reactor, a controlled chain reaction is maintained: a neutron hits a U-235 nucleus, causing it to fission, and the released neutrons go on to cause further fission. Control rods absorb excess neutrons to regulate the reaction rate. The energy released as heat is used to produce steam that drives turbines to generate electricity. Fission is also used in nuclear weapons where the chain reaction is uncontrolled.
Nuclear fusion is the joining of two light nuclei to form a heavier nucleus, releasing a tremendous amount of energy. This is the process that powers the Sun and other stars, where hydrogen nuclei (protons) fuse to form helium. The fusion reaction requires extremely high temperatures (millions of degrees Celsius) and pressures to overcome the electrostatic repulsion between the positively charged nuclei. On Earth, achieving and containing these conditions is a major challenge; experimental fusion reactors use magnetic confinement (tokamaks) or inertial confinement. Fusion has the potential to provide nearly limitless clean energy, with abundant fuel (deuterium from water) and no long-lived radioactive waste, unlike fission. However, practical, controlled fusion power plants do not yet exist.
Radiation cannot be seen, smelled, or felt, so special detectors are required. The Geiger-Müller (GM) tube is the most common school laboratory instrument. When radiation enters the tube, it ionises the gas inside, causing a brief current pulse that is counted and often displayed as a count rate (counts per second) or total counts. Other detectors include photographic film, which darkens when exposed to radiation (used in film badges for workers), and cloud chambers, where visible tracks reveal the paths of alpha and beta particles. In a cloud chamber, alpha tracks are short and thick, beta tracks are longer and thinner, and gamma rays produce scattered, wispy tracks.
📚 AS Physics Unit 1 Insert June 2019: Application Question Techniques | AS物理 Unit 1 2019年6月数据表应用题技巧
The June 2019 AS Physics Unit 1 insert is a powerful tool packed with essential formulae, constants, and data tables. Mastering how to navigate this resource during application questions can significantly boost your exam performance. This guide will show you proven techniques to extract and apply the right information quickly and accurately.
The insert is divided into sections: kinematics, dynamics, materials, waves, and constants. Familiarise yourself with its structure before the exam so you can locate any formula within seconds.
For example, the ‘Kinematics’ section typically lists equations like v = u + at and s = ut + ½at², while ‘Materials’ includes Young’s modulus equation. Cross check each formula you use against the insert to avoid transcription errors.
例如，“运动学”部分通常列出像 v = u + at 和 s = ut + ½at² 这样的方程，而“材料”部分则包含杨氏模量方程。针对每个你使用的公式，都要与数据表进行核对，以避免誊写错误。
2. Extracting Key Formulae from the Data Sheet | 从公式表提取关键公式
The insert provides standard equations in symbolic form. Do not rely on your memory alone; copying the formula from the insert ensures it is written correctly with appropriate symbols like s, u, v, a, t, F, E, λ, etc.
If you need to rearrange a formula, first copy the original from the insert onto your answer sheet. This acts as a safety check and earns method marks. For instance, to find time t from v = u + at, write the base equation, then isolate t = (v – u)/a.
如果你需要重新整理公式，首先将数据表中的原始公式抄写到答题纸上。这既是一种安全检查，也能获得方法分。例如，要根据 v = u + at 求时间 t，先写出基本方程，然后分离出 t = (v – u)/a。
The insert includes constants such as acceleration due to gravity g = 9.81 m s⁻², the Planck constant h = 6.63 × 10⁻³⁴ J s, and the speed of light in a vacuum c = 3.00 × 10⁸ m s⁻¹. Always check which value is appropriate for the context; sometimes a rounded value like g = 9.8 is used in calculations.
数据表包含各类常数，例如重力加速度 g = 9.81 m s⁻²，普朗克常数 h = 6.63 × 10⁻³⁴ J s，以及真空中的光速 c = 3.00 × 10⁸ m s⁻¹。务必根据上下文确定合适的值；有时计算中会使用约值，如 g = 9.8。
In application questions, you may need to multiply or divide constants. For example, when calculating photon energy E = hf, obtain h from the insert and check the frequency f in the question.
在应用题中，你可能需要对常数进行乘法或除法运算。例如，计算光子能量 E = hf 时，从数据表中获取 h，并注意题目中的频率 f。
4. Using the Data Tables for Material Properties | 使用数据表获取材料特性
The insert often includes a table of material properties such as Young’s modulus, breaking stress, or resistivity. You must select the correct row based on the material named in the question.
When solving a problem like ‘Calculate the extension of a steel wire’, locate Young’s modulus for steel, note the unit (Pa), and apply E = stress/strain with careful unit conversions.
