AS Physics Unit 2 Past Paper: January 2019 Experimental Investigation | AS物理单元2：2019年1月真题实验探究

📚 AS Physics Unit 2 Past Paper: January 2019 Experimental Investigation | AS物理单元2：2019年1月真题实验探究

This article unpacks a classic AS Physics Unit 2 experimental task — determining the resistivity of a metal wire — based on the style and demands of the January 2019 past paper. We will examine the underlying theory, step-by-step methodology, data processing using graphical analysis, uncertainty evaluation, and how to avoid common exam pitfalls. Whether you are revising for a mock or the final assessment, this walkthrough will strengthen your practical skills and exam technique.

本文基于2019年1月AS物理单元2真题的实验探究风格，详细剖析一个经典实验任务——测定金属丝的电阻率。我们将讲解基本理论、逐步操作流程、利用图像分析处理数据、不确定度评估，以及如何避开常见考试陷阱。无论你是在准备模拟考还是最终评估，这篇解析都将提升你的实验技能和应试技巧。

1. Experimental Setup Overview | 实验装置概述

The experiment requires a circuit that can simultaneously measure the potential difference (p.d.) across a length of wire and the current flowing through it. A typical arrangement includes a power supply, a switch, an ammeter connected in series with the wire, and a voltmeter connected in parallel across the test length. A metre ruler is used to measure the length of wire between the crocodile clips, while a micrometer screw gauge measures the wire’s diameter at several points. By varying the length and recording the corresponding resistance, a graph can be plotted to determine resistivity.

本实验需要一个能同时测量一段金属丝两端电势差(p.d.)和流过电流的电路。典型装置包括电源、开关、与金属丝串联的电流表，以及并联在待测长度两端的电压表。用米尺测量鳄鱼夹之间金属丝的长度，用千分尺在多个位置测量金属丝直径。通过改变长度并记录对应的电阻值，可绘制图像来求出电阻率。

2. Theory: Resistivity and Ohm’s Law | 理论：电阻率与欧姆定律

Resistance R of a uniform wire is directly proportional to its length L and inversely proportional to its cross-sectional area A. This relationship is expressed as R = ρL / A, where ρ is the resistivity of the material. The cross-sectional area A is calculated from the diameter d using A = πd² / 4. Combining these gives ρ = (R × πd²) / (4L). In the investigation, R is obtained from V/I for each length, assuming ohmic behaviour at constant temperature.

均匀金属丝的电阻 R 与其长度 L 成正比，与横截面积 A 成反比。关系式为 R = ρL / A，其中 ρ 为材料的电阻率。横截面积 A 由直径 d 通过 A = πd² / 4 计算得出。联立得到 ρ = (R × πd²) / (4L)。在本探究中，假设恒温下金属丝满足欧姆定律，每条长度的 R 由 V/I 得到。

3. Equipment List | 器材清单

The following apparatus is typically required:

通常需要以下器材：

• A long constantan or nichrome wire mounted on a metre ruler — 一根固定在米尺上的长康铜丝或镍铬丝

• Micrometer screw gauge (resolution 0.01 mm) — 千分尺（分辨率0.01 mm）

• Digital ammeter (0–1 A) and digital voltmeter (0–5 V) — 数字电流表(0–1 A)和数字电压表(0–5 V)

• Low-voltage d.c. power supply or battery pack — 低压直流电源或电池组

• Switch and connecting leads with crocodile clips — 开关及带鳄鱼夹的导线

• Jockey or flying lead for precise length adjustment — 滑动触头或活动导线用于精确调节长度

4. Step-by-Step Procedure | 实验步骤

First, use the micrometer to measure the diameter of the wire at a minimum of five different positions along its length, recording each reading to 0.01 mm. Calculate the mean diameter and then the cross-sectional area.

首先，用千分尺在金属丝至少五个不同位置测量直径，每个读数记录到0.01 mm。计算平均直径，再求出横截面积。

Set up the circuit with the wire stretched along the ruler. Connect the crocodile clips exactly 1.000 m apart. Close the switch briefly, record the voltmeter reading V and ammeter reading I, then open the switch to prevent heating. Calculate R = V/I.

连接电路，将金属丝沿米尺拉直。将鳄鱼夹精确地夹在相距1.000 m处。短暂闭合开关，记录电压表读数V和电流表读数I，随即断开开关以防发热。计算R = V/I。

Reduce the length L in steps (e.g., 0.900 m, 0.800 m, …, 0.200 m), each time repeating the readings and calculating resistance. Aim for at least six different lengths. Avoid touching the wire when current flows.

逐步减小长度 L（例如0.900 m, 0.800 m, …, 0.200 m），每次重复读数并计算电阻。至少取六个不同长度。通电时避免触碰金属丝。

5. Data Collection and Recording | 数据收集与记录

A well-structured table is essential. Record L, V, I, and calculated R for each trial. Include columns for diameter measurements and the temperature of the wire (if monitored). An example layout:

结构清晰的表格至关重要。记录每次试验的 L, V, I 以及计算的 R。包含直径测量和金属丝温度（若监测）的栏目。示例表格：

L / m	V / V	I / A	R = V/I / Ω
1.000	2.14	0.42	5.10
0.800	1.90	0.46	4.13
0.600	1.62	0.51	3.18

Always maintain consistent significant figures based on instrument precision. The resistivity value will later be compared with the accepted value for the alloy used.

