📚 Experimental Investigation in OxfordAQA PH04 June 2023 | OxfordAQA PH04 2023年6月实验探究
In the June 2023 OxfordAQA PH04 examination, candidates tackled a practical investigation requiring the determination of the resistivity of a metal wire. This article unpacks the key experimental techniques, data analysis methods, and common pitfalls, guided by the official mark scheme. Mastering these skills is essential not only for this paper but also for developing a robust scientific approach.
在2023年6月OxfordAQA PH04考试中，考生需要完成一项测定金属导线电阻率的实验探究。本文结合官方评分方案，解析关键的实验技巧、数据分析方法以及常见误区。掌握这些技能不仅对这份试卷至关重要，也有助于培养严谨的科学思维。
1. Overview of the PH04 Experimental Task | PH04 实验任务概述
The question required students to design an experiment to measure the resistivity (ρ) of a metal wire by varying its length and recording the corresponding resistance. Resistivity is an intrinsic property linking resistance, length and cross-sectional area through the equation ρ = RA/L.
题目要求学生设计一个实验，通过改变导线长度并记录对应的电阻来测量其电阻率ρ。电阻率是一个固有属性，通过公式ρ = RA/L 将电阻、长度和横截面积联系起来。
The independent variable was the length L of the wire, and the dependent variable was the resistance R. The cross-sectional area A was kept constant by using the same wire throughout, while temperature was controlled by using small currents to avoid heating.
实验中的自变量是导线长度L，因变量是电阻R。通过全程使用同一根导线保持横截面积A不变，同时采用小电流控制温度，避免热效应。
2. Designing the Investigation | 设计探究方案
A clear plan begins by identifying the variables and ensuring a fair test. The length L must be measured accurately with a metre rule, and the diameter d must be determined at several points using a micrometer screw gauge to calculate area A = πd²/4.
清晰的方案首先需要确定变量并确保公平测试。长度L要用米尺精确测量，直径d需用千分尺在多点测量，以计算面积A = πd²/4。
The circuit should be set up to measure both voltage V and current I, allowing calculation of resistance via R = V/I. Alternatively, an ohmmeter can be used directly, but the voltmeter-ammeter method offers better insight into linearity and consistency.
电路应当能够测量电压V和电流I，通过R = V/I计算出电阻。也可以直接使用欧姆表，但伏安法能更好地检验线性关系和数据一致性。
To maintain a constant temperature, the current must not exceed a safe limit, typically below 0.5 A. Switching off between readings prevents drift. The wire should be clamped taut without stretching, and connections must be secure with crocodile clips.
为保持温度恒定，电流不得超过安全限值，一般低于0.5 A。每次读数后断电可防止漂移。导线应夹紧拉直但不拉伸，用鳄鱼夹确保连接牢固。
3. Apparatus and Instrument Precision | 仪器与测量精度
The metre rule typically has a precision of ±1 mm, but readings can be taken to the nearest 0.5 mm if the rule has millimetre marks. To reduce parallax error, the eye must be perpendicular to the scale when reading both the rule and the micrometer.
米尺的典型精度为±1 mm，但如果尺子上标有毫米刻度，读数可精确到0.5 mm。为减少视差，读取米尺和千分尺时视线必须与刻度垂直。
A micrometer screw gauge can measure the diameter to ±0.01 mm. Zero error must be checked before use by closing the jaws gently; any reading off zero must be recorded and subtracted from all measurements. At least three diameter readings are taken along the wire and averaged.
千分尺可测量直径至±0.01 mm。使用前必须检查零点误差，轻轻闭合钳口；任何偏离零点的读数都应记录并从所有测量值中减去。至少沿导线取三个直径读数并求平均值。
The voltmeter and ammeter should be analogue or digital with suitable ranges to minimise percentage uncertainty. A digital multimeter often provides higher resolution.
电压表和电流表可以是模拟或数字式，需选择合适的量程以减小百分比不确定度。数字万用表通常提供更高的分辨率。
4. Circuit Diagram and Setup | 电路图与连接
The standard circuit places the ammeter in series with the wire and the voltmeter in parallel across the test length. A variable resistor or rheostat can be used to limit the current, but many simple designs use a low-voltage DC supply and rely on the wire’s own resistance.
标准电路是将安培表与待测导线串联，伏特表并联在测试长度两端。可使用变阻器或其他限流电阻，但许多简单设计会使用低压直流电源并依靠导线自身的电阻。
Each crocodile clip defines the measured length segment. It is vital to attach the voltmeter clips inside the ammeter clips to avoid including contact resistance in the voltage reading, ensuring R = V/I represents only the wire segment.