在解决诸如“计算一根钢线的伸长量”这类问题时，找到钢的杨氏模量，注意单位（Pa），并应用 E = 应力/应变，同时进行仔细的单位换算。
5. Handling Graphs and Experimental Data | 处理图表和实验数据
Application questions often present graphs with axes labelled in quantities found in the insert. For example, a force-extension graph may require you to find the gradient (k) and relate it to Young’s modulus using the formula from the insert.
Use the insert to confirm the relationship: stress = force/area, strain = extension/original length, so E = (F/A) / (ΔL/L) → gradient of F vs ΔL = EA/L. Pick points on the straight-line section to calculate gradient accurately.
6. Dimensional Analysis for Formula Verification | 量纲分析验证公式
When in doubt about a rearranged formula, use dimensional analysis with the help of units provided in the insert. Check that both sides of the equation have the same base units (m, kg, s, A, etc.).
For example, from the insert, power P = work/time. If you derive P = Fv, check: F in N = kg m s⁻², v in m s⁻¹, so Fv has units kg m² s⁻³, which matches watt (J/s = kg m² s⁻³). This confirms correctness.
例如，从数据表得知，功率 P = 功/时间。如果你推导出 P = Fv，检查：F 的单位为 N = kg m s⁻²，v 的单位为 m s⁻¹，因此 Fv 的单位为 kg m² s⁻³，这与瓦特（J/s = kg m² s⁻³）相符。这证实了公式的正确性。
7. Unit Conversion Strategies | 单位转换策略
Many students lose marks by forgetting to convert units such as cm to m or mm² to m². The insert lists quantities in standard SI units, so always convert given data to SI before substituting into formulae.
许多学生因忘记单位转换（如 cm 转为 m，或 mm² 转为 m²）而丢分。数据表以标准国际单位列出各量，因此在代入公式前，务必先将给定数据转换为国际单位。
Create a quick conversion table: 1 cm = 1 × 10⁻² m, 1 mm = 1 × 10⁻³ m, 1 g = 1 × 10⁻³ kg. For area conversions, (1 mm)² = (1 × 10⁻³ m)² = 1 × 10⁻⁶ m². Practice these until they become automatic.
制作一个快速换算表：1 cm = 1 × 10⁻² m，1 mm = 1 × 10⁻³ m，1 g = 1 × 10⁻³ kg。对于面积换算，(1 mm)² = (1 × 10⁻³ m)² = 1 × 10⁻⁶ m²。反复练习直到熟能生巧。
8. Applying the Formula ‘V = fλ’ and Wave Phenomena | 应用公式 V = fλ 及波动现象
The wave equation V = fλ appears in the insert and is central to problems on interference, diffraction, and stationary waves. Identify V as the speed of the wave (often light c for electromagnetic waves) provided in the insert.
波动方程 V = fλ 出现在数据表中，它在涉及干涉、衍射和驻波的问题中至关重要。确定 V 为波速（对于电磁
Published by TutorHao | AS Physics Revision Series | aleveler.com
Kinematics forms the bedrock of classical mechanics, describing motion without reference to its causes. In both IB and WJEC syllabi, a firm grasp of vectors, uniformly accelerated motion, and graphical analysis is essential. This article systematically covers every key topic, from basic definitions to projectile motion, equipping you with the tools needed for exam success.
A scalar is a physical quantity that only possesses magnitude (size). Distance, speed, mass, and time are typical scalars. A vector, on the other hand, has both magnitude and direction; displacement, velocity, acceleration, and force are vectors. Understanding this distinction is the first step in kinematics, as vector addition requires special rules, such as the tip-to-tail method or component resolution.
In IB and WJEC exams, you may be asked to add displacement vectors using scale diagrams or right-angled trigonometry. For non-right-angled triangles, the cosine rule a² = b² + c² − 2bc cos θ and the sine rule are often needed.
2. Displacement, Velocity and Acceleration | 位移、速度与加速度
Displacement (s) is the change in position of an object—it is a vector pointing from start to finish, with SI unit metre (m). Velocity (v) is the rate of change of displacement; thus, it too is a vector. Speed, by contrast, is the scalar rate of change of distance. Acceleration (a) is defined as the rate of change of velocity, meaning any change in either magnitude or direction constitutes acceleration.
Average velocity is given by vₐᵥ = Δs / Δt, while instantaneous velocity is the gradient of a displacement–time graph. Similarly, average acceleration is aₐᵥ = Δv / Δt. In constant acceleration contexts, these definitions lead directly to the SUVAT equations.
