📚 A-Level Physics Unit 5 Question Paper Jan 2020: Mastering Experimental Investigations | A-Level 物理第五单元 2020 年 1 月真题：掌握实验探究
The January 2020 A-Level Physics Unit 5 question paper placed a strong emphasis on practical skills and experimental analysis. This component tests your ability to design investigations, process uncertain data, and evaluate procedures critically. In this in‑depth revision guide, we will unpack the key ideas behind the January 2020 experimental scenario, progressing step by step from the theoretical background to the final evaluation.
2020 年 1 月的 A-Level 物理第五单元试卷着重考查实验技能与数据分析能力。这一模块旨在检测你设计探究活动、处理含不确定度数据以及批判性评估实验方案的能力。在本篇深度复习指南中，我们将围绕 Jan 2020 的实验情境，从理论基础到最终评估，一步步拆解关键要点。
1. Understanding the Experimental Context | 理解实验情境
The January 2020 Unit 5 paper typically presented a scenario involving a physical quantity that cannot be measured directly, requiring you to derive it through a graphical method. A common example was the determination of the time constant of a capacitor‑resistor circuit, the specific heat capacity of a liquid, or the decay constant of a radioactive source.
2020 年 1 月的第五单元通常给出一个无法直接测量的物理量，要求通过图像方法来推导，常见例子包括测定电容器‑电阻电路的时间常数、液体的比热容或放射源的衰变常量。
In such questions, you are expected to identify the independent, dependent, and controlled variables, and suggest a suitable range and interval for measurements. The mark scheme rewards clear justification of choices, for example, why a data logger might be preferred over a stopwatch.
在此类问题中，你需要识别自变量、因变量与控制变量，并提出合适的测量范围与间隔。评分标准青睐对选择做出清晰的理由解释，例如，为什么数据记录器比秒表更可取。
2. Designing the Data Table | 设计数据表格
A well‑structured results table must show repeated readings and a column for mean values. Headings should include both the quantity and its unit, separated by a forward slash or presented as quantity / unit. For the January 2020 paper, you would be expected to record voltage across a discharging capacitor at equal time intervals, or temperature change over time.
一个结构清晰的数据表格必须显示重复读数以及一列平均值。表头应包含物理量及其单位，用斜线分隔或呈现为 物理量 / 单位。在 2020 年 1 月的试卷中，你可能需要记录电容放电时等间隔的电压值，或者温度随时间的变化。
If the dependent variable is expected to be small, using a digital voltmeter or a thermocouple with higher resolution reduces reading uncertainty. The table must also reflect the precision of the instruments used, for example, a voltmeter reading to 0.01 V.
若因变量预期较小，使用分辨率更高的数字电压表或热电偶可以减小读数不确定度。表格还必须反映所用仪器的精度，例如电压表读到 0.01 V。
| Time t / s | Voltage V / V (trial 1) | Voltage V / V (trial 2) | Mean V / V |
|---|---|---|---|
| 0 | 6.00 | 6.00 | 6.00 |
| 10 | 4.43 | 4.45 | 4.44 |
| 20 | 3.28 | 3.30 | 3.29 |
3. Graph Plotting and Linearisation | 图像绘制与线性化
The core of the experimental analysis is to manipulate the raw data to produce a straight‑line graph. For a capacitor discharge, the exponential decay V = V₀ e–t/RC is linearised by taking the natural logarithm: ln V = ln V₀ – ight line with a negative gradient whose magnitude is the reciprocal of the time constant.
实验分析的核心是处理原始数据以产生一条直线图像。对于电容放电，指数衰减 V = V₀ e–t/RC 可通过取自然对数线性化：ln V = ln V₀ – (1/RC) t。作 ln V‑t 图将得到一条负斜率的直线，斜率绝对值是时间常数的倒数。
In the January 2020 paper, candidates were often required to calculate logarithmic values and present them alongside uncertainties. The number of significant figures for ln V should match the decimal places of the voltage uncertainty, not necessarily the significant figures of the original reading.
在 2020 年 1 月试卷中，常要求考生计算对数值，并连同不确定度一起列出。ln V 的有效数字位数应匹配电压不确定度的小数位数，而非原始读数的有效数字位数。
ln V = ln V₀ – (1/RC) t
Before plotting, axes must be fully labelled with quantity and unit, and scales chosen so that the plotted points occupy more than half the grid in each direction. The line of best fit and the worst acceptable line are both required for uncertainty estimation.
