📚 PH02 Experimental Investigation Review (23 May 2023) | PH02 实验探究复习 (2023年5月23日)
The PH02 International AS Physics paper for 23 May 2023 included a demanding experimental investigation that tested students’ ability to plan, carry out, analyse and evaluate a practical task. In this article, we break down the core structure of such an investigation, using resistivity measurement as a model example, to help you master the essential skills examined in PH02 practical questions. Whether you are preparing for a resit or simply consolidating your understanding of experimental physics, this guide will walk you through each critical stage with clarity and academic precision.
2023年5月23日的PH02国际AS物理试卷包含了一道颇具挑战性的实验探究题，考查了学生规划、实施、分析和评价实际实验任务的能力。本文以电阻率测量为范例，拆解这类探究题的核心结构，帮助你掌握PH02实验题所考察的关键技能。无论你是在为补考做准备，还是想巩固对实验物理的理解，本指南都会清晰而严谨地引导你走完每一个重要环节。
1. Understanding the Experimental Context | 了解实验背景
In the PH02 syllabus, experimental investigations often revolve around one of the core topics: mechanics, materials, waves, or electricity. The May 2023 paper placed a strong emphasis on electrical measurements, specifically the determination of the resistivity of a metal wire. The question required students to demonstrate familiarity with the underlying principle that resistance R is directly proportional to the length L of a uniform conductor, with the proportionality constant being ρ/A, where ρ is the resistivity and A is the cross-sectional area.
在PH02教学大纲中，实验探究通常围绕力学、材料、波或电学等核心课题展开。2023年5月的试卷重点考查了电学测量，具体内容是测定金属导线的电阻率。题目要求学生熟练掌握其基本原理：均匀导体的电阻R与长度L成正比，比例系数为ρ/A，其中ρ为电阻率，A为横截面积。
Understanding this context is vital because the practical assessment is not merely about following a recipe but about applying theoretical knowledge to design a reliable procedure, minimise uncertainty, and interpret graphical data. The resistivity experiment, with its straightforward linear relationship, provided an excellent platform for testing these competencies.
理解这一背景至关重要，因为实验评估并非只是照方抓药，而是要求将理论知识用于设计可靠的步骤、减小不确定度并解读图像数据。电阻率实验具有简单的线性关系，为考查这些能力提供了一个绝佳的平台。
2. Planning the Investigation | 实验计划
The first step in any PH02 practical question is to formulate a clear plan. The candidate must identify the independent, dependent, and control variables. For resistivity, the independent variable is the length L of the wire; the dependent variable is the resistance R (or the current I and voltage V from which R is calculated); control variables include the temperature and the material of the wire, as well as its cross-sectional area A.
任何PH02实验题的第一步都是拟定清晰的计划。考生必须确定自变量、因变量和控制变量。在电阻率实验中，自变量是导线的长度L；因变量是电阻R（或电流I与电压V，由此计算R）；控制变量包括导线的温度、材料以及横截面积A。
A common planning requirement is to describe how to measure the diameter of the wire using a micrometer screw gauge. The plan should state that multiple readings should be taken along the wire to obtain a mean diameter and to check for uniformity. The length L needs to be measured with a metre ruler, and the distance between the probes or crocodile clips must be recorded carefully to avoid parallax error.
典型的计划要求是描述如何使用千分尺测量导线直径。计划中应说明，要在导线的不同位置多次测量以求得平均直径并检查其均匀性。长度L需用米尺测量，并须仔细记录探针或鳄鱼夹之间的距离，以避免视差误差。
Moreover, the circuit design should be sketched: a simple series circuit consisting of the test wire, a power supply, an ammeter, and a switch, with a voltmeter connected in parallel across the wire section being measured. It is also advisable to include a rheostat to control the current and limit heating effects.