When acceleration is constant, five key variables—displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t)—are linked by four equations. In the IB data booklet and WJEC formulae sheet they appear as:
In solving problems, always list the known quantities and the variable you need, then select the equation that includes only one unknown. Pay attention to direction: assign a positive sign to one direction (usually the initial motion) and treat opposite vectors as negative.
For example, a car accelerates from 10 m s⁻¹ to 30 m s⁻¹ over 80 m. Use v² = u² + 2as to find a: 30² = 10² + 2a(80) → a = 5.0 m s⁻².
例如，一辆汽车从 10 m s⁻¹ 加速到 30 m s⁻¹，行驶了 80 m。使用 v² = u² + 2as 求 a：30² = 10² + 2a(80) → a = 5.0 m s⁻²。
4. Displacement–Time Graphs | 位移–时间图像
A displacement–time (s–t) graph plots displacement on the vertical axis against time on the horizontal axis. The gradient at any point equals the instantaneous velocity. A straight line indicates constant velocity, while a curved line indicates changing velocity (acceleration). A horizontal line means the object is at rest.
It is vital not to confuse the shape of the graph with the actual path of the object. A downward-sloping straight line, for instance, does not mean the object is moving downwards; it means the object is moving in the negative direction with constant speed, assuming displacement is defined along a straight line.
The velocity–time (v–t) graph is arguably the most powerful kinematic graph. Its gradient gives the instantaneous acceleration, and the area under the curve (between the line and the time axis) gives the displacement. Areas above the time axis correspond to positive displacement, while areas below represent negative displacement.
In IB and WJEC questions, you may be asked to sketch a v–t graph from a description of motion or to calculate displacement by counting squares or by dividing the area into simple geometric shapes (rectangles, triangles, trapezoids). Remember that a straight sloping line in a v–t graph indicates constant acceleration.
Acceleration–time (a–t) graphs are less common but still appear. A horizontal line indicates constant acceleration. The area under an a–t graph gives the change in velocity (Δv). If the graph line lies above the axis, the velocity increases; if below, it decreases. A zero line means uniform velocity.
When given a piecewise a–t graph, you can find the final velocity by adding the initial velocity to the total area. This is especially useful in jerk-related problems (jerk = rate of change of acceleration), although jerk is not part of the core syllabus.
Free fall is motion under the influence of gravity alone, with negligible air resistance. Near the Earth’s surface, all objects experience a constant downward acceleration due to gravity, g ≈ 9.81 m s⁻². In kinematics problems, you can apply the SUVAT equations by setting a = g (or a = −g depending on your sign convention).
自由落体是仅在重力作用下、空气阻力可忽略不计的运动。在地球表面附近，所有物体都受到一个恒定的、向下的重力加速度 g ≈ 9.81 m s⁻²。在运动学问题中，可以根据你设定的正方向，设 a = g（或 a = −g），然后应用匀加速运动方程。
A classic exam question involves an object thrown vertically upward. At the highest point, its velocity is zero, but its acceleration is still g downwards. The time to reach maximum height is t = u/g, and the total time of flight (returning to the same level) is 2u/g. Symmetry is a powerful problem-solving tool here.
一个经典的考题涉及竖直上抛的物体。在最高点，其速度为零，但加速度仍为向下的 g。到达最高点所需的时间为 t = u/g，而飞行的总时间（落回同一水平面）为 2u/g。此处的对称性是极有力的解题工具。
8. Projectile Motion | 抛体运动
Projectile motion is two-dimensional motion under constant gravitational acceleration. The key is to resolve the initial velocity into horizontal (uₓ = u cos θ) and vertical (uᵧ = u sin θ) components. The horizontal motion has constant velocity (aₓ = 0), while the vertical motion experiences constant acceleration (aᵧ = −g, taking upward as positive).
抛体运动是在恒定重力加速度下的二维运动。关键在于将初速度分解为水平分量（uₓ = u cos θ）和竖直分量（uᵧ = u sin θ）。水平方向上为匀速运动（aₓ = 0），而竖直方向上则具有恒定的加速度（aᵧ = −g，取向上为正）。
The time of flight is determined solely by the vertical motion: t = (2u sin θ)/g for a projectile landing at the same height. The horizontal range is then R = uₓ t = (u² sin 2θ)/g, showing that the maximum range is achieved at θ = 45° in the absence of air resistance.
飞行的总时间完全由竖直运动决定：对于落回同一高度的抛体，t = (2u sin θ)/g。水平射程则为 R = uₓ t = (u² sin 2θ)/g，这表明在没有空气阻力的情况下，当 θ = 45° 时可获得最大射程。
9. Relative Motion | 相对运动
Motion is always measured relative to a frame of reference. The relative velocity of object A with respect to B is given by vₐ_b = vₐ − v_b . For example, if a car moves east at 20 m s⁻¹ and a truck moves east at 15 m s⁻¹, the car’s velocity relative to the truck is 5 m s⁻¹ east. If they move in opposite directions, the magnitude of relative velocity is the sum of their speeds.
