📚 9630-PH03 International A-Level Physics Specimen Paper v4.2: Experimental Investigation | 9630-PH03 国际A-Level物理样题v4.2：实验探究
This article explores the experimental investigation presented in the 9630-PH03 international A-level Physics specimen paper v4.2, focusing on the practical skills required to plan, carry out, analyse and evaluate a physics experiment. The task exemplifies the assessment of Unit 3 practical competencies, where students must demonstrate understanding of measurement techniques, uncertainty calculations, and critical evaluation of procedures.
本文探讨了 9630-PH03 国际 A-level 物理样题 v4.2 中的实验探究，重点阐述计划、实施、分析和评估物理实验所需的实践技能。该任务体现了第三单元实践能力的考核，要求学生展示对测量技术、不确定度计算和实验步骤批判性评估的理解。
1. Overview of the Specimen Task | 样题任务概述
The 9630-PH03 specimen paper v4.2 sets a practical investigation in which a student is asked to study the discharge of a capacitor through a fixed resistor. The core objective is to determine the time constant of the circuit and subsequently calculate the capacitance, comparing it with the manufacturer’s value. The task integrates circuit assembly, data logging, graphical analysis, and uncertainty propagation.
9630-PH03 样题 v4.2 布置了一项实践探究，要求学生研究电容器通过固定电阻的放电过程。核心目标是测定电路的时间常数，进而计算电容值，与标称值进行对比。该任务综合了电路搭建、数据记录、图像分析和不确定度传递。
2. Experimental Aim and Hypothesis | 实验目的与假设
The aim is to verify the exponential decay relationship for a capacitor discharging through a resistor and to calculate the capacitance using the time constant obtained from a ln V versus t graph. The hypothesis is that the discharge follows the equation V = V0e−t/RC, and therefore a plot of ln V against t will be a straight line with gradient equal to −1/RC.
实验目的是验证电容器通过电阻放电的指数衰减关系，并利用 ln V–t 图像得到的时间常数计算电容。假设放电遵循方程 V = V0e−t/RC，因此 ln V 对 t 作图应得到一条直线，其斜率等于 −1/RC。
3. Apparatus and Setup | 仪器与装置
The apparatus listed in the specimen task includes: a 470 μF electrolytic capacitor, a 10 kΩ resistor, a 6 V d.c. power supply, a single-pole double-throw (SPDT) switch, a digital voltmeter, a stopwatch, and connecting leads. The capacitor is first charged by connecting it to the supply, and then discharged through the resistor while voltage readings are taken at regular time intervals.
样题中列出的仪器包括：一个 470 μF 电解电容器，一个 10 kΩ 电阻，一个 6 V 直流电源，一个单刀双掷 (SPDT) 开关，一个数字电压表，一块秒表以及连接导线。首先将电容器连接到电源充电，然后通过电阻放电，同时每隔一定时间记录电压读数。
4. Method and Data Collection | 方法与数据收集
The SPDT switch is used to connect the capacitor to the power supply until the voltmeter reads a steady 6.00 V. The switch is then thrown to the discharge position, and the stopwatch is started simultaneously. Voltage readings are taken every 10 seconds for a total of 60 seconds. The experiment is repeated twice to reduce random error, and an average V is calculated for each time point.
使用单刀双掷开关将电容器连接到电源，直到电压表读数为稳定的 6.00 V。然后将开关拨至放电位置，同时启动秒表。每 10 秒记录一次电压读数，共记录 60 秒。实验重复两次以减少随机误差，并计算每个时间点的平均电压 V。
5. Results and Raw Data | 结果与原始数据
Sample data collected in the investigation are presented in the table below. The capacitor’s nominal value is 470 μF ± 20% and the resistor is 10 kΩ ± 5%. The corresponding time constant RC is 4.7 s, and the expected discharge behaviour should follow this constant.
本次探究收集的样本数据列于下表。电容器标称值为 470 μF ± 20%，电阻为 10 kΩ ± 5%。对应的时间常数 RC 为 4.7 s，预期的放电行为应遵循该常数。
| Time t / s | Voltage V / V | ln(V / V) |
|---|---|---|
| 0 | 6.00 | 1.79 |
| 10 | 2.52 | 0.924 |
| 20 | 1.06 | 0.058 |
| 30 | 0.44 | −0.821 |
| 40 | 0.19 | −1.661 |
| 50 | 0.08 | −2.526 |
| 60 | 0.03 | −3.507 |
6. Data Processing: Calculating Time Constant | 数据处理：计算时间常数
Starting from the capacitor discharge law V = V0e−t/RC, we take the natural logarithm of both sides to linearise the relationship:
ln V = ln V0 − (1/RC) t
This is in the form y = c + mx, where y = ln V, x = t, and the gradient m = −1/RC. By plotting ln V against t, the time constant τ = RC can be found from τ = −1 / gradient.