此外，还应画出电路设计简图：一个由待测导线、电源、电流表和开关组成的简单串联电路，并在所测导线段两端并联一个电压表。建议加入变阻器以控制电流并限制热效应。
3. Gathering and Recording Data | 收集与记录数据
When gathering data, precision and consistency are paramount. The length of the wire should be varied in regular increments, e.g. from 0.20 m up to 1.00 m, recording the corresponding current I and potential difference V for each length. The resistance R is calculated using R = V/I. It is good practice to take repeat readings for each length and then average them to reduce random error.
收集数据时，精确性和一致性至关重要。导线的长度应按固定步长变化，例如从0.20 m增至1.00 m，记录每段长度对应的电流I和电压V。电阻R由R = V/I计算得出。优良的做法是对每个长度进行重复测量并取平均值，以减小随机误差。
A sample data table is shown below. Notice how the columns are clearly labelled with units and that calculated quantities are presented alongside raw data.
下面是一个示例数据表。注意各列均清晰标明了单位，且计算所得的量与原始数据并列展示。
| Length L / m | Current I / A | Potential difference V / V | Resistance R / Ω |
|---|---|---|---|
| 0.20 | 0.48 | 0.92 | 1.92 |
| 0.40 | 0.47 | 1.80 | 3.83 |
| 0.60 | 0.46 | 2.64 | 5.74 |
| 0.80 | 0.46 | 3.54 | 7.70 |
| 1.00 | 0.45 | 4.35 | 9.67 |
Recording the diameter d is equally crucial. The micrometer should be used at several points and the readings recorded to at least 0.01 mm precision. Suppose the following diameters were obtained: 0.274 mm, 0.276 mm, 0.275 mm. The mean diameter is calculated, and the radius r is found, allowing the cross-sectional area A = πr² to be determined.
记录直径d同样至关重要。应在不同位置使用千分尺，并记录读数至至少0.01 mm精度。假设获得以下直径：0.274 mm、0.276 mm、0.275 mm。计算平均直径，求得半径r，进而确定横截面积A = πr²。
4. Graphical Analysis and Linearization | 图像分析与线性化
The PH02 investigation expects students to plot a suitable graph that yields a straight line through the origin, confirming the mathematical model R = (ρ/A) L. A graph of R (y-axis) against L (x-axis) should be plotted on graph paper, with axes scaled appropriately and labelled with units. The experimental points should be marked clearly, and a line of best fit drawn.
PH02实验探究要求考生绘制合适的图像，得到一条通过原点的直线，以验证数学模型R = (ρ/A)L。应在坐标纸上绘制R（y轴）相对L（x轴）的图像，坐标轴比例须得当，并标注单位。实验点应清晰标出，并画出最佳拟合线。
If the best-fit line passes through the origin within experimental error, the prediction is verified. The gradient of the line, m, is given by m = ΔR/ΔL = ρ/A. Therefore, resistivity ρ can be expressed as ρ = m × A.
若最佳拟合线在实验误差范围内通过原点，则验证了预测。该直线的斜率m由m = ΔR/ΔL = ρ/A给出。因此，电阻率ρ可表示为ρ = m × A。
Placing the relationship in a linear form is a skill tested repeatedly in PH02. Candidates must avoid common pitfalls such as forcing the line through the origin when it is not justified or misreading scale divisions.
将关系式线性化是PH02反复考查的一项技能。考生必须避免常见的错误，比如在没有依据的情况下强行让直线通过原点，或者错误读取分度值。
5. Calculating Resistivity from the Graph | 从图像计算电阻率
Using the gradient from the graph and the pre-calculated cross-sectional area, the resistivity is determined. For example, if the gradient m is found to be 9.60 Ω m⁻¹ and the mean wire diameter is 0.275 mm, then the radius r = 0.1375 × 10⁻³ m, and area A = π(0.1375 × 10⁻³)² = 5.94 × 10⁻⁸ m². The resistivity is thus:
利用图像斜率和预先计算的横截面积即可确定电阻率。举例来说，若求得斜率m为9.60 Ω m⁻¹，平均导线直径为0.275 mm，则半径r = 0.1375 × 10⁻³ m，面积A = π(0.1375 × 10⁻³)² = 5.94 × 10⁻⁸ m²。因此，电阻率为：
ρ = m × A = 9.60 × 5.94 × 10⁻⁸ = 5.70 × 10⁻⁷ Ω m
This value can be compared with the accepted resistivity for the material, e.g. constantan (~4.9 × 10⁻⁷ Ω m) or nichrome (~1.1 × 10⁻⁶ Ω m). Any discrepancy should be discussed in the evaluation, with reference to experimental uncertainties.
