📚 Excelling in AS Physics Practical Investigations: Insights from PH02 January 2023 | 精通AS物理实验探究：2023年1月PH02试卷深度解析
The PH02 International AS Physics paper of January 2023 provides a brilliant framework for sharpening practical investigation skills required at this level. Across its structured questions, you encounter core experiments such as determining the acceleration of free fall, measuring the resistivity of a wire, and validating Ohm’s law. This article unpacks the experimental techniques, data analysis methods, and error evaluation approaches that are embedded in that paper, offering a revision companion designed to boost your confidence and accuracy in AS practical-based assessments.
2023年1月的PH02国际AS物理试卷为训练这个阶段所需的实验探究技能提供了绝佳的框架。在试卷的结构化问题中，你会遇到测定重力加速度、测量金属丝电阻率以及验证欧姆定律等核心实验。本文深入解析了这份试卷中涉及的实验技术、数据分析方法和误差评估方式，提供一份旨在提升你在AS实验类评估中信心与准确度的复习指南。
1. Understanding the Structure of PH02 Practical Questions | 理解PH02实验题结构
The PH02 paper typically presents practical-based questions in a scaffolded manner: you are asked to identify suitable apparatus, outline a procedure, record and tabulate readings, process data using correct formulae, draw and analyse graphs, and finally evaluate sources of error together with possible improvements. Marks are distributed across all these competencies, so a systematic approach is vital.
PH02试卷通常以递进的方式呈现实验类试题：要求你确定合适的仪器、概述实验步骤、记录并列表读数、用正确公式处理数据、绘制并分析图像，最后评估误差来源并提出可能的改进措施。分数分布在这些能力点上，因此系统化的解题思路至关重要。
Familiarity with the mark scheme language is also key. Examiners expect precise terminology, such as ‘systematic error’, ‘zero error’, ‘parallax error’, ‘percentage uncertainty’, and ‘line of best fit’. Knowing how to justify the number of significant figures in a calculated value is equally important.
熟悉评分标准的措辞同样关键。考官期望准确的术语，例如”系统误差”、”零误差”、”视差”、”百分比不确定度”和”最佳拟合线”。懂得如何说明计算值有效数字位数的合理性也同样重要。
2. Experiment 1: Determining g Using a Simple Pendulum | 实验一：用单摆测定重力加速度g
One of the classic investigations reappearing in AS practicals is the determination of g. The relationship T = 2π√(L/g) is rearranged to g = 4π²L / T². By varying the length L of a light string and measuring the period T for small-amplitude oscillations, you can deduce g either by direct calculation for each trial or, more reliably, from the gradient of a T²–L graph.
AS实验中反复出现的经典探究之一就是测定重力加速度g。公式T = 2π√(L/g)可变形为g = 4π²L / T²。通过改变轻质细线的长度L并测量小振幅摆动下的周期T，你可以通过每次试验直接计算g，或者更可靠地通过T²–L图像的斜率求出g。
A typical data set collected by a student might look like the table below. The time for 20 oscillations is recorded to reduce the impact of reaction time, and the period T is then found by dividing by 20. Uncertainty in L is ±0.001 m if a metre rule is carefully used; uncertainty in t₂₀ might be ±0.2 s.
学生采集的一组典型数据可能如下表所示。记录20次摆动的时间以减少反应时间的影响，然后将总时间除以20得到周期T。若仔细使用米尺，L的不确定度为±0.001 m；t₂₀的不确定度可能为±0.2 s。
| L (m) | t₂₀ (s) | T (s) | T² (s²) |
|---|---|---|---|
| 0.600 | 31.2 | 1.56 | 2.43 |
| 0.800 | 36.0 | 1.80 | 3.24 |
| 1.000 | 40.2 | 2.01 | 4.04 |
| 1.200 | 44.1 | 2.21 | 4.88 |
Plotting T² against L yields a straight line through the origin. The gradient m is equal to 4π²/g, therefore g = 4π²/m. The PH02 paper often asks you to calculate the gradient, determine g, and comment on the agreement with the accepted value of 9.81 m s⁻².
绘制T²–L图可得到一条通过原点的直线。斜率m等于4π²/g，因此g = 4π²/m。PH02试卷经常要求你计算斜率、求出g值，并就其结果与公认值9.81 m s⁻²的一致性做出评论。
3. Experiment 2: Measuring the Resistivity of a Metal Wire | 实验二：测量金属丝的电阻率
The resistivity ρ of a wire is found from the formula ρ = RA/L, where R is resistance, A is cross-sectional area, and L is length. A is calculated using the wire’s diameter d: A = πd²/4. Hence, ρ = (V/I) × (πd²/4) / L = πVd² / (4IL). The PH02 paper might require you to describe how to measure d with a micrometer screw gauge (resolution 0.01 mm) and to minimise the error by measuring at several orientations along the wire.