运动总是相对于参考系来测量的。物体 A 相对于 B 的相对速度为 vₐ_b = vₐ − v_b 。例如，若一辆车以 20 m s⁻¹ 向东行驶，一辆卡车以 15 m s⁻¹ 向东行驶，则车相对于卡车的速度为 5 m s⁻¹ 向东。若它们反向行驶，相对速度的大小则为两者速率之和。
In river-crossing problems, a boat’s velocity relative to the water combines with the water’s velocity relative to the ground. The resultant velocity determines the actual path. Vector addition through a scale diagram or component resolution yields the drift and the time to cross.
A frequent mistake is confusing distance and displacement. Distance is the total path length (scalar), while displacement is the straight-line separation from start to finish (vector). Similarly, average speed is total distance divided by time, whereas average velocity is displacement divided by time—these quantities are often different when direction changes.
Always check your sign convention before substituting into SUVAT equations. Draw a clear vector diagram for relative motion and projectile problems. When reading graphs, carefully note the axes labels—many errors arise from misidentifying a v–t graph as an s–t graph. Finally, practise multi-step problems where you analyse motion in phases (e.g., acceleration, constant velocity, deceleration) because they are common in both IB and WJEC papers.
Resistance is a core concept in IGCSE Physics that links voltage, current and the properties of materials. Understanding how to calculate resistance, how it varies in different components, and how resistors behave in circuits is essential for both theory papers and practical experiments. This revision guide covers every key point you need, from Ohm’s law to I-V characteristics and energy transfer in resistors.
Resistance is a measure of how much a component opposes the flow of electric current. It is given the symbol R and is measured in ohms (Ω). The resistance of a component can be determined using the ratio of the potential difference (voltage) across it to the current flowing through it: R = V / I. A high resistance means the component allows only a small current for a given voltage.
电阻衡量元件对电流的阻碍程度，符号为 R，单位是欧姆（Ω）。元件的电阻可通过其两端的电势差（电压）与通过它的电流之比来计算：R = V / I。高电阻意味着在给定电压下电流较小。
2. Ohm’s Law | 欧姆定律
Ohm’s law states that, for a metallic conductor at constant temperature, the current through it is directly proportional to the potential difference across it. In other words, the resistance remains constant as long as the temperature does not change. The relationship is expressed by the equation:
V = I × R
where V is the potential difference in volts (V), I is the current in amperes (A), and R is the resistance in ohms (Ω).
欧姆定律指出，对于温度恒定的金属导体，通过它的电流与两端的电势差成正比。也就是说，只要温度不变，电阻保持恒定。这个关系用公式表示为：V = I × R，其中 V 为电压（伏特），I 为电流（安培），R 为电阻（欧姆）。
3. Factors Affecting Resistance | 影响电阻的因素
The resistance of a wire depends on four main factors:
Length (L): resistance increases with length; R ∝ L
Cross-sectional area (A): resistance decreases as area increases; R ∝ 1/A
Material: each material has a characteristic resistivity
Temperature: for most metal conductors, resistance increases when temperature rises
In contrast, insulators and semiconductors (like thermistors) often show a decrease in resistance with increasing temperature. The change in resistance with temperature is put to use in many sensing circuits.
Resistivity (ρ) is a material property that quantifies how strongly a material opposes current flow. The resistance of a uniform wire is given by:
R = ρ L / A
where ρ is the resistivity (unit: ohm metre, Ω·m), L is the length, and A is the cross-sectional area. A low resistivity means the material is a good conductor.
电阻率（ρ）是表征材料阻碍电流能力的物理量。均匀导线的电阻由下式给出：R = ρ L / A，其中 ρ 为电阻率（单位：欧姆·米，Ω·m），L 为长度，A 为横截面积。电阻率越低，材料的导电性越好。
5. Resistors in Series | 串联电阻
When resistors are connected in series, the total resistance is simply the sum of the individual resistances:
Rtotal = R₁ + R₂ + R₃ + …
The current is the same through each resistor, while the total voltage from the source is divided among them. For example, a 4 Ω and a 6 Ω resistor in series give a total resistance of 10 Ω.
