Physics Exam Prep: Core Experiments & High-Frequency Topics | 物理备考：核心实验归纳与高频考点总结

📚 Physics Exam Prep: Core Experiments & High-Frequency Topics | 物理备考：核心实验归纳与高频考点总结

Practical work is a core part of A-Level physics, and examiners love to test the methodology behind each experiment: how to measure, how to reduce errors, and how to analyse the data graphically. This article gathers the most frequently tested experiments and the key skills you need to score full marks.

实验是 A-Level 物理的核心环节，考官特别喜欢考查实验背后的方法：如何测量、如何减小误差、如何作图分析。本文汇总了最高频的实验考点和拿分技巧，帮助你在考前高效复盘。

1. Measurement Instruments & Uncertainties | 测量仪器与不确定度

Common instruments include the vernier calliper (resolution 0.01 mm) and the micrometer screw gauge (resolution 0.001 mm). Digital instruments usually show their absolute uncertainty directly; for analogue instruments we quote half the smallest division.

常用测量仪器包括游标卡尺（分辨率 0.01 mm）和螺旋测微器（分辨率 0.001 mm）。数字式仪表通常直接给出绝对不确定度；模拟式仪表则取最小刻度的一半。

For repeated readings, the random uncertainty is often estimated as half the range: (maximum − minimum) ÷ 2. Systematic errors, such as a zero error, affect every reading equally.

对于多次重复读数，随机不确定度通常取“极差的一半”：(最大值 − 最小值) ÷ 2。系统误差（如零误差）则影响每次读数的整体偏移。
Know the percentage uncertainty formula: percentage uncertainty = (absolute uncertainty ÷ measured value) × 100%.

必须掌握百分比不确定度公式：百分比不确定度 = (绝对不确定度 ÷ 测量值) × 100%。
When combining uncertainties, add absolute uncertainties for addition/subtraction and add percentage uncertainties for multiplication/division/powers.

不确定度的合成规则：加减法用绝对不确定度相加；乘除法或幂运算用百分比不确定度相加。

2. Free Fall & Acceleration Due to Gravity | 自由落体与重力加速度

This experiment aims to measure g by timing a falling object over known distances. With light gates, the time between two gates gives the average velocity; with a trapdoor timer, electronic timing avoids human reaction error.

该实验通过测量物体下落通过已知距离的时间来求重力加速度 g。使用光电门可测平均速度；利用电子计时器或“陷阱门”装置则可避免人眼反应误差。

s = ½gt² ⇒ plot s against t², gradient = g/2

Release the ball from rest using an electromagnet; ensure the ball falls vertically and that s is measured from the bottom of the ball to the trapdoor.

用电磁铁释放小球，保证初速度为零；确保高度 s 从小球底部量到计时器落点。
Take multiple readings for each height and plot s on the y-axis against t² on the x-axis. The slope of the straight line gives g/2, so g = 2 × gradient.

每个高度重复多次，以 s 为纵轴、t² 为横轴作图。直线的斜率等于 g/2，因此 g = 2 × 斜率。
Systematic errors include air resistance and measuring from the wrong point; random errors come from timing and parallax. Using a digital timer or light gates improves precision.

系统误差包括空气阻力、高度测量起点错误；随机误差来自计时和视差。使用数字计时器或光电门可以提高精确度。

3. Hooke’s Law & Spring Constant | 胡克定律与劲度系数

Hooke’s law states that the extension of a spring is proportional to the applied force, provided the limit of proportionality is not exceeded. The spring constant k is the force per unit extension.

胡克定律指出：在比例极限内，弹簧的伸长量与所受外力成正比。劲度系数 k 表示单位伸长量所需的外力。

F = kΔL ⇒ gradient of F − ΔL graph = k

Use a metre ruler to measure the initial length of the spring, then add masses one by one and record the new length. Extension ΔL = new length − original length.