金属丝的电阻率ρ通过公式ρ = RA/L求得，其中R是电阻，A是横截面积，L是长度。A通过金属丝直径d计算：A = πd²/4。因此，ρ = (V/I) × (πd²/4) / L = πVd² / (4IL)。PH02试卷可能要求你描述如何用螺旋测微器（分度值0.01 mm）测量直径d，并通过沿金属丝多处测量不同方位来减小误差。
A common circuit includes a power supply, ammeter in series with the wire, and voltmeter in parallel across the test length. A variable resistor is used to control the current and prevent significant heating. The table below simulates a set of readings, with the calculated resistance R = V/I for each trial.
常见电路包含电源串联安培计并与待测金属丝连接，伏特计并联在测试长度两端，并使用变阻器控制电流以防止明显发热。下表模拟了一组读数，每次试验都计算了电阻R = V/I。
| d (mm) | L (m) | V (V) | I (A) | R = V/I (Ω) |
|---|---|---|---|---|
| 0.25 | 1.000 | 2.10 | 0.42 | 5.00 |
| 0.25 | 0.800 | 1.68 | 0.42 | 4.00 |
From these, ρ can be calculated. Note that uncertainty in d has the largest impact because it appears squared. Using the percentage uncertainty rule Δρ/ρ ≈ 2(Δd/d) + ΔV/V + ΔI/I + ΔL/L helps quantify the overall uncertainty.
由此可计算ρ。注意直径d的不确定度影响最大，因为它以平方形式出现。应用百分比不确定度规则Δρ/ρ ≈ 2(Δd/d) + ΔV/V + ΔI/I + ΔL/L，有助于量化总不确定度。
4. Investigating Ohm’s Law and I-V Characteristics | 探究欧姆定律与I-V特性
To verify Ohm’s law for a metallic conductor at constant temperature, you change the applied voltage using a potential divider or variable resistor and record the corresponding current. A graph of I versus V yields a straight line through the origin, confirming that I ∝ V. The reciprocal of the gradient gives the resistance R.
为了验证恒温下金属导体的欧姆定律，你利用分压器或变阻器改变施加的电压，并记录相应的电流。I–V图是一条过原点的直线，证实I ∝ V。斜率的倒数即为电阻R。
In the PH02 paper, you might also compare a fixed resistor with a filament lamp or diode. For the lamp, the I-V graph curves away from the straight line at higher voltages because the filament temperature increases, raising its resistance. A diode shows negligible current until a threshold voltage is reached, after which forward current rises steeply. Being able to sketch these characteristics and link them to microscopic behaviour is frequently examined.
在PH02试卷中，你可能还需要比较固定电阻器与灯丝灯泡或二极管的特性。灯泡的I–V图在高电压下偏离直线，因为灯丝温度升高导致电阻增大。二极管在达到阈值电压之前电流极小，此后正向电流急剧上升。能够画出这些特性曲线并将其与微观机制联系起来，是经常考查的内容。
5. Data Analysis: Handling Uncertainties and Errors | 数据分析：处理不确定度与误差
Every measured quantity carries an absolute uncertainty. For a metre rule it is typically ±1 mm, for a digital ammeter it might be ±0.01 A, and for a stopwatch ±0.1 s. When combining measurements, the rules for uncertainties depend on the mathematical operation. For quantities added or subtracted, absolute uncertainties add. For multiplication, division, or powers, percentage uncertainties are added, paying attention to the power index.
每个被测量都带有绝对不确定度。米尺的典型不确定度为±1 mm，数字安培计可能为±0.01 A，秒表为±0.1 s。当测量值组合时，不确定度规则取决于运算方式。加减运算时，绝对不确定度直接相加；乘除或幂运算时，百分比不确定度相加，并注意指数。
Consider ρ = πVd² / (4IL). If V = 2.10 ± 0.01 V (0.48%), I = 0.42 ± 0.01 A (2.4%), d = 0.25 ± 0.01 mm (4.0%), and L = 1.000 ± 0.001 m (0.1%), then percentage uncertainty in ρ ≈ 0.48% + 2×4.0% + 2.4% + 0.1% = 11.0%. This shows that improving the diameter measurement — by using a micrometer with smaller uncertainty or taking more readings — has the greatest effect on overall precision.