For resistors in parallel, the total resistance is found from the reciprocal formula:
1 / Rtotal = 1 / R₁ + 1 / R₂ + 1 / R₃ + …
The voltage across each parallel resistor is the same, while the total current splits between the branches. For two resistors, a shortcut is Rtotal = (R₁ × R₂) / (R₁ + R₂). For example, a 4 Ω and a 12 Ω resistor in parallel give a total resistance of (4×12)/(4+12) = 48/16 = 3 Ω.
An ohmic conductor follows Ohm’s law. Its current-voltage (I-V) graph is a straight line passing through the origin, showing that current is directly proportional to voltage. The resistance is constant and can be found from the inverse of the gradient (or from R = V/I at any point). A fixed metal resistor at constant temperature is a typical example.
欧姆导体遵循欧姆定律，其电流-电压（I-V）图是一条通过原点的直线，表明电流与电压成正比。电阻恒定，可通过斜率倒数求出（或用任意一点的 R = V/I 计算）。恒温下的固定金属电阻就是一个典型例子。
A filament lamp does not obey Ohm’s law because its temperature changes significantly. As the current increases, the filament heats up, causing its resistance to rise. The I-V graph is a curve that gets less steep at higher voltages, indicating increasing resistance. The graph is symmetric for positive and negative voltages.
A diode allows current to flow easily in one direction (forward bias) but has very high resistance in the opposite direction (reverse bias). In forward bias, a small voltage (about 0.6–0.7 V for a silicon diode) is needed before the current rises sharply. The I-V graph shows almost zero current in reverse bias until breakdown, and a steep rise in forward bias above the threshold.
10. Variable Resistor and Potentiometer | 可变电阻与电位器
A variable resistor (rheostat) allows the resistance in a circuit to be changed by moving a sliding contact along a resistive track. It can be used to control the current in a circuit. A potentiometer is connected as a voltage divider: the two end terminals are connected across a supply, and the sliding contact provides an adjustable output voltage between zero and the full supply voltage.
11. Light-Dependent Resistor (LDR) and Thermistor | 光敏电阻与热敏电阻
An LDR (light-dependent resistor) has a resistance that decreases as the light intensity falling on it increases. In the dark its resistance is very high; in bright light it becomes low. A thermistor is a temperature-sensitive resistor. Most common types have a negative temperature coefficient (NTC), meaning resistance decreases as temperature rises.
Both are widely used in sensor circuits—for example, an LDR in a light-operated switch, or a thermistor in a temperature alarm. They are often connected in series with a fixed resistor to form a potential divider.
12. Energy Transfer and Power in Resistors | 电阻中的能量转移与功率
When a current passes through a resistor, electrical energy is converted into thermal energy (heat). The power (energy per second) dissipated is given by:
P = I × V = I² × R = V² / R
where P is in watts (W). The total energy transferred over a time t is E = P × t = I² R t = V I t. This heating effect is the basis of devices like electric heaters and fuses. A fuse uses a thin wire that melts and breaks the circuit if the current exceeds a safe value.
当电流通过电阻时，电能转化为内能（热）。耗散的功率（每秒能量）由下式给出：P = I × V = I² × R = V² / R，单位为瓦特（W）。在时间 t 内转移的总能量为 E = P × t = I² R t = V I t。这种热效应是电热器和熔断器的基础。保险丝中用一根细丝，在电流超过安全值时熔断，从而断开电路。
Calculating the correct fuse rating involves choosing a value slightly above the normal operating current of the appliance, so that the fuse protects the device without blowing during normal use.
Refraction is a vital topic for both IB and WJEC physics, describing how waves change speed and direction when passing from one medium to another. Understanding Snell’s law, refractive index, total internal reflection, and practical applications like optical fibres and prisms will help you tackle exam questions confidently.
When a wave travels from one transparent medium to another, its speed changes due to the difference in optical density. If the wave hits the boundary at an angle other than 90°, this speed change causes the wave to change direction – a phenomenon called refraction.
The frequency of the wave remains unchanged during refraction, but the wavelength adjusts according to v = fλ. Thus, a decrease in speed results in a shorter wavelength.
折射过程中波的频率保持不变，但波长会根据 v = fλ 进行调整。因此，速度减小会导致波长变短。
For light, refraction is responsible for many everyday effects, such as a straw appearing bent in a glass of water and the formation of rainbows.
对于光来说，折射是许多日常现象的原因，例如吸管在水中看起来弯曲以及彩虹的形成。
2. Snell’s Law and Refractive Index | 斯涅尔定律与折射率
Snell’s law quantitatively describes refraction. It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media, and is equal to the inverse ratio of the speeds or the ratio of the refractive indices.
where n₁ and n₂ are the absolute refractive indices of the first and second medium, θ₁ is the angle of incidence and θ₂ is the angle of refraction, both measured from the normal.