绘图前，坐标轴须完整标注物理量和单位，选定比例尺使数据点在每个方向占据超过一半的坐标纸。最佳拟合线与最差可接受线都需要绘制，用以估计不确定度。
4. Uncertainty in Gradient and Derived Quantity | 斜率及导出量的不确定度
the data points (accounting for error bars). If the gradient m = Δy/Δx, its absolute uncertainty Δm = (mmax – mmin) / 2.
斜率的不确定度通过绘制两条极端线求得：一条最陡、一条最平缓，且均要与数据点（考虑到误差棒）合理一致。若斜率 m = Δy/Δx，其绝对不确定度 Δm = (mmax – mmin) / 2。
For the capacitor example, the time constant RC = |1/gradient| ly proportional to m. You must show the propagation of uncertainty clearly in your answer.
以电容器为例，时间常数 RC = |1/斜率|。RC 的百分不确定度等于斜率的百分不确定度，因为 RC 与 m 成反比。作答中必须清晰地展示不确定度的传递。
%U(RC) = %U(gradient)
When error bars are small and the line fits well, the numerical value of the derived quantity can be quoted to an appropriate number of significant figures, typically matching the precision of the uncertainty.
当误差棒较小且直线拟合良好时，导出量的数值可保留适当的有效数字，通常与不确定度的精度匹配。
5. Identifying Anomalous Points | 识别异常点
Anomalous data points are those that lie well outside the general trend, often visible as points far from the line of best fit beyond the margins of uncertainty bars. In the exam, you must circle an anomaly on the graph, suggest a possible cause (e.g., misreading the voltmeter, allowing the capacitor to discharge partially before starting the timer), and state whether that point should be excluded when drawing the line of best fit.
异常数据点是指明显偏离总体趋势的点，通常表现为远离最佳拟合线且超出不确定度棒范围。在考试中，你需要在图上圈出异常点，给出可能的原因（例如误读电压表、启动计时器前电容器已有部分放电），并说明在绘制最佳拟合线时是否应剔除该点。
Exclusion is justified only if the anomaly can be explained by an experimental mistake, not by natural variation. The mark scheme often asks you to repeat the whole procedure to confirm.
只有当异常可由实验失误而非自然变化解释时，剔除才合理。评分标准常要求你重复整个流程以确认。
6. Evaluating the Accuracy and Precision | 评估准确度与精密度
Accuracy can be assessed by comparing the experimental result with a known or accepted reference value, calculating the percentage difference. In the January 2020 paper, you might have been asked to judge whether the experiment is accurate by looking at whether the accepted value lies within the calculated uncertainty range.
通过将实验结果与已知或认可参考值比较，计算百分差异，可以评估准确度。在 2020 年 1 月试卷中，可能要求你通过检查认可值是否落在计算出的不确定度范围内，来判断实验是否准确。
Precision is reflected in the size of the uncertainty bars and the percentage uncertainty of your final result. A smaller percentage uncertainty indicates higher precision. You may be required to comment on whether the quoted precision matches the instrument resolution.
精密度反映在不确定度棒的大小以及最终结果的百分不确定度上。百分不确定度越小，精密度越高。你可能需要评论所宣称的精密度是否与仪器分辨率匹配。
7. Limitations and Procedural Improvements | 局限性及程序改进
Every experiment has limitations. For a capacitor discharge investigation, the internal resistance of the voltmeter can provide a parallel leakage path, reducing the effective resistance and shortening the time constant. This systematic error could be reduced by using a high‑impedance voltmeter or a data logger with negligible current draw.
每个实验都有局限性。对于电容放电探究，电压表的内阻会提供一条并联泄漏通路，降低有效电阻并缩短时间常数。通过使用高阻抗电压表或功耗可忽略的数据采集器，可减小此类系统误差。
Another common limitation is reaction time when using a manual stopwatch, which introduces a random uncertainty. Better precision can be achieved by using a motion sensor or a digital timer triggered by an electronic gate. The January 2020 mark scheme expected specific, practical improvements rather than vague statements.
另一个常见局限是使用手动秒表时的反应时间，这会引入随机不确定度。使用运动传感器或通过电子门触发的数字计时器可获得更好的精密度。2020 年 1 月的评分标准期待具体、可操作的改进，而非空泛的陈述。
8. Handling Logarithmic Uncertainties | 处理对数不确定度
n: Δ(ln Q) ≈ ΔQ / Q. This is critical for the capacitor discharge or radioactive decay linearisation tasks that appeared in the Jan 2020 paper.
