AQA AS Physics Unit 3: Practical Skills & Data Analysis from the January 2019 Paper | AQA AS物理单元3：2019年1月考卷中的实验技能与数据分析

📚 AQA AS Physics Unit 3: Practical Skills & Data Analysis from the January 2019 Paper | AQA AS物理单元3：2019年1月考卷中的实验技能与数据分析

Unit 3 of the AQA AS Physics specification is a practical and data analysis paper, testing how well you can plan, execute, and interpret experiments. One notable exam series is January 2019, where a common long-answer question focused on measuring the electrical resistivity of a metal wire. This article will break down the key skills needed for such questions, using the January 2019 style as a reference, and guide you through every step from variables to evaluation.

AQA AS物理大纲中的单元3是一份实验与数据分析试卷，考查你规划实验、动手操作并解读数据的能力。2019年1月是一个值得关注的考试系列，其中一道常见的长答题聚焦于测量金属丝的电阻率。本文将以此为参照，逐一拆解这类题目所需的各项关键技能，从变量控制到误差评估全程引导。

1. Identifying Variables: Independent, Dependent, and Control | 识别变量：自变量、因变量与控制变量

In any resistivity experiment, the independent variable is the length L of the wire, which you deliberately change. The dependent variable is the resistance R of the wire, which you measure using an ohmmeter or a voltmeter-ammeter method. Control variables include the cross-sectional area A of the wire, the temperature, and the material of the wire; these must remain constant to ensure a fair test.

在任何电阻率实验中，自变量是金属丝的长度L，即你主动改变的量。因变量是金属丝的电阻R，通过欧姆表或伏安法测量得到。控制变量包括金属丝的横截面积A、温度和材料种类；这些量必须保持不变，以确保实验的公平性。

Independent variable: length L (in metres).
Dependent variable: resistance R (in ohms).
Control variables: cross-sectional area, temperature, material type.

For the January 2019 paper, you may be asked to state these explicitly. A common mistake is to state ‘voltage’ as the independent variable when using a voltmeter-ammeter method, but the applied voltage is actually kept constant while the wire length is varied.

对于2019年1月的试卷，你可能会被要求明确陈述这些变量。一个常见错误是在使用伏安法时将“电压”当作自变量，但实际上施加的电压是保持恒定的，而改变的是金属丝长度。

2. Experimental Setup: The Circuit and the Wire | 实验装置：电路与金属丝

The standard setup involves a battery (or a power supply), an ammeter in series with the wire, and a voltmeter connected in parallel with the tested length of the wire. The wire is fixed to a metre ruler, and one end of a jockey (a movable contact) allows you to select different lengths L of the wire.

标准装置包括电池（或电源）、与金属丝串联的电流表，以及与被测金属丝长度并联的电压表。金属丝固定在一米尺上，通过滑动探针（可移动接触点）来选择不同的金属丝长度L。

To reduce contact resistance, the wire should be cleaned with sandpaper before starting, and the jockey should make firm contact with the wire. Also, keep the current low (e.g., below 0.5 A) to avoid heating the wire, which would change its resistivity.

为了减少接触电阻，实验前应用砂纸清洁金属丝，并且探针要与金属丝紧密接触。此外，电流应保持较小（例如低于0.5 A），以避免金属丝发热，否则其电阻率会发生变化。

Use a new piece of wire for each length to avoid kinks or stretching.
Switch off the circuit between readings to prevent heating.
Repeat readings at each length and calculate the mean resistance.

In the January 2019 paper, there was a diagram showing a circuit with a split variable resistor. Make sure you can draw and label this circuit correctly from memory.

在2019年1月的试卷中，电路图含有一个分压可变电阻器。你需要确保能够凭记忆正确绘制并标注这个电路。

3. Measuring the Diameter and Cross-Sectional Area | 测量直径与横截面积

The cross-sectional area A of the wire is calculated from its diameter using the formula A = πd²/4. The diameter should be measured using a micrometer screw gauge, which has a resolution of 0.01 mm. To improve accuracy, measure the diameter in at least three places along the wire and at two perpendicular orientations at each place, then take the average.