用米尺测量弹簧原长，然后逐次增加砝码并记录新的长度。伸长量 ΔL = 新长度 − 原长。
Plot F on the y-axis against ΔL on the x-axis. A straight line through the origin confirms Hooke’s law; the slope equals k in N m⁻¹.

以 F 为纵轴、ΔL 为横轴作图。过原点的直线验证胡克定律；斜率即为劲度系数 k，单位 N m⁻¹。
Avoid exceeding the elastic limit: take care not to overload the spring; remove masses and test whether the spring returns to its original length. Add weights gently to avoid oscillations.

不要超过弹性限度：避免加载过重；取下砝码后应检查弹簧是否回到原长。加砝码时要轻放，防止弹簧振动。

4. Stationary Waves & Speed of Sound | 驻波与声速测定

Stationary wave experiments commonly use a vibrating string or a sound tube. On a string, the fundamental frequency is related to string length, tension and mass per unit length.

驻波实验常使用振动弦线或声波管。对弦线而言，基频与弦长、张力和线密度有关。

v = √(T/μ), f = v/(2L) ⇒ plot f against 1/L, slope = v/2

Keep the tension constant using a hanging mass over a pulley; vary L by adjusting the position of a movable bridge until a clear stationary wave forms.

用跨过滑轮的悬挂重物保持张力恒定；通过移动桥的位置改变弦的有效长度 L，直到出现稳定的驻波。
Record the resonance length L for different frequencies from a signal generator. Plot frequency f against 1/L; the gradient equals v/2, allowing you to calculate wavelength or wave speed.

记录信号发生器在不同频率下的共振弦长 L。作 f 与 1/L 图，斜率为 v/2，可进一步求波速或波长。
For sound speed, use a tube with a loudspeaker and a microphone or a tuning fork; find the first and second resonance lengths. The difference between successive antinodes equals λ/2.

测声速时可用扬声器和传声器（或音叉）配合共鸣管；找出相邻两次共振长度之差，正好等于半波长 λ/2。

5. Refractive Index & Critical Angle | 折射率与临界角

Snell’s law links the angles of incidence and refraction with the refractive index. Candidates are often asked to plot a straight-line graph to determine n.

斯涅耳定律将入射角与折射角同折射率联系起来。考试中常要求通过线性图像来求折射率 n。

n = sin i / sin r ⇒ plot sin i against sin r, gradient = n

Use a ray box and a semicircular glass block. The flat face allows a straight incident ray; mark the ray paths and measure angles with a protractor.

使用 ray box 和半圆形玻璃砖。让光线从平面射入，描出光路后用量角器测量入射角 i 与折射角 r。
Repeat for multiple angles, then plot sin i on the y-axis against sin r on the x-axis. The slope gives the refractive index; the line should pass through the origin.

改变入射角多次测量，以 sin i 为纵轴、sin r 为横轴作图。斜率即折射率 n，直线应过原点。
For total internal reflection, the critical angle c satisfies sin c = 1/n. Use the curved face as the entry face and vary the angle inside the block until the emergent ray disappears.

全反射时临界角 c 满足 sin c = 1/n。让光线从弧面射入，逐渐增大内部入射角，直到折射光刚好消失，即可读出临界角。

6. Ohm’s Law & I–V Characteristics | 欧姆定律与伏安特性

Ohm’s law applies to metallic conductors at constant temperature. Components such as filament lamps and diodes show non-ohmic behaviour because their resistance changes with current.

欧姆定律适用于温度恒定的金属导体。白炽灯和二极管具有非欧姆特性，因为其电阻随电流变化。

Build a circuit with a variable resistor (rheostat) to control the potential difference. Connect the ammeter in series and the voltmeter in parallel with the component.

用滑动变阻器（电位器）控制电压。电流表与元件串联，电压表与元件并联。
Record pairs of I and V over the full range. For a fixed resistor, plot V against I: the gradient is R. For a filament lamp, the curve flattens because resistance increases with temperature.

