AS Physics Electricity Experimental Investigation | AS 物理电学实验探究

📚 AS Physics Electricity Experimental Investigation | AS 物理电学实验探究

Electricity is at the heart of modern physics, and the ability to design, carry out, and analyse electrical experiments is a core skill in the Oxford AQA International AS Physics course. This article provides a structured walk-through of the key experimental techniques, circuit arrangements, and data analysis methods that you will need to master for your topic test. We will explore the investigation of Ohm’s law, resistivity, internal resistance of a cell, and potential divider behaviour, always emphasising the link between practical choices and the underlying theory.

电学是现代物理学的核心，而设计、实施和分析电学实验的能力是牛津 AQA 国际 AS 物理课程的关键技能。本文系统梳理了你需要在主题测试中掌握的重要实验技术、电路连接方式和数据分析方法。我们将深入探究欧姆定律、电阻率、电源内阻以及分压器特性等实验，始终强调实际操作选择与基础理论之间的紧密联系。

1. Building a Circuit and Selecting Meters | 搭建电路与选择电表

When constructing a circuit for an electrical investigation, it is essential to consider the correct placement of ammeters and voltmeters. An ammeter must always be connected in series with the component whose current you wish to measure, so that the same current passes through both. A voltmeter must be connected in parallel across the component to measure the potential difference between its two terminals. Using digital multimeters reduces the systematic error caused by the finite resistance of analogue meters, but you should still be aware that a real voltmeter has a very high (but not infinite) resistance, and a real ammeter has a very low (but not zero) resistance.

在搭建电路开展电学探究时，必须考虑电流表和电压表的正确接法。电流表必须与被测元件串联，以便同一电流流过两者。电压表必须并联在元件两端，以测量其两个接线端之间的电势差。使用数字万用表可以减小由模拟表计有限内阻引起的系统误差，但你仍需注意，真实的电压表内阻极高（但并非无穷大），而真实的电流表内阻极低（但并非零）。

2. Investigating Ohm’s Law and I–V Characteristics | 探究欧姆定律与伏安特性曲线

Ohm’s law states that, for an ohmic conductor at constant temperature, the current I through it is directly proportional to the potential difference V across it, giving the relation V = IR. To test this, you can set up a simple circuit with a fixed resistor, a variable power supply, an ammeter in series, and a voltmeter in parallel. By varying the supply voltage and recording pairs of V and I, you can plot an I–V graph. A straight line through the origin confirms ohmic behaviour, and the gradient of the V–I graph (or the reciprocal of the I–V gradient) gives the resistance R.

欧姆定律指出，对于温度恒定的欧姆导体，通过它的电流 I 与两端电势差 V 成正比，关系为 V = IR。为了验证这一定律，你可以搭建一个简单电路：包括一个固定电阻、一个可调电源、串联的电流表和并联的电压表。通过改变电源电压并记录 V 和 I 的数值对，可以描绘 I–V 图像。一条过原点的直线即证实了欧姆特性，而 V–I 图线的斜率（或 I–V 图线斜率的倒数）给出电阻 R。

3. Non-Ohmic Devices: Filament Lamp and Diode | 非欧姆器件：灯丝灯泡和二极管

Not all components obey Ohm’s law. A filament lamp has a tungsten wire whose resistance increases with temperature. As the current increases, the filament heats up, causing the I–V graph to curve and flatten at higher voltages. A semiconductor diode, on the other hand, allows current to flow easily in one direction (forward bias) but almost blocks it in the reverse direction. The forward I–V characteristic shows a sharp rise after a threshold voltage (about 0.6 V for silicon), while the reverse characteristic is almost horizontal at zero current until breakdown. In your topic test, you may be asked to describe these curves or to suggest a circuit that can safely measure them, often including a protective resistor to limit current.

并非所有元件都遵循欧姆定律。灯丝灯泡的钨丝电阻随温度升高而增大。随着电流增加，灯丝发热，使 I–V 图像在较高电压处弯曲并趋于平缓。半导体二极管则相反，它在一个方向（正向偏置）容易导电，而在反向几乎阻断电流。正向 I–V 特性显示在阈值电压（硅管约 0.6 V）后急剧上升，而反向特性在击穿前几乎是零电流的水平线。在主题测试中，你可能需要描述这些曲线，或提出能安全测量它们的电路，通常包含一个限流保护电阻。

4. Measuring Resistivity of a Metal Wire | 测量金属丝的电阻率

The resistivity ρ of a material is defined by R = ρL / A, where R is resistance, L is length, and A is cross-sectional area. To determine ρ for a metal wire, you can measure R for several different lengths of the same wire, keeping the cross-sectional area constant. Use a metre rule to measure L and a micrometer screw gauge to measure the diameter d at several points, then calculate A = πd²/4. Plot a graph of R (on the y‑axis) against L (on the x‑axis). The gradient is ρ / A, so ρ = gradient × A. This experiment requires careful zero‑error correction of the micrometer and good electrical contacts to avoid fluctuating readings.