金属丝的横截面积A通过其直径使用公式A=πd²/4计算。直径应使用千分尺测量，其分辨率为0.01 mm。为提高准确度，应沿金属丝至少取三个位置、每个位置在两个相互垂直的方向上测量直径，然后取平均值。

A = π × (d/2)² = πd²/4

Why is this important? Because the cross-sectional area is squared in the formula R = ρL/A, a small error in d leads to a relatively large error in A and hence in ρ. For example, if d = 0.26 mm and you measure it as 0.28 mm, the area changes by about 16%.

为什么这很重要？由于在公式R=ρL/A中横截面积是平方项，直径的小误差会导致面积以及电阻率ρ的较大误差。例如，若实际直径d=0.26 mm，但测成0.28 mm，面积将改变约16%。

Always record the zero reading of the micrometer first and correct for it.
Do not overtighten the ratchet—this compresses the wire and gives a false low reading.
Repeat the diameter measurement for at least five different points along the wire.

4. Data Collection: Recording Voltage and Current | 数据采集：记录电压与电流

For each length L, you record the potential difference V across the wire and the current I through it. The resistance is then calculated as R = V/I. If you use a digital ammeter and voltmeter, record the values with the appropriate number of significant figures, typically to the same decimal place as the instrument resolution.

对于每个长度L，记录金属丝两端的电势差V和通过它的电流I。电阻通过R=V/I计算。如果使用数字电流表和电压表，应以与仪器分辨率一致的有效位数记录数值，通常保留到相应的小数位。

R = V / I

To reduce random error, take several sets of readings: for each length, vary the applied voltage slightly (by adjusting the variable resistor) and measure V and I three times, then compute R each time and average. Alternatively, you can plot a graph of V against I and use the gradient as R.

为减少随机误差，应采集多组读数：对每个长度，略微改变施加电压（通过调节可变电阻器），测量三次V和I，分别计算R后取平均值。或者可以绘制V对I的图线，用斜率来表示R。

Use thick connecting wires with low resistance.
Ensure the jockey contact is clean and sharp.
Record all raw data in a table with correct headings and units.

In January 2019, the question provided a table of current and voltage values, and you had to calculate the resistance for each pair. Practise doing this quickly, treating the numbers exactly as given and then rounding to a sensible number of significant figures.

在2019年1月的考题中，问题给出了电流和电压值表，要求你计算每组的电阻。请练习快速计算，先按给定数值精确计算，再四舍五入到合理有效位数。

5. Plotting the Graph and Calculating ρ | 绘制图线并计算ρ

Once you have resistance R for several lengths L, plot a graph of R on the y-axis against L on the x-axis. The relationship is R = (ρ/A)L, which is a straight line through the origin. The gradient of the line equals ρ/A, so you can calculate ρ by multiplying the gradient by the cross-sectional area A.

在获得多个长度L对应的电阻R后，以R为纵轴、L为横轴作图。关系式R=(ρ/A)L是一条过原点的直线。直线的斜率等于ρ/A，因此将斜率乘以横截面积A即可算出ρ。

ρ = gradient × A

When plotting the graph, choose a scale that uses at least half of the grid. Add error bars if you have estimated the uncertainty in R; the line of best fit should pass through all the error bars if the data is consistent. Use a sharp pencil and draw the line as a single thin straight line, not a wavy curve through every point.

作图时，应选择至少用掉网格一半的刻度比例。如果估算出R的不确定度，应添加误差棒；若数据一致，最佳拟合直线应穿过所有误差棒。使用削尖的铅笔画出细而直的直线，而不是连接每个点的弯曲曲线。

Label both axes with quantity and unit, e.g., “R / Ω”.
Use a large triangle to calculate the gradient, showing your working.
State whether the line passes through the origin; if not, explain why (e.g., contact resistance or zero error).

From the January 2019 paper, the resistance values ranged from about 0.40 Ω to 1.20 Ω over lengths of 0.10 m to 0.60 m. The gradient was approximately 1.67 Ω/m. Given a wire diameter of 0.38 mm, the cross-sectional area was 1.13 × 10⁻⁷ m², giving ρ = (1.67)(1.13 × 10⁻⁷) = 1.89 × 10⁻⁷ Ω·m, which is close to the accepted value for constantan.