每个鳄鱼夹界定被测长度段落。关键是要将伏特表夹子接在安培表夹子的内侧，以避免接触电阻影响电压读数，确保R = V/I仅代表导线段落本身的电阻。
5. Data Collection Procedure | 数据采集步骤
Start with the maximum length, e.g., 1.000 m, and decrease in steps of 0.100 m. For each length, record the voltage V and current I, then compute R. Immediately reduce the current or switch off after each reading.
从最大长度开始，例如1.000 m，并以0.100 m的步长递减。对每个长度记录电压V和电流I，然后计算R。每次读数后立即减小电流或断电。
Repeat readings for each length are highly recommended. Taking two sets of V and I allows a check for consistency and calculation of a mean resistance. Any anomalous results should be repeated and noted.
强烈建议对每个长度重复读数。记录两组V和I可检验一致性并计算平均电阻。任何异常结果都应重新测量并注明。
6. Recording Measurements in a Table | 将测量数据记录在表格中
A well-structured table is essential. Columns should include: length L/m, voltage V/V, current I/A, resistance R/Ω, and mean resistance if repeats are taken. All headings must state the quantity and its unit separated by a solidus (/).
结构清晰的表格至关重要。列应包括：长度L/m，电压V/V，电流I/A，电阻R/Ω，若重复则加上平均电阻。所有表头必须标明物理量与其单位，用斜线(/)分隔。
Example data:
示例数据：
| Length L / m | Voltage V / V | Current I / A | Resistance R / Ω | Mean R / Ω |
|---|---|---|---|---|
| 0.200 | 0.42 | 0.40 | 1.05 | 1.07 |
| 0.300 | 0.63 | 0.40 | 1.58 | 1.59 |
| 0.400 | 0.84 | 0.40 | 2.10 | 2.11 |
| 0.500 | 1.05 | 0.40 | 2.63 | 2.64 |
| 0.600 | 1.26 | 0.40 | 3.15 | 3.16 |
All resistances should be given to a consistent number of significant figures, reflecting the precision of the measurements.
所有电阻值应保留一致的有效数字，以体现测量精度。
7. Plotting the Graph | 绘制图表
Plot a graph of resistance R (y-axis) against length L (x-axis). Since ρA is constant, R = (ρ/A)L, yielding a straight line through the origin. The axes must be labelled clearly with quantities and units, and scales chosen to occupy more than half the graph paper.
绘制电阻R（纵轴）对长度L（横轴）的图像。因ρA为常数，R = (ρ/A)L，图像为一条过原点的直线。坐标轴必须清晰标注物理量与单位，分度需使数据点占据超过半张坐标纸。
Data points should be plotted with small crosses or dots surrounded by circles. A line of best fit is drawn, passing through the origin if the intercept is consistent with zero. Students must not force the line through the origin if data suggests otherwise, but in this experiment a systematic error may cause a small positive intercept.
数据点应用小十字或加圈圆点标出。画一条最佳拟合直线，若截距与零一致则通过原点。若数据显示出偏差，不可强行过原点，但本实验中系统误差可能导致一个微小的正截距。
8. Determining Resistivity from the Graph | 从图像求电阻率
The gradient m of the straight line equals ρ/A. Calculate the gradient using a large triangle that covers at least half the line. Use m = (R₂ – R₁)/(L₂ – L₁), reading coordinates directly from the line, not from data points.
直线的斜率m等于ρ/A。计算斜率时，用一个能覆盖直线至少一半的大三角形，使用m = (R₂ – R₁)/(L₂ – L₁)，坐标应从直线上读取，而非数据点。
Once the gradient is found and the cross-sectional area A has been calculated from the mean diameter, resistivity is obtained from ρ = m × A. The value must be quoted with appropriate units (Ω m) and compared to the accepted value for the metal, e.g., 1.72 × 10⁻⁸ Ω m for copper.
求得斜率并计算出平均直径对应的横截面积A后，由ρ = m × A得出电阻率。数值必须标出适当单位（Ω m），并与该金属的公认值进行比较，例如铜的电阻率为1.72 × 10⁻⁸ Ω m。
9. Uncertainty Analysis | 不确定度分析
The percentage uncertainty in resistivity can be estimated from the component uncertainties. For the gradient, use the difference between the steepest and shallowest lines of best fit that remain within the scatter of points: %U_gradient = (max gradient – min gradient) / (2 × best gradient) × 100%.