The refractive index n of a medium is defined as the ratio of the speed of light in vacuum c to the speed of light in the medium v: n = c / v. This value is always greater than or equal to 1.
介质的折射率 n 定义为真空中的光速 c 与介质中的光速 v 之比：n = c / v。这个值总是大于或等于 1。
3. Direction of Bending | 偏向法线还是远离法线
When light passes from a medium of lower refractive index (faster speed) to a medium of higher refractive index (slower speed), it bends towards the normal. For example, from air (n ≈ 1.00) into glass (n ≈ 1.50).
Conversely, when moving from a higher-index medium to a lower-index medium, light bends away from the normal. This is observed when light exits glass into air.
相反，当从高折射率介质进入低折射率介质时，光线会远离法线弯曲。这在光从玻璃射入空气时可以观察到。
A quick way to remember: Light always takes the path that reduces travel time, as described by Fermat’s principle, resulting in the shortest optical path.
一个快速记忆法：根据费马原理，光总是选择减少旅行时间的路径，从而导致最短光程。
4. Critical Angle and Total Internal Reflection | 临界角与全内反射
When light travels from a denser medium to a less dense medium (n₁ > n₂), there is a specific angle of incidence, called the critical angle θc, for which the angle of refraction is 90°. For angles of incidence greater than θc, all light is reflected back into the denser medium, a phenomenon known as total internal reflection (TIR).
The critical angle depends only on the ratio of the refractive indices. Two conditions must be met for TIR: light must travel from a higher to lower refractive index, and the angle of incidence must exceed θc.
5. Optical Fibres and TIR Applications | 光纤与全内反射应用
Optical fibres use total internal reflection to transmit light signals over long distances with minimal loss. A typical optical fibre consists of a core with a higher refractive index surrounded by cladding with a lower refractive index. Light entering the core at an angle greater than the critical angle is continuously reflected along the fibre.
Other applications of TIR include prismatic periscopes, retroreflectors (like bicycle reflectors), and endoscopes used in medicine. TIR is more efficient than metallic reflection because almost no energy is absorbed.
其他 TIR 应用包括棱镜潜望镜、回射器（如自行车反射器）以及医学内窥镜。全内反射比金属反射更高效，因为几乎没有能量被吸收。
6. Dispersion and the Prism | 色散与棱镜
Dispersion occurs because the refractive index of a material varies slightly with the wavelength (colour) of light. In glass, shorter wavelengths (blue light) travel slower and are refracted more than longer wavelengths (red light). When white light passes through a glass prism, it splits into a spectrum of colours – red, orange, yellow, green, blue, indigo, violet.
A prism demonstrates that white light is a mixture of different colours, and that each colour is bent by a different amount, with violet deviating the most and red the least. This is directly linked to the wavelength dependence of the refractive index.
Lenses use the principle of refraction at curved surfaces to converge or diverge light. A convex lens (thicker in the middle) refracts parallel rays to meet at a focal point, while a concave lens (thinner in the middle) spreads them apart.
透镜利用曲面上的折射原理来会聚或发散光线。凸透镜（中间厚）将平行光线折射后会聚于焦点，而凹透镜（
Published by TutorHao | IB Physics Revision Series | aleveler.com
Mastering experimental skills is essential for success in IGCSE AQA Physics. Whether you are tackling the practical paper or applying concepts to written questions, a solid grasp of planning, measuring, recording, graphing and evaluating will set you apart. This guide breaks down every key component of experimental work, giving you clear strategies to collect reliable data and draw valid conclusions.
The independent variable is the one you deliberately change during the investigation. For example, when investigating Hooke’s Law, you might change the mass added to a spring.
自变量是你在研究过程中有意改变的变量。例如，在探究胡克定律时，你可能会改变悬挂在弹簧上的质量。
The dependent variable is the one you measure for each change in the independent variable. In the spring experiment, you measure the extension of the spring.
因变量是你针对自变量的每次改变所测量的量。在弹簧实验中，你测量的是弹簧的伸长量。
Control variables are all the other factors that could affect the outcome; these must be kept constant to ensure a fair test. Typical control variables for a spring investigation include using the same spring throughout, the same ruler to measure extension and keeping the temperature constant.
Start by writing a clear step-by-step method. List all the apparatus you need, specifying quantities and ranges. For example: ‘Clamp a metre ruler vertically. Hang a spring from the clamp. Attach a pointer to the bottom of the spring. Add a 100 g mass hanger and record the pointer reading as the original length. Then add 100 g masses one at a time, recording the new pointer reading each time.’