以2019年1月试卷为例，电阻值从约0.40 Ω到1.20 Ω，对应长度从0.10 m到0.60 m。斜率约为1.67 Ω/m。若金属丝直径为0.38 mm，横截面积为1.13 × 10⁻⁷ m²，则ρ=(1.67)(1.13 × 10⁻⁷)=1.89 × 10⁻⁷ Ω·m，这与康铜的标准值接近。

6. Uncertainty and Percentage Errors | 不确定度与百分比误差

Every measurement has an uncertainty. For a digital ammeter reading to 0.01 A, the absolute uncertainty is often taken as ±0.005 A (half the last digit). The percentage uncertainty is the absolute uncertainty divided by the reading, multiplied by 100%. To combine uncertainties when multiplying or dividing quantities, you add the percentage uncertainties.

每次测量都存在不确定度。对于分辨率为0.01 A的数字电流表，绝对不确定度通常取±0.005 A（最后一位的一半）。百分比不确定度等于绝对不确定度除以读数再乘以100%。当乘法或除法组合不确定度时，应相加各个百分比不确定度。

% uncertainty of ρ = % uncertainty of gradient + 2 × % uncertainty of d

The factor of 2 comes from the fact that d is squared in the formula for A. For example, if gradient has a 3% uncertainty and diameter has a 2% uncertainty, the percentage uncertainty in ρ is 3% + 2 × 2% = 7%.

因子2来源于d在面积公式中被平方。例如，若斜率的百分比不确定度为3%，直径为2%，则ρ的百分比不确定度为3% + 2 × 2% = 7%。

Use the range of repeated readings to find the uncertainty in R: uncertainty = (max − min)/2.
For a metre ruler, the absolute uncertainty in one length reading is ±0.5 mm; if two ends are read, it becomes ±1 mm.
Express final uncertainties to one significant figure, e.g., ρ = (1.9 ± 0.2) × 10⁻⁷ Ω·m.

The January 2019 question specifically asked for the percentage uncertainty in the diameter. If the micrometer reads 0.38 mm with an uncertainty of ±0.01 mm, the percentage uncertainty is (0.01/0.38) × 100% = 2.6%.

2019年1月考题中明确要求计算直径的百分比不确定度。若千分尺读数为0.38 mm，不确定度为±0.01 mm，则百分比不确定度为(0.01/0.38) × 100% = 2.6%。

7. Evaluating the Procedure: Sources of Error | 评估实验过程：误差来源

The main systematic error in this experiment is heating of the wire due to the current. As the temperature rises, the resistivity of most metals increases, leading to a higher resistance than expected. To minimise this, use a low current, switch off the circuit between readings, and do not send current through the wire for prolonged periods.

本实验的主要系统误差是电流导致金属丝发热。温度升高时，大多数金属的电阻率会增大，导致电阻偏高。为减少此误差，应使用小电流、在两次读数之间关闭电路，并且不要长时间让电流通过金属丝。

Contact resistance between the jockey and wire adds extra resistance in series.
The wire may not be perfectly uniform in diameter or purity.
Parallax error when reading the metre ruler or micrometer.
Zero error in the micrometre or ammeter.

You should also state the direction of each error if possible. For example, contact resistance makes R values too high, so the gradient and the calculated ρ will be slightly overestimated. A zero error on the ammeter that adds 0.02 A to every reading will make every resistance too small.

如有可能，还应指出每个误差的方向。例如，接触电阻会使R值偏高，因此斜率和计算出的ρ会被轻微高估。电流表指针偏移（零点是0.02 A）会使每次读数偏高，从而使电阻偏小。

8. Improving the Experiment | 改进实验方案

To produce a more reliable value of ρ, you can make several improvements. First, use four-probe (Kelvin) connections to eliminate the effect of contact and lead resistance. This involves using two additional probes to measure the voltage across the wire while a separate pair of leads carries the current.