该值可与材料公认的电阻率进行比较，例如康铜（约4.9 × 10⁻⁷ Ω m）或镍铬合金（约1.1 × 10⁻⁶ Ω m）。在评估环节应结合实验不确定度讨论任何偏差。
6. Uncertainty Evaluation | 不确定度评估
Evaluating total uncertainty is a feature of high-mark PH02 questions. For resistivity, the percentage uncertainty is found by combining the uncertainties in length, diameter, and resistance. The expression is:
评估总不确定度是PH02高分题的特色。对于电阻率，其百分数不确定度由长度、直径和电阻的不确定度合成得到。表达式为：
Δρ/ρ = ΔR/R + 2(Δd/d) + ΔL/L (for uncorrelated, independent measurements)
If, for instance, ΔL = ±0.01 m, Δd = ±0.01 mm on a d=0.275 mm, and ΔR from the graph is ±0.10 Ω on a typical R, the total percentage uncertainty can be computed. Candidates should then quote the final resistivity with an appropriate absolute uncertainty.
举例来说，若ΔL = ±0.01 m，在d=0.275 mm时Δd = ±0.01 mm，且由图像得出的ΔR为±0.10 Ω（典型R值），即可计算总百分数不确定度。之后，考生应用适当的绝对不确定度表示最终的电阻率。
PH02 examiners look for clear demonstration that the student understands how to scale uncertainties using the partial derivative method, especially the factor of 2 in the diameter term because A ∝ d². This is a frequent differentiator between grade levels.
PH02考官会留意考生是否能清晰展示如何用偏导数法缩放不确定度，特别是直径项因A ∝ d²而引入的因子2。这经常是区分不同成绩等级的关键点。
7. Common Sources of Error and Improvements | 常见误差来源与改进
A significant portion of the experimental investigation mark is reserved for evaluating the procedure and suggesting improvements. Common errors in the resistivity experiment include heating of the wire, which increases resistance and distorts the linear relationship; parallax error when measuring length; zero error on the micrometer; and contact resistance at the crocodile clips.
实验探究题有相当一部分分数用于评价实验步骤并建议改进。电阻率实验中常见的误差包括：导线发热导致电阻增大并使线性关系失真；测量长度时的视差误差；千分尺的零点误差；以及鳄鱼夹处的接触电阻。
To reduce heating, candidates should suggest switching the current off between readings or using a low current. Parallax error can be minimised by reading the scale at eye level and using a ruler with a mirror strip. Zero error should be checked and corrected before usage. Contact resistance can be mitigated by using knife-edge probes and by ensuring tight, clean connections.
为减少发热，考生应建议在两次读数之间关闭电流或使用低电流。视差误差可通过在视线水平读数和使用带镜面标尺的直尺来减小。使用前应检查并修正零点误差。接触电阻可通过使用刀刃探针并确保连接紧密、清洁来减轻。
Additionally, the diameter measurement is a dominant source of uncertainty; therefore, the improvement could involve using a travelling microscope for higher precision or taking many more repeated readings to reduce the random error in the mean diameter.