在量程范围内记录多组 (I, V) 数据。定值电阻的 V–I 图为直线，斜率等于 R；灯泡的曲线逐渐变平，说明温度升高导致电阻增大。
For a diode, reverse current is negligible and forward current rises sharply after a threshold voltage. Always include a protective resistor to avoid overheating.

二极管的反向电流几乎为零，正向电流超过阈值电压后急剧上升。实验中应串联保护电阻，防止过热损坏元件。

7. Resistivity & Metre Bridge | 电阻率与滑线电桥

The resistivity of a wire can be found by measuring its resistance R, its length L and its cross-sectional area A. Use a metre bridge to measure R more precisely than with an ohmmeter.

测量金属丝电阻率需要测电阻 R、长度 L 和横截面积 A。使用滑线电桥（惠斯通电桥）可比欧姆表获得更精确的电阻值。

ρ = RA/L, A = πd²/4 ⇒ plot R against L, slope = ρ/A

Measure the diameter d with a micrometer at several points and in two perpendicular directions; average d and use A = πd²/4.

用螺旋测微器在多个位置、两个互相垂直方向测量直径 d，取平均后再计算横截面积 A = πd²/4。
Use a metre bridge to measure R for different lengths L of wire. Plot R on the y-axis against L on the x-axis; the slope equals ρ/A.

用滑线电桥测量不同长度 L 下的电阻 R。以 R 为纵轴、L 为横轴作图，斜率为 ρ/A。
Keep the wire straight, avoid stretching it, and ensure room temperature is constant because resistivity depends on temperature. Account for end errors by using a “zero-length” correction.

保持金属丝拉直且避免拉伸；由于电阻率随温度变化，应保持室温恒定。还要考虑端部修正（end correction）以消除接触电阻影响。

8. Internal Resistance & EMF | 内阻与电动势

A battery can be modelled as an ideal EMF in series with an internal resistance r. Measuring the terminal voltage V as current I changes allows both E and r to be found.

电池可等效为理想电动势与内阻 r 的串联。通过测量不同电流下的路端电压 V，可同时求出电动势 E 和内阻 r。

E = V + Ir ⇒ V = −rI + E

Vary the load using a variable resistor (or a few known resistors) and record corresponding voltmeter and ammeter readings.

用滑动变阻器（或若干已知电阻）改变外电路负载，记录每一组电压表和电流表读数。
Plot V on the y-axis against I on the x-axis. The y-intercept equals the EMF E; the gradient equals −r, so internal resistance is the negative gradient.

以 V 为纵轴、I 为横轴作图。纵轴截距等于电动势 E；斜率为 −r，因此内阻等于斜率的相反数。
Take readings quickly and over a wide range of currents. Alternatively, measure the open-circuit voltage (I = 0) directly as E, but the graph method is more reliable.

测量速度要快，且电流变化范围要大。也可直接测开路电压（I = 0）视为 E，但作图法的可靠性更高。

9. Capacitor Charge / Discharge | 电容充放电

When a capacitor discharges through a resistor, the voltage decays exponentially. The time constant τ = RC determines how quickly the capacitor discharges.

电容器经电阻放电时，电压呈指数衰减。时间常数 τ = RC 决定放电快慢。

V = V₀ e^(−t/RC) ⇒ plot ln V against t, gradient = −1/RC

Charge the capacitor fully, then discharge through a known resistor while logging V and t with a data logger or voltmeter at regular intervals.

先将电容器充满电，再经已知电阻放电。使用数据采集器或电压表按固定时间间隔记录 V 和 t。
Plot the natural logarithm of V against t. Since ln V = ln V₀ − t/RC, the slope is linear and equals −1/RC. Use a known R to calculate C.

作 ln V 对 t 的图。因为 ln V = ln V₀ − t/RC，图像为直线，斜率等于 −1/RC。已知 R 即可求出 C。
Alternatively, measure the current during discharge; the area under the I–t graph gives the total charge Q, so C = Q/V₀.