电阻率的百分比不确定度可通过各分量不确定度估算。对于斜率，可基于仍落在数据点散布范围内的最陡和最浅最佳拟合线之差来计算：%U_斜率 = (最大斜率 – 最小斜率) / (2 × 最佳斜率) × 100%。
The diameter d introduces a significant uncertainty because area depends on d². The percentage uncertainty in A is twice that in d: %U_A = 2 × (Δd/d) × 100%, where Δd is the absolute uncertainty from the micrometer (e.g., ±0.01 mm) plus any observed spread in readings.
直径d会引入显著不确定度，因为面积依赖于d²。A的百分比不确定度是d的两倍：%U_A = 2 × (Δd/d) × 100%，其中Δd是千分尺的绝对不确定度（如±0.01 mm）加上读数间观测到的分散度。
The total percentage uncertainty in ρ combines the gradient and area contributions: %U_ρ = %U_gradient + %U_A. An absolute uncertainty range can then be given.
ρ的总百分比不确定度由斜率和面积的不确定度合成：%U_ρ = %U_斜率 + %U_A。随后可给出绝对不确定度范围。
10. Error Identification and Improvement | 误差识别与改进
Random errors arise from fluctuating readings, parallax, and slight variations in wire thickness. These can be reduced by taking multiple measurements and using averaging. Repeating the experiment with a longer wire range improves gradient precision.
随机误差来源于读数波动、视差以及导线粗细的微小变化。可通过多次测量取平均来减小。扩大导线长度范围并重复实验能提高斜率精度。
Systematic errors include zero error on the micrometer, loose connections adding contact resistance, or the wire not being uniform. Zero error can be eliminated by correction; contact resistance is minimised by careful clip placement. Using a diameter measured at several points averages out non-uniformity.
系统误差包括千分尺的零点误差、连接松动带来的接触电阻或导线不均匀。零点误差可通过修正消除；细致的夹子布局可最小化接触电阻；在多点测量直径则能平均掉不均匀性。
Heating effects can be systematic if current is too high, causing resistance to increase. Using a constant low current and switching off between readings avoids this drift. A thermometer could monitor temperature for further rigour.
若电流过高，热效应会成为系统误差，导致电阻增大。使用恒定的低电流并在读数间断电可避免漂移。更严谨的做法是用温度计监控温度。
11. Mark Scheme Insights for Top Marks | 根据评分方案获得高分的要点
The mark scheme rewards clear descriptions of how to reduce uncertainty: calculating area from a mean diameter, taking repeated readings, and using a large graph. Candidates must mention specific instruments and justify choices.
评分方案青睐清晰描述如何减小不确定度的答案：通过平均直径计算面积、重复读数、使用大尺寸图表等。考生须提及具体仪器并说明选择理由。
It also expects that the gradient is used to find resistivity, not a single pair of values. The line of best fit must be described, and any anomalous points identified and excluded from the line. Stating that the expected line passes through the origin with reasoning about zero length implying zero resistance can earn additional marks.
评分方案要求使用斜率而非单对点求电阻率。必须描述最佳拟合线，识别并排除异常点。通过推理说明零长度意味着零电阻，预期图像过原点，可获得额外分数。
Uncertainty calculations must show a combination of relevant uncertainties, especially acknowledging the dominant role of diameter. A comparison with the accepted value should be presented together with an evaluation of the reliability of the result.
不确定度计算必须体现相关不确定度的合成，尤其要承认直径的主导作用。需将实验结果与公认值进行比较，并对结果的可靠性作出评价。
12. Conclusion: Linking Experiment to Theory | 结论：实验联系理论
This investigation reinforces the linear relationship between resistance and length for a uniform conductor, confirming Ohm’s law at constant temperature. By determining resistivity, students see how a material property can be extracted from simple measurements.
本实验探究巩固了均匀导体中电阻与长度之间的线性关系，验证了恒温条件下的欧姆定律。通过测定电阻率，学生体验到如何从简单测量中提取材料属性。
Careful error analysis shows that the largest source of uncertainty is the diameter measurement, highlighting the importance of using a micrometer correctly. The process models real-world physics experimentation, where meticulous technique and thoughtful interpretation are far more valuable than a single numeric answer.
细致的误差分析表明，最大的不确定度来源是直径测量，凸显了正确使用千分尺的重要性。这一过程模拟了真实的物理实验，其中严谨的操作和深思熟虑的解读远比单独一个数字答案更有价值。
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