此外，直径测量是主导的不确定度来源；因此，改进措施可包括使用游标显微镜以获得更高精度，或采集更多重复读数以减小平均直径的随机误差。
8. Applying Skills to Other Core PH02 Experiments | 将技能应用于其他PH02核心实验
The investigational framework discussed above—plan, linearise, graph, uncertainty, evaluate—is transferable to any PH02 practical context. For instance, in determining the internal resistance r and e.m.f. E of a cell, the equation E = V + Ir is rearranged to V = -r I + E, giving a linear graph of V against I with gradient -r and intercept E.
上文讨论的实验框架——计划、线性化、绘图、不确定度、评估——可迁移至任何PH02实验场景。例如，在测定电池内阻r和电动势E时，方程E = V + Ir可变形为V = -r I + E，由此得到V对I的线性图像，斜率为-r，截距为E。
Similarly, when investigating the Young modulus of a copper wire, the stress-strain relationship leads to a linear plot, and the graphical gradient yields the modulus. All these experiments demand the same systematic approach to data handling, error analysis, and critical evaluation. The May 2023 paper rewarded candidates who showed a deep understanding of these generic scientific skills.
类似地，在研究铜丝的杨氏模量时，应力-应变关系可导出线性图像，其斜率即为模量。所有此类实验都要求采用同样系统的数据处理、误差分析和批判性评价方法。2023年5月的试卷奖励了那些对这些通用科学技能有深刻理解的考生。
9. Examiner’s Tips for PH02 Practical Questions | 考官对PH02实验题的提示
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Always state the precision of your instruments and justify it. For example, ‘The micrometer reads to 0.01 mm, so the absolute uncertainty is ±0.005 mm.’
务必说明所用仪器的精度并给出依据。例如，“千分尺可读至0.01 mm，因此绝对不确定度为±0.005 mm。”
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When drawing a line of best fit, do not default to the origin unless the theory demands it and the data support it. Use a transparent ruler and balance points above and below the line.
绘制最佳拟合线时，除非理论要求且数据支持，否则不要默认通过原点。使用透明直尺，并使直线上方和下方的点数大致均衡。
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In the evaluation, link every suggestion for improvement directly to a specific source of error. Vague statements like ‘be more careful’ gain no credit.
在评估环节，每条改进建议都要直接联系到一个具体的误差来源。诸如“更小心一些”之类的笼统表述不得分。
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Calculate uncertainties explicitly and show the combination steps. Use the worst-case scenario or statistical combination method as appropriate, and always express the final result with its absolute uncertainty.
明确地计算不确定度并展示合成步骤。视情况采用最差情形法或统计合成法，并始终用绝对不确定度表示最终结果。
10. Practice Example: Resistivity of Constantan Wire | 练习示例：康铜丝电阻率的测量
To consolidate your understanding, work through this mini-problem based on the PH02 style. A student measures the resistance of a constantan wire at various lengths and obtains the following processed data:
为巩固理解，请完成这道基于PH02风格的迷你练习题。某学生测量了康铜丝在不同长度下的电阻，并得到以下处理后的数据：
| Length L / m | 0.20 | 0.40 | 0.60 | 0.80 | 1.00 |
|---|---|---|---|---|---|
| Resistance R / Ω | 1.92 | 3.83 | 5.74 | 7.70 | 9.67 |
The mean diameter of the wire was 0.275 ± 0.01 mm. (a) Plot the graph of R against L and determine the gradient. (b) Calculate the resistivity and its percentage uncertainty. (c) Comment on the validity of the result if the accepted value is 4.9 × 10⁻⁷ Ω m.
导线平均直径为0.275 ± 0.01 mm。(a) 绘制R-L图像并求斜率。(b) 计算电阻率及其百分数不确定度。(c) 若公认值为4.9 × 10⁻⁷ Ω m，评述该结果的有效性。
Such exercises mirror the PH02 investigation and will sharpen your ability to tackle unseen practical tasks. Remember that the real paper may present a slightly different context, but the underlying methodology remains constant.
这类练习与PH02探究题如出一辙，能提升你处理陌生实验任务的能力。请记住，真实试卷可能呈现略微不同的情境，但其底层方法论保持恒定。
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