在计算 ln Q 的绝对不确定度时，其中 Q 是带有不确定度 ±ΔQ 的被测量，必须使用微分近似：Δ(ln Q) ≈ ΔQ / Q。对于 Jan 2020 试卷中出现的电容放电或放射性衰变线性化任务，这一点至关重要。
is small uncertainty might be invisible if the graph scale is too coarse, so choose a scale that shows the error bars clearly.
这些不确定度值随后成为图像上竖直误差棒的长度。例如，若 V = 2.50 V ± 0.05 V，则 Δ(ln V) = 0.05/2.50 = 0.02。如果图像比例尺太粗，这个小不确定度可能不可见，因此应选择能清晰显示误差棒的比例尺。
9. Use of ICT and Data Loggers | 信息通信技术与数据记录器的使用
The specification encourages the use of ICT. A data logger sampling at 10 Hz with a voltage sensor can record many data points automatically, eliminating human reaction time and reducing random errors. In the Jan 2020 context, you might be asked to explain why a data logger improves the investigation compared with manual readings.
考试大纲鼓励使用信息通信技术。以 10 Hz 采样率配合电压传感器的数据记录器能自动记录大量数据点，消除人的反应时间并减小随机误差。在 Jan 2020 的情境中，你可能要解释为何数据记录器相比于人工读数能改善探究。
However, a data logger can introduce a systematic offset if not calibrated properly. Always mention the need for zeroing sensors and checking calibration against a standard before starting.
然而，若未正确校准，数据记录器可能引入系统偏移。务必提及开始前需要将传感器归零，并根据标准件检查校准。
10. Safety and Risk Assessment | 安全与风险评估
Although Unit 5 experiments are often low‑risk, a brief safety statement is sometimes required. For an electrical investigation, avoid shorting the capacitor, use insulated leads, and ensure the power supply is limited below hazardous voltages. For thermal experiments, mention the use of heat‑resistant mats and careful handling of hot liquids.
虽然第五单元的实验通常风险较低，但有时需要简写安全说明。对于电学探究，应避免电容器短路，使用绝缘导线，并确保电源限制在危险电压以下。对于热学实验，要提到使用隔热垫并小心操作热液体。
Risk assessment also includes the safe disposal of materials, such as returning a radioactive source to its lead‑lined container immediately after use, a detail that often appears in the context of nuclear decay investigations.
风险评估还包括安全处置材料，例如放射源使用后立即放回铅衬容器，这一细节常出现在核衰变探究的背景中。
11. Comparing Methods and Drawing Conclusions | 比较方法并得出结论
Questions often ask you to explain whether a different experimental method would give a more reliable result. For instance, could charging the capacitor through a large resistance and measuring the current yield a better determination of RC? You must weigh the advantages (e.g., direct measurement of current avoids differentiation errors) against new sources of error (ammeter internal resistance).
题目经常要求你解释另一种实验方法是否会给出更可靠的结果。例如，通过一个大电阻给电容器充电并测量电流是否能更好地测定 RC？你必须权衡其优点（例如直接测量电流避免了微分误差）与新引入的误差来源（电流表内阻）。
olute and percentage uncertainty, and relate it to the accepted value. A statement such as “ within the range X ± ΔX, suggesting the result is accurate within experimental uncertainty” is what examiners look for.
你的结论必须陈述实验值、其绝对与百分不确定度，并将其与认可值联系起来。像“认可值在 X ± ΔX 范围内，表明结果在实验不确定度范围内是准确的”这样的表述，正是考官想看到的。
12. Final Check: Common Pitfalls in Jan 2020 Paper | 最后检查：2020年1月试卷常见失分点
Many candidates lost marks by plotting raw voltage versus time instead of ln V against t, forgetting that the exponential relationship must be linearised. Others used inconsistent decimal places in logarithmic columns or forgot to multiply the gradient uncertainty by the conversion factor to obtain the final uncertainty.
许多考生因绘制原始电压‑时间图而非 ln V‑t 图而失分，忘记了指数关系必须线性化。还有些考生在对数列中使用了不一致的小数位数，或忘记将斜率不确定度乘以转换因子以获得最终不确定度。
Always double‑ t / s, ln(V / V)) is mandatory. And finally, state the relationship clearly in a form like “Since V = V₀ e–t/RC, the gradient of the ln V vs t graph is –1/RC”.
务必仔细检查表头：斜线规范（如 t / s、ln(V / V)）是必须的。最后，以类似“由于 V = V₀ e–t/RC，ln V‑t 图的斜率为 –1/RC”的形式清晰地陈述关系。
Published by TutorHao | Physics Revision Series | aleveler.com
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