从电容器放电规律 V = V0e−t/RC 出发，对两边取自然对数以线性化关系：
ln V = ln V0 − (1/RC) t
此式形如 y = c + mx，其中 y = ln V，x = t，斜率 m = −1/RC。通过绘制 ln V–t 图像，可由 τ = −1/斜率 求得时间常数 τ = RC。
7. Graphical Analysis and Logarithmic Linearisation | 图像分析与对数线性化
Using the data from the table, a graph of ln V versus t is plotted. A straight line is drawn through the points, confirming the exponential relationship. The gradient of the best-fit line is calculated to be approximately −0.210 s−1. Hence the time constant is τ = −1 / (−0.210 s−1) = 4.76 s. This value is close to the nominal 4.7 s.
利用表格中的数据，绘制了 ln V–t 图像。通过各数据点作出一条直线，从而证实了指数关系。最佳拟合线的斜率约为 −0.210 s−1。因此时间常数为 τ = −1 / (−0.210 s−1) = 4.76 s。该值接近标称的 4.7 s。
8. Uncertainty Analysis | 不确定度分析
Uncertainties arise from the voltmeter (±0.01 V) and the stopwatch (±0.5 s). The dominant uncertainty is determined by drawing the steepest and shallowest plausible lines on the ln V–t graph. If the maximum gradient is −0.220 s−1 and the minimum gradient is −0.200 s−1, the corresponding time constants are 4.55 s and 5.00 s. The absolute uncertainty in τ is approximately ±(5.00 − 4.55)/2 = ±0.23 s. The percentage uncertainty in τ is about 4.8%.
不确定度来源于电压表 (±0.01 V) 和秒表 (±0.5 s)。通过在 ln V–t 图像上画出尽可能最陡和最平缓的合理直线，可以确定主要不确定度。若最大斜率为 −0.220 s−1，最小斜率为 −0.200 s−1，相应的时间常数分别为 4.55 s 和 5.00 s。τ 的绝对不确定度约为 ±(5.00 − 4.55)/2 = ±0.23 s。τ 的百分比不确定度约为 4.8%。
9. Calculating Capacitance and Comparison | 计算电容并进行比较
Since τ = RC, the experimental capacitance is C = τ / R = 4.76 s / 10×103 Ω = 4.76×10−4 F = 476 μF. The percentage difference from the nominal 470 μF is (6/470)×100% ≈ 1.3%. This lies well within the component tolerance, indicating good agreement with the manufacturer’s stated value.
由于 τ = RC，实验电容为 C = τ / R = 4.76 s / 10×103 Ω = 4.76×10−4 F = 476 μF。与标称值 470 μF 的百分比差异为 (6/470)×100% ≈ 1.3%。该值完全在元件容差范围内，表明与制造商标定值吻合良好。
10. Error Sources and Improvements | 误差来源与改进
The main sources of error in this investigation include reaction time when starting the stopwatch, the finite internal resistance of the voltmeter, and leakage current through the capacitor dielectric. To improve accuracy, a data-logger with a voltage sensor could replace manual readings, removing reaction-time errors. A buffer amplifier could be used to minimise the loading effect of the voltmeter on the RC circuit.
本次探究的主要误差来源包括：启动秒表时的反应时间、电压表有限的内阻以及电容器介质的漏电流。为提高精度，可使用带电压传感器的数据采集器代替人工读数，消除反应时间误差。也可使用缓冲放大器以尽量减少电压表对 RC 电路的负载效应。
11. Practical Skills Assessment in the Specimen | 样题中的实践技能评估
The 9630-PH03 specimen paper evaluates a candidate’s ability to record data with appropriate precision, recognise the need for repeated measurements, choose suitable graph scales, handle logarithmic transformation, and determine uncertainties from a graph. The mark scheme rewards consistent significant figures, correct unit conversion, and explicit statements about safety precautions and reliability.
9630-PH03 样题评估考生的以下能力：以适当的精度记录数据、认识到重复测量的必要性、选择合适的坐标轴标度、处理对数变换以及从图像中确定不确定度。评分标准奖励一致的有效数字、正确的单位换算，以及对安全预防措施和可靠性的明确陈述。
12. Conclusion and Evaluation | 结论与评价
The experimental investigation successfully verified the exponential discharge of a capacitor and yielded a capacitance value within 1.3% of the nominal value. The time constant determined graphically was 4.76 ± 0.23 s, consistent with the expected 4.7 s. This specimen task illustrates how careful planning, rigorous data collection, and thorough uncertainty analysis are essential for high-level practical physics examinations.
该实验探究成功验证了电容器的指数规律放电，所得电容值与标称值相差仅 1.3%。通过图像确定的时间常数为 4.76 ± 0.23 s，与预期的 4.7 s 一致。该样题任务说明，精心的计划、严格的数据收集和彻底的不确定度分析对于高水平的物理实验考试至关重要。
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