以ρ = πVd² / (4IL)为例。若V = 2.10 ± 0.01 V (0.48%)，I = 0.42 ± 0.01 A (2.4%)，d = 0.25 ± 0.01 mm (4.0%)，L = 1.000 ± 0.001 m (0.1%)，则ρ的百分比不确定度 ≈ 0.48% + 2×4.0% + 2.4% + 0.1% = 11.0%。由此可见，改进直径测量——通过使用不确定度更小的螺旋测微器或增加读数次数——对整体精度影响最大。
6. Graph Plotting and Gradient Calculations | 绘图与斜率计算
Good graph practice is heavily rewarded. Use more than half of the graph paper in both directions, label axes with quantities and units (e.g., T² / s²), and avoid awkward scales such as divisions of 3. Plot data points with small neat crosses, then draw a single straight line of best fit that has a roughly equal number of points on either side.
规范的绘图技巧能赢得可观的分数。两轴方向都要利用坐标纸一半以上的区域，坐标轴标注物理量及单位（如T² / s²），避免使用诸如一格代表3的别扭标度。用细小整齐的十字标出数据点，然后画出唯一的最佳拟合直线，使两侧点的数量大致相等。
The gradient is taken from a large triangle drawn on the line, not from data points. Coordinates (x₁, y₁) and (x₂, y₂) from the line give m = (y₂ – y₁) / (x₂ – x₁). In the pendulum case, m = 4π²/g, so g = 4π²/m. If the line does not pass through the origin, a systematic error may be present — such as a miscalibrated rule or an incorrect zero for the length measurement of the pendulum.
计算斜率要利用在拟合线上画出的大三角形，而非直接使用数据点。线上的坐标(x₁, y₁)和(x₂, y₂)给出斜率m = (y₂ – y₁) / (x₂ – x₁)。在单摆实验中，m = 4π²/g，因此g = 4π²/m。若拟合线不通过原点，可能存在系统误差——例如米尺刻度不准确或单摆长度测量的零点不正确。
7. Evaluating Systematic vs Random Errors | 评估系统误差与随机误差
Systematic errors shift all readings in the same direction. Examples include a zero error in a micrometer or ammeter, a clock that runs consistently slow, or ignoring the mass of the pendulum string. These affect accuracy but not precision, and they cannot be reduced by taking more readings — only by correcting the instrument or refining the procedure.
系统误差使所有读数向同一方向偏移。例如螺旋测微器或安培计的零误差、走时偏慢的秒表，或忽略了摆线质量。此类误差影响准确度但不影响精密度，增加测量次数无法减小它——只能通过校正仪器或改进操作流程来消除。
Random errors scatter readings around the true value due to unpredictable variations, such as reaction time in starting and stopping a stopwatch or fluctuations in the power supply. Repeating measurements and averaging helps minimise their effect. In a graph, the scatter of points indicates the extent of random uncertainty; error bars are drawn to represent the absolute uncertainty in each variable.
随机误差因难以预测的变化使读数分散在真值周围，例如启动和停止秒表时的反应时间或电源的波动。重复测量并取平均值有助于减小其影响。在图像上，数据点的分散程度指示随机不确定度的大小；可绘制误差棒来表示每个变量上的绝对不确定度。
8. Improving Experimental Precision | 提高实验精度
Precision can be enhanced by using instruments with higher resolution, timing many oscillations (e.g., 20 or 50), and taking diameter measurements in multiple orientations and positions along the wire. In electrical experiments, allowing the current to stabilise and avoiding significant heating also improves repeatability.
通过使用分辨率更高的仪器、记录多次摆动次数（如20或50次）、在金属丝多个方向和位置测量直径，可以提升精密度。在电学实验中，让电流稳定并避免显著发热也能改善重复性。
Digital sensors and data loggers, where available, dramatically reduce human reaction errors. However, even with basic equipment, careful technique — such as aligning the eye perpendicular to the scale to avoid parallax — makes a measurable difference. The PH02 mark scheme often credits these small but crucial details.
若条件允许，使用数字传感器和数据记录仪可大幅减小人为反应误差。但即使使用基础设备，仔细的操作——如眼睛垂直于刻度以消除视差——也能产生可观的改善。PH02评分标准通常会对这些细小但关键的细节给分。
9. Interpreting Anomalous Data Points | 解释
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