为获得更可靠的ρ值，可进行多项改进。首先，使用四探针（开尔文）接法来消除接触电阻和导线电阻的影响。即用两个额外的探针测量金属丝两端的电压，而另外两根导线负责通电流。

Second, use a longer wire or a wider range of lengths to make the graph scale larger. Third, repeat the whole experiment with a new wire sample to check consistency. Fourth, keep the laboratory temperature recorded and, if the room is not air-conditioned, note that temperature drift could affect the data.

其次，使用更长的金属丝或更宽的长度范围，使图线比例更大。第三，用新的金属丝样品重复整个实验，以检查一致性。第四，记录实验室温度，若房间无空调，应注明温度漂移可能影响数据。

Use a resistance box in series to limit current precisely.
Measure the length of the wire between the knife-edge contacts, not including the ends that are clamped.
Take more readings, e.g., every 0.05 m, to increase the reliability of the gradient.

In the January 2019 mark scheme, credit was given for explaining that the micrometer should be checked for zero error before use, and that the wire should be taut but not stretched because stretching changes its area and resistivity.

在2019年1月评分标准中，解释千分尺使用前应检查零点误差，以及金属丝应拉紧但不要拉伸（因为拉伸会改变其截面积和电阻率），属于得分点。

9. Worked Example: January 2019 Style Question | 实例演练：2019年1月题型

Let’s work through a typical Unit 3 question. A student measures the diameter of a wire of length 1.00 m using a micrometer, obtaining the following data: d₁ = 0.38 mm, d₂ = 0.37 mm, d₃ = 0.39 mm. The student then measures R for lengths L = 0.10 m, 0.20 m, 0.30 m, 0.40 m, 0.50 m, 0.60 m, obtaining R values that when plotted give a gradient of 1.67 Ω/m.

让我们解答一道典型的单元3题目。学生用千分尺测量一根长为1.00 m的金属丝直径，得到以下数据：d₁=0.38 mm, d₂=0.37 mm, d₃=0.39 mm。随后测量长度L=0.10 m、0.20 m、0.30 m、0.40 m、0.50 m、0.60 m的电阻，作图得到斜率为1.67 Ω/m。

Step 1: Calculate the mean diameter. (0.38 + 0.37 + 0.39)/3 = 0.38 mm. Step 2: Convert to metres: 0.38 mm = 3.8 × 10⁻⁴ m. Step 3: Calculate the area: A = π(3.8 × 10⁻⁴)²/4 = 1.134 × 10⁻⁷ m². Step 4: Use the gradient: ρ = 1.67 × 1.134 × 10⁻⁷ = 1.89 × 10⁻⁷ Ω·m.

第一步：计算平均直径。(0.38+0.37+0.39)/3=0.38 mm。第二步：换算为米：0.38 mm = 3.8 × 10⁻⁴ m。第三步：计算面积：A=π(3.8 × 10⁻⁴)²/4=1.134 × 10⁻⁷ m²。第四步：利用斜率：ρ=1.67 × 1.134 × 10⁻⁷=1.89 × 10⁻⁷ Ω·m。

Step 5: Determine the percentage uncertainty in the diameter. The range is 0.39 − 0.37 = 0.02 mm, so half-range = 0.01 mm. Percentage uncertainty = (0.01/0.38) × 100% = 2.6%.

第五步：计算直径的百分比不确定度。极差为0.39−0.37=0.02 mm，半极差=0.01 mm。百分比不确定度=(0.01/0.38) × 100% = 2.6%。

Step 6: Estimate the absolute uncertainty in ρ. If the percentage uncertainty in the gradient is 3%, then total % uncertainty = 3% + 2 × 2.6% = 8.2%. Absolute uncertainty = 0.082 × 1.89 × 10⁻⁷ = 1.6 × 10⁻⁸ Ω·m. Final answer: ρ = (1.89 ± 0.16) × 10⁻⁷ Ω·m.