务必根据仪器精度保持一致的的有效数字位数。稍后可将电阻率值与所用合金的标准值进行比较。

6. Graphical Analysis | 图像分析

Plot a graph of resistance R (y-axis) against length L (x-axis). The relationship R = (ρ/A) × L indicates that the data should produce a straight line passing through the origin, with gradient m = ρ/A. Use a sharp pencil, label axes with units, and draw a best-fit line. If the line does not pass through the origin, it suggests a systematic error such as contact resistance.

绘制电阻 R（纵轴）对长度 L（横轴）的图像。关系式 R = (ρ/A) × L 表明数据应产生一条过原点的直线，其斜率 m = ρ/A。用削尖的铅笔画图，标注坐标轴及单位，并画出最佳拟合线。若直线不过原点，暗示存在接触电阻等系统误差。

To find the gradient, select two well-separated points on the best-fit line — do not use raw data points. Gradient = ΔR / ΔL. The gradient’s unit will be Ω m⁻¹.

计算斜率时，在最佳拟合线上选取两个相距较远的点——切勿使用原始数据点。斜率 = ΔR / ΔL，斜率单位为 Ω m⁻¹。

7. Calculating Resistivity from Gradient | 由梯度计算电阻率

Since gradient = ρ/A, resistivity ρ = gradient × A. Substitute the mean cross-sectional area A (in m²) to obtain ρ. For instance, if gradient = 5.02 Ω m⁻¹ and d = 0.315 mm, A = π(0.315×10⁻³)²/4 = 7.79×10⁻⁸ m². Then ρ = 5.02 × 7.79×10⁻⁸ = 3.91×10⁻⁷ Ω m.

由于斜率 = ρ/A，电阻率 ρ = 斜率 × A。代入平均横截面积 A（单位 m²）求出 ρ。例如，若斜率为5.02 Ω m⁻¹，直径 d = 0.315 mm，则 A = π(0.315×10⁻³)²/4 = 7.79×10⁻⁸ m²，那么 ρ = 5.02 × 7.79×10⁻⁸ = 3.91×10⁻⁷ Ω m。

Compare this value with the accepted resistivity for the wire material (e.g., constantan ~ 4.9×10⁻⁷ Ω m). A percentage difference can be calculated to evaluate accuracy.

将此值与金属丝材料的公认电阻率（如康铜约为4.9×10⁻⁷ Ω m）进行比较，可计算百分比差异以评估准确度。

8. Sources of Uncertainty and Percentage Error | 不确定度来源与百分比误差

The main uncertainties arise from the diameter measurement, length measurement, and the readings of V and I. The percentage uncertainty in cross-sectional area is twice the percentage uncertainty in diameter because area depends on d². For a micrometer of resolution 0.01 mm, the absolute uncertainty is ±0.005 mm. If the mean diameter d = 0.315 mm, %uncertainty in d = (0.005/0.315)×100% ≈ 1.6%, so %uncertainty in A ≈ 3.2%.

主要不确定度来源于直径测量、长度测量以及电压电流的读数。横截面积的不确定度百分比是直径不确定度百分比的两倍，因为面积与 d² 成正比。对于分辨率为0.01 mm的千分尺，绝对不确定度为±0.005 mm。若平均直径 d = 0.315 mm，直径的%不确定度 ≈ 1.6%，因此 A 的%不确定度 ≈ 3.2%。

The length measurement using a metre ruler has an absolute uncertainty of about ±1 mm. For a length of 0.800 m, this gives ~0.13%. The combined effect can be estimated by adding percentage uncertainties. Temperature rise due to current flow introduces further systematic error, as resistance increases with temperature.

用米尺测量长度，绝对不确定度约为±1 mm。对于0.800 m的长度，这约为0.13%。可将各百分比不确定度相加来估算总效应。电流导致温升会引入额外的系统误差，因为电阻随温度升高而增大。

9. Improvements and Modifications | 改进与修改

To reduce heating error, use a low current and keep the circuit switched on only while taking readings. A rheostat can be included to control current precisely, ensuring it remains constant across all lengths. Taking a larger number of diameter readings along the wire and at different orientations reduces random error in A. Using a travelling microscope instead of a metre ruler improves length precision. Investigating with a different wire material allows direct comparison of resistivity values.

为减少发热误差，应使用小电流，并仅在读取读数时接通电路。可串联变阻器精确控制电流，确保在所有长度下电流恒定。沿金属丝多方位、多次测量直径可减少面积 A 的随机误差。使用移测显微镜替代米尺可提高长度精度。用不同材料的金属丝进行实验，可以直接比较电阻率值。

10. Common Exam Pitfalls | 常见考试陷阱

Many students confuse resistance with resistivity. Resistivity is a material property independent of dimensions, while resistance depends on both material and geometry. Forgetting to convert units (e.g., mm² to m²) causes power-of-ten errors. Using raw data points to calculate gradient instead of points from the line of best fit is penalised. Misinterpreting the y-intercept as zero without justification also loses marks. Finally, always state that the wire must be at constant temperature for Ohm’s law to be valid.

许多学生混淆电阻与电阻率。电阻率是材料属性，与尺寸无关；电阻则同时取决于材料和几何形状。忘记单位换算（如 mm² 转 m²）会导致数量级错误。使用原始数据点而非最佳拟合线上的点来计算斜率会被扣分。未提供理由就宣称截距为零也会失分。最后，务必说明金属丝必须保持恒温，欧姆定律才成立。

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