📚 AS Level Physics Unit 2 Insert Jun19: Experimental Investigation | AS物理 Unit2 Jun19 插页：实验探究
The June 2019 AS Physics Unit 2 insert paper presents a practical investigation task that challenges students to design, measure, analyse and evaluate. This article uses a classic resistivity experiment—measuring the resistivity of a metal wire—as a model to demonstrate the key skills assessed in such an insert. We cover theory, apparatus, procedure, data handling, graphical analysis, uncertainty estimation and error discussion, providing a comprehensive revision guide for AS-level experimental physics.
2019年6月的AS物理Unit 2插页试题给出了一项实验探究任务，考查学生设计、测量、分析和评估的能力。本文以经典的电阻率实验——测量金属导线的电阻率——为例，展示此类插页试题所考核的关键技能。我们将涵盖理论、装置、步骤、数据处理、图像分析、不确定度估算和误差讨论，为AS阶段的物理实验提供一份全面的复习指南。
1. Understanding the Task | 理解任务
The insert typically provides a circuit diagram, a list of apparatus, and a set of instructions to determine a physical quantity—in this case, the resistivity of the material of a wire. The student is expected to plan the experiment, take precise measurements, record data, plot a suitable graph, and use the graph to calculate resistivity.
插页通常提供一个电路图、一份器材清单以及一组确定某个物理量——此处为导线材料的电阻率——的指令。学生需要规划实验、精确测量、记录数据、绘制合适的图像，并利用图像计算出电阻率。
2. Theory Behind the Experiment | 实验背后的理论
The resistance R of a uniform wire of length L and cross-sectional area A is given by R = ρL/A, where ρ is the resistivity. By rearranging, ρ = RA/L. For a wire with a circular cross-section of diameter d, A = πd2/4. Therefore, ρ = (Rπd2)/(4L). If we measure R for various lengths L while keeping d constant, a graph of R against L should be a straight line through the origin, with gradient = ρ/A. Hence, resistivity can be found from gradient × A.
均匀导线的电阻 R 与其长度 L 和横截面积 A 的关系为 R = ρL/A，其中 ρ 为电阻率。变形后得 ρ = RA/L。对于直径为 d 的圆形截面导线，A = πd2/4，因此 ρ = (Rπd2)/(4L)。如果在保持直径不变的情况下测量不同长度 L 对应的电阻 R，则 R 对 L 作图应是一条过原点的直线，其斜率等于 ρ/A。由此，电阻率 ρ = 斜率 × A。
R = ρ L / A
3. Apparatus and Setup | 设备与装置
The apparatus includes a constantan or nichrome wire (mounted on a metre ruler), a micrometer screw gauge, a digital multimeter or a voltmeter and ammeter, a power supply, a variable resistor (rheostat), connecting leads with crocodile clips, and a metre rule. The wire is attached along a metre ruler, and connections are made to measure voltage across and current through the wire. A variable resistor is used to control the current and avoid heating.
设备包括一根康铜或镍铬导线（固定在米尺上）、一个千分尺（螺旋测微器）、数字万用表或伏特计与安培计、电源、变阻器、带鳄鱼夹的导线和一把米尺。导线沿米尺固定，连接电路以测量导线两端的电压和通过的电流。变阻器用于控制电流，避免导线过热。
4. Procedure and Measurements | 步骤与测量
Use the micrometer to measure the diameter d of the wire at several points and calculate the mean diameter. Ensure the zero error of the micrometer is checked and corrected before taking readings.
用千分尺在导线不同位置测量直径 d，计算平均直径。测量前确保检查并修正千分尺的零误差。
Set up the circuit with the wire, ammeter in series, and voltmeter in parallel across the test length. Start with the longest length, e.g., 1.00 m. Adjust the rheostat to keep the current small (< 0.5 A) to minimise heating and resistance drift.
搭建电路，将待测导线与安培计串联，伏特计并联在测试段两端。从最长长度开始，例如1.00 m。调节变阻器使电流较小（小于0.5 A），以减少热效应和电阻漂移。
Record the current I and potential difference V. Calculate R = V/I. Repeat for different lengths (e.g., 0.90 m, 0.80 m, …, 0.20 m) by moving the crocodile clip. For each length, take several V and I readings and average them to reduce random uncertainty.
记录电流 I 和电势差 V，计算 R = V/I。通过移动鳄鱼夹改变测试长度（如0.90 m、0.80 m……至0.20 m），重复测量。每个长度下读取多组 V 和 I 值并取平均以减小随机不确定度。
5. Data Recording and Tables | 数据记录与表格
Organise the measurements in a table with columns: Length L / m, Voltage V / V, Current I / A, Resistance R / Ω. Include rows for each length, and note the diameter measurements separately. An example table is shown below.
将测量数据整理成表格，列应包括：长度 L / m、电压 V / V、电流 I / A、电阻 R / Ω。每种长度对应一行，直径测量单独记录。下面是一个示例表格。
| L / m | V / V | I / A | R / Ω |
|---|---|---|---|
| 1.000 | 2.82 | 0.20 | 14.1 |
| 0.900 | 2.54 | 0.20 | 12.7 |
| 0.800 | 2.26 | 0.20 | 11.3 |
| 0.700 | 1.98 | 0.20 | 9.90 |
| 0.600 | 1.70 | 0.20 | 8.50 |
| 0.500 | 1.42 | 0.20 | 7.10 |
Diameter readings (example): d = 0.30, 0.31, 0.30, 0.29 mm. Mean d = 0.30 mm = 3.0×10−4 m.
直径读数（示例）：d = 0.30, 0.31, 0.30, 0.29 mm。平均直径 d = 0.30 mm = 3.0×10−4 m。
6. Graphical Analysis: R vs. L | 图像分析：R 与 L 关系图Published by TutorHao | AS Physics Revision Series | aleveler.com
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