首先写出清晰的、分步骤的实验方法。列出你需要的所有仪器，注明数量和量程。例如：“将一把米尺垂直固定。在铁架台上悬挂一根弹簧。在弹簧底部安装一个指针。挂上一个 100 g 的砝码架，记录指针读数作为原长。然后每次增加一个 100 g 砝码，记录每次新的指针读数。”
Decide on a suitable range for the independent variable and the number of readings. A minimum of five or six readings is usually expected. Plan to repeat each measurement at least twice to check for consistency and to calculate an average.
Indicate how you will ensure a fair test by controlling key variables and minimising errors. Mention that you will take repeats and identify potential hazards.
说明你将如何通过控制关键变量和减少误差来确保测试的公平性。提到你将进行重复测量并识别潜在的危险。
3. Taking Measurements | 进行测量
Use the most appropriate instrument for the quantity being measured. For length, a metre ruler is fine for longer distances, but a vernier caliper or micrometer screw gauge gives greater precision for small dimensions. For time, a stopwatch is suitable, but a light gate with a datalogger is far more accurate.
Avoid parallax error by viewing the scale perpendicularly. When reading a liquid level in a measuring cylinder, read the bottom of the meniscus at eye level. Always record readings to the full precision of the instrument, including the uncertainty if required.
Take repeat readings and calculate the mean. Discard anomalous results that are clearly far from the others. The mean is calculated by adding all acceptable values and dividing by the number of values. This reduces the impact of random errors.
4. Minimising Errors and Uncertainties | 减少误差和不确定性
Random errors cause readings to be scattered around the true value. They can be reduced by taking many readings, using repeats and averaging. For timing, measuring a longer interval (e.g. timing 20 swings of a pendulum instead of one) reduces the effect of human reaction time.
Systematic errors shift all readings in one direction. A common example is a zero error on a measuring instrument: a balance that reads 0.5 g with nothing on it will cause all mass readings to be 0.5 g too high. Check instruments for zero errors before starting and adjust or subtract the error.
系统误差会使所有读数朝一个方向偏移。一个常见的例子是测量仪器的零误差：一架空载时读数为 0.5 g 的天平会导致所有质量读数偏高 0.5 g。开始实验前检查仪器零误差，并进行调整或扣除该误差。
The uncertainty in a single reading taken from a scale is usually half the smallest scale division. For a digital instrument, the uncertainty is the smallest digit shown. When you take multiple readings, the uncertainty can be estimated as half the range of the values (maximum – minimum).
Draw a table with clear column headings, including the quantity and its unit separated by a slash or placed in brackets. For example: Mass / kg, Length / cm, Temperature / °C. Keep the number of decimal places consistent for each column, reflecting the precision of the measuring instrument.
Record all raw data in the table. If you need a calculated quantity, such as extension, show the calculation clearly. Extension = new length – original length. Do not forget to include the units in any calculated column header.
Plot the independent variable on the horizontal (x) axis and the dependent variable on the vertical (y) axis. Label each axis with the quantity and unit, for example ‘Extension / cm’. Choose a sensible scale that uses more than half the graph paper and makes plotting easy (go up in steps of 1, 2, 4, 5, 10 etc., not 3 or 7).
Plot each data point as a small, neat cross (×) or a dot with a circle around it. Do not use just a dot; it is easy to lose. If error bars are required, draw them showing the uncertainty range for each point.
Draw a line of best fit. This is a single straight line or smooth curve that shows the trend, with points evenly scattered on either side. Ignore obvious anomalous points; circle them and label them as ‘anomalous’. Use a sharp pencil and a transparent ruler for a straight line.
A straight line through the origin shows that the two variables are directly proportional. The equation takes the form y = kx, where k is the gradient. If the line does not go through the origin, the relationship is linear but not directly proportional, and the equation is y = mx + c.
一条经过原点的直线表明两个变量成正比关系。方程的形式为 y = kx，其中 k 是斜率。如果直线不经过原点，则关系是线性的但不是正比的，方程为 y = mx + c。
To find the gradient of a straight-line graph, choose two points on the line that are well apart (do not use data points). Gradient = Δy/Δx = (y₂ – y₁) / (x₂ – x₁). The unit of the gradient is the unit of y divided by the unit of x. For a spring graph of force against extension, the gradient gives the spring constant, N/m.
要计算直线图形的斜率，在直线上选取两个相距较远的点（不要使用数据点）。斜率 = Δy/Δx = (y₂ – y₁) / (x₂ – x₁)。斜率的单位是 y 的单位除以 x 的单位。对于力与伸长量的弹簧图，斜率就是弹簧常数，单位为 N/m。
The area under a velocity–time graph gives the distance travelled; the area under a force–distance graph gives the work done. Check what the gradient and intercept mean physically for the experiment you have carried out.