也可测量放电过程中的电流；I–t 图线下的面积等于总电荷量 Q，从而 C = Q/V₀。

10. Half-Life & Radioactive Decay | 半衰期与放射性衰变

Radioactive decay follows a statistical exponential law. The half-life t½ can be found by plotting the activity or corrected count rate against time.

放射性衰变服从统计性的指数规律。通过记录计数率随时间变化，可求出半衰期 t½。

t½ = ln2/λ ⇒ plot ln(activity) against t, gradient = −λ

First measure and subtract the background radiation count by taking readings with no source present. Then record the count rate of the source at regular time intervals.

首先在无放射源时测量本底计数并扣除。然后按固定时间间隔记录放射源的计数率。
Plot ln(activity) against time. The negative gradient gives the decay constant λ, and then t½ = ln2/λ. This method is more accurate than reading half-life from a curve.

作 ln(活度) 对时间的图。直线斜率的相反数为衰变常数 λ，再由 t½ = ln2/λ 求半衰期。这比直接从曲线上读半衰期更准确。
Keep the distance between the source and GM tube constant; use repeated readings and a long enough total time to reduce random fluctuations.

保持放射源与盖革计数器之间的距离不变；多次重复读数，并让总测量时间足够长，以减少随机涨落的影响。

11. Photoelectric Effect Basics | 光电效应基础

The photoelectric effect provides evidence for the photon model. The key equation connects photon energy, work function and maximum kinetic energy of emitted electrons.

光电效应为光子模型提供了关键证据。其核心方程将光子能量、逸出功和电子最大动能联系在一起。

hf = Φ + K_max, eVs = K_max

In the experiment, a photosensitive metal plate is illuminated with monochromatic light. The stopping potential Vs just prevents photoelectrons from reaching the anode.

实验中用单色光照射金属板，恰好阻止光电子到达阳极的反向电压即截止电压 Vs。
Vary the frequency f of the light and measure the corresponding stopping potential Vs. Plot Vs against f: the slope is h/e, and the x-intercept equals the threshold frequency f₀.

改变入射光频率 f，测量对应的截止电压 Vs。作 Vs 对 f 的图，斜率为 h/e，与横轴的交点就是截止频率 f₀。
Hence the work function Φ = hf₀. If you know e, the Planck constant can be obtained directly from the gradient.

因此逸出功 Φ = hf₀。若已知电子电荷 e，由图像斜率可直接求得普朗克常数 h。

12. Graph Skills & Error Analysis | 作图技巧与误差分析

Many experiment questions do not ask for the result, but for the graph you would draw and how you would improve reliability. Master these universal skills before the exam.

很多实验题不直接问结果，而是考“作什么图”和“如何提高可靠性”。考前一定要掌握这些通用技能。

Choose linearised plots that produce a straight line, and state clearly what the gradient and intercept represent physically.

尽量选择能变成直线的线性化作图，并清楚说明斜率和截距的物理意义。
When plotting, put the independent variable on the x-axis and the dependent variable on the y-axis; use a sharp pencil, error bars if needed, and a line of best fit that balances the points.

作图时自变量在 x 轴、因变量在 y 轴；用削尖的铅笔画图，需要时画出误差棒，使最佳拟合线位于数据点之间平衡的位置。
To reduce uncertainty: repeat readings, take a wider range, use digital sensors, ensure controlled variables are kept constant, and remove systematic errors like zero errors.

减小不确定度的方法：多次测量取平均、扩大测量范围、改用数字传感器、控制变量不变，以及修正零误差等系统误差。
In “suggest an improvement” questions, focus on one specific source of error and state the practical change, not just “be more careful”.

遇到“提出改进建议”的题目，要针对某个具体误差来源说明实际改动，不能笼统地写“更仔细”或“操作准确”。

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Physics Exam Prep: Core Experiments & High-Frequency Topics | 物理备考：核心实验归纳与高频考点总结