第六步：估算ρ的绝对不确定度。若斜率的百分比不确定度为3%，则总百分比不确定度=3% + 2 × 2.6% = 8.2%。绝对不确定度=0.082 × 1.89 × 10⁻⁷ = 1.6 × 10⁻⁸ Ω·m。最终结果：ρ=(1.89 ± 0.16) × 10⁻⁷ Ω·m。

10. Common Exam Questions and Mark Scheme Points | 常见考题与得分点

Exam questions in Unit 3 often begin with “State the independent and dependent variables” (2 marks), followed by “Calculate the cross-sectional area” (2 marks), then “Plot a graph” (4 marks), and finally “Evaluate the accuracy” (3 marks). Knowing which marks are available helps you structure your answers.

单元3的考题通常以“陈述自变量和因变量”（2分）开始，接着是“计算横截面积”（2分），然后“绘图”（4分），最后“评估准确性”（3分）。了解哪些分数可用有助于你组织答案。

For “State one control variable”, do not write “the wire”; be specific: “the material of the wire” or “temperature”.
For “Explain why the current should be kept small”, refer to reducing heating to keep resistivity constant.
For “How would you improve the accuracy of the diameter measurement?”, mention using a digital micrometer with higher resolution or measuring at multiple points.

In the January 2019 paper, one question showed a table of V and I values and asked for R. A mark was awarded for correctly substituting and another for the unit. A further mark was given for repeating readings and calculating a mean, so always write “to reduce random errors” when explaining repetition.

在2019年1月的试卷中，一题给出了V和I的值表并要求计算R。正确代入数值得1分，正确写单位得1分（即1欧姆）。另有一分给“重复读数并求平均值”（以减少随机误差）。解释重复测量原因时，务必写出“以减小随机误差”。

11. Linking Practical Work to Theory | 将实验与理论联系起来

The resistivity ρ is an intrinsic property of a material, independent of its shape or size. The resistance R depends on the geometry via R = ρL/A. Therefore, a long thin wire has a higher resistance than a short thick wire of the same material. This idea is tested both in multiple-choice questions and in data analysis questions.

电阻率ρ是材料的内在属性，与形状或尺寸无关。电阻R通过R=ρL/A依赖几何形状。因此，同一材料的长而细的金属丝比短而粗的金属丝电阻更大。这一概念在选择题和数据分析题中都会被考查。

In the January 2019 paper, you were also asked to describe how the resistance of a wire changes when it is stretched. When a wire is stretched to double its length, its cross-sectional area halves (assuming constant volume). Thus the resistance increases by a factor of four. State this explicitly: R ∝ L² when volume is conserved.

在2019年1月试卷中，你还会被要求描述金属丝被拉伸时电阻如何变化。当金属丝被拉伸至两倍长度时，其横截面积减半（假设体积恒定）。因此电阻变为原来的四倍。明确写出：体积恒定时R ∝ L²。

If volume V = AL is constant, then A = V/L, so R = ρL/A = ρL²/V

12. Final Revision Checklist for Unit 3 | 单元3最终复习清单

Before entering the exam, make sure you can perform each of the following tasks without looking at your notes. This checklist is designed to cover every skill that appeared in the January 2019 paper and is likely to reappear in future sessions.

走进考场前，请确保你能在不看笔记的情况下完成以下每项任务。这份清单覆盖了2019年1月试卷中出现并很可能再次出现的每项技能。

Draw the circuit diagram for measuring resistance using the voltmeter-ammeter method.
State the formula for resistivity and rearrange it to find any unknown quantity.
Use a micrometer to measure a small length such as a wire diameter.
Convert mm² to m² correctly using powers of ten.
Plot a graph of R against L, draw a line of best fit, and calculate the gradient from a large triangle.
Use the gradient to calculate ρ and express the result with the correct unit (Ω·m).
Calculate percentage uncertainty and combine uncertainties in multiplication/division.

Practise with the actual January 2019 past paper under timed conditions. After marking, highlight the sections where you lost marks and revisit the corresponding topic in this article. Repeating this process for other past papers will significantly boost your confidence and your grade.

请在限时条件下练习2019年1月的真题。批改后，标出失分部分并重新阅读本文对应章节。多次重复这一过程将显著提升你的信心和成绩。

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AQA AS Physics Unit 3: Practical Skills & Data Analysis from the January 2019 Paper | AQA AS物理单元3：2019年1月考卷中的实验技能与数据分析