8. Evaluating Results and Drawing Conclusions | 评估结果并得出结论
State clearly whether your results support the original hypothesis or prediction. For example: ‘The graph was a straight line through the origin, confirming that the extension of the spring is directly proportional to the applied force up to the limit of proportionality.’
Identify the main sources of uncertainty or error in your experiment. Typical examples include reaction time when using a stopwatch, difficulty in judging the exact centre of the pendulum bob, parallax when reading a ruler, or energy losses due to friction.
Suggest specific improvements that would increase accuracy or reliability. Instead of saying ‘use better equipment’, propose practical steps: ‘Use a light gate connected to a datalogger to measure the time precisely’, or ‘Clamp the ruler and use a set square to avoid parallax error when reading the pointer position’.
Measuring density: For a regular solid, measure mass using a balance and calculate volume from linear dimensions (e.g. V = l × w × h). For an irregular solid, find volume by displacement in a measuring cylinder or Eureka can. For a liquid, measure mass of the liquid directly and volume with a measuring cylinder. Calculate density ρ = m / V.
测量密度：对于规则固体，用天平测量质量，通过线度计算体积（例如 V = l × w × h）。对于不规则固体，使用量筒或 Eureka 溢出罐通过排水法求体积。对于液体，直接测量液体质量和用量筒测体积。计算密度 ρ = m / V。
Springs and Hooke’s Law: Set up as described. Plot force (weight of masses in N) against extension (cm or m). Gradient equals spring constant k. If too much weight causes a permanent stretch, the limit of proportionality has been passed.
Ohm’s Law circuit: Set up a series circuit with a known resistor, a variable power supply or rheostat, an ammeter in series and a voltmeter in parallel. Vary the voltage, measure I and V. Plot I against V; a straight line through the origin confirms I ∝ V, so resistance R = V/I is constant.
欧姆定律电路：搭建串联电路，包含一个已知电阻、一个可变电源或变阻器、串联一个电流表、并联一个电压表。改变电压，测量 I 和 V。以 I 对 V 作图；过原点的直线证实 I ∝ V，因此电阻 R = V/I 是恒定的。
Reflection and refraction: To verify the law of reflection, use a ray box, a plane mirror on a sheet of paper and a protractor. Trace incident and reflected rays; the angle of incidence should equal the angle of reflection. For refraction, shine a ray through a glass block and measure angles i and r; calculate the refractive index n = sin i / sin r. Note: sin is used, but using sin tables or calculator. Do not attempt to use arcsin in a simple IGCSE context.
反射与折射：要验证反射定律，可使用射线箱、一张纸上的平面镜和量角器。描出入射光线和反射光线；入射角应等于反射角。对于折射，让光线穿过玻璃块，测量角度 i 和 r；计算折射率 n = sin i / sin r。注意：使用正弦，但 IGCSE 通常使用正弦值表格或计算器，不需要反三角函数。
Measuring speed or acceleration: Use a trolley on a ramp with a light gate or ticker-tape timer. For average speed, measure distance travelled and time taken: v = s/t. For acceleration, change the angle and find acceleration from v² = u² + 2as or by measuring final speed after a measured distance.
Pendulum period: Suspend a bob from a string, measure length l from pivot to centre of bob. Time for 20 complete swings and find period T = total time / 20. Investigate how T depends on l. Plot T² against l; you should obtain a straight line through the origin, showing T² ∝ l. From gradient, compare with T = 2π√(l/g).
单摆周期：将摆球悬挂在细线上，测量从悬点到摆球中心的长度 l。记录 20 个完整摆动的时间，求周期 T = 总时间 / 20。探究 T 如何随 l 变化。以 T² 对 l 作图；应得到过原点的直线，表明 T² ∝ l。根据斜率与公式 T = 2π√(l/g) 进行比较。
10. Safety in the Lab | 实验室安全
Always wear eye protection when springs, masses, hot liquids or electrical circuits are involved. Tie back long hair and remove dangling jewellery. Keep the workspace tidy to avoid tripping over bags or cables.
When using weights and springs, do not stand directly underneath the hanging masses; a falling mass could cause injury. Add masses gently and clamp stands securely to the bench.
For electrical circuits, never handle bare wires when the power is on. Use low voltages (typically below 6 V) and switch off the power when making adjustments. Check that insulation is intact and do not overload circuits.
If you are using hot water or a heater, use tongs or heat-resistant gloves. Place hot objects on a heatproof mat. In all cases, know the location of the fire extinguisher and first aid kit.