材料的电阻率 ρ 由 R = ρL / A 定义，其中 R 为电阻，L 为长度，A 为截面积。要测定金属丝的电阻率，你可以测量同一根导线在不同长度下的 R，并保持截面积不变。用米尺测量 L，用螺旋测微计在多个位置测量直径 d，然后计算 A = πd²/4。描绘 R（纵轴）对 L（横轴）的图像，其斜率为 ρ / A，故 ρ = 斜率 × A。该实验需要仔细校正螺旋测微计的零误差，并保证良好电接触以避免读数波动。

5. Investigating Series and Parallel Combinations | 探究串联与并联组合

When resistors are connected in series, the total resistance is the sum of the individual resistances: R_total = R₁ + R₂ + … . In parallel, the reciprocal of the total resistance equals the sum of reciprocals: 1/R_total = 1/R₁ + 1/R₂ + … . These rules can be verified experimentally by measuring the total resistance of a known combination using an ohmmeter or by applying a known p.d. and measuring the current. You must be able to explain these observations using the conservation of charge and energy: in series the current is the same through all components, while in parallel the p.d. is the same across each branch.

当电阻串联时，总电阻等于各个电阻之和：R_总 = R₁ + R₂ + … 。并联时，总电阻的倒数等于各电阻倒数之和：1/R_总 = 1/R₁ + 1/R₂ + … 。这些规律可以通过实验验证：用欧姆表直接测量已知组合的总电阻，或施加已知电压并测量电流。你必须能用电荷守恒和能量守恒解释这些现象：串联时通过所有元件的电流相同，并联时各支路两端电势差相同。

6. Determining the EMF and Internal Resistance of a Cell | 测定电源的电动势和内阻

A real cell can be modelled as a source of electromotive force (e.m.f.) ε in series with an internal resistance r. The terminal p.d. V across the cell is given by V = ε – Ir, where I is the current delivered by the cell. To find ε and r, you can use a variable load resistor, ammeter, and voltmeter. By recording V and I for a range of load resistances, you can plot a graph of V against I. This gives a straight line with intercept ε on the y‑axis and gradient –r. The experiment is most accurate if the current range is kept low enough to avoid significant heating of the internal resistance, which would change r.

真实电源可以等效为一个电动势 ε 与内阻 r 串联的模型。电源两端的路端电压 V = ε – Ir，其中 I 为电源输出的电流。要测定 ε 和 r，你可以使用一个可变负载电阻、电流表和电压表。通过记录不同负载电阻下的 V 和 I，可以描绘 V-I 图像。图像为一条直线，y 轴截距为 ε，斜率为 –r。为了获得更高的准确度，电流范围应保持较低，以免内阻显著发热而改变 r 的值。

7. The Potential Divider Circuit | 分压器电路

A potential divider typically consists of two resistors in series across a voltage source, allowing the output voltage V_out to be a fraction of the input voltage V_in. The unloaded output is V_out = V_in × (R₂ / (R₁ + R₂)). In an experimental investigation, you can replace one of the fixed resistors with a variable resistor, light‑dependent resistor (LDR), or thermistor to create a sensor circuit. You should be able to measure V_out with a voltmeter and show how it varies with resistance. Remember that connecting a load across the output effectively places its resistance in parallel with R₂, altering the output voltage unless the load resistance is much larger than R₂.

分压器通常由两个电阻串联在电压源两端构成，其输出电压 V_out 为输入电压 V_in 的一部分。空载时 V_out = V_in × (R₂ / (R₁ + R₂))。在实验探究中，你可以将其中一个固定电阻替换为可变电阻、光敏电阻（LDR）或热敏电阻，从而构建传感器电路。你应能使用电压表测量 V_out 并展示它随电阻的变化规律。请记住，在输出端接入负载实际上是将其电阻与 R₂ 并联，除非负载电阻远大于 R₂，否则会改变输出电压。

8. Using an LDR and Thermistor in Sensing Circuits | 在传感电路中使用 LDR 和热敏电阻

A light‑dependent resistor (LDR) has a resistance that decreases as the light intensity increases. A thermistor (negative temperature coefficient, NTC) has a resistance that decreases as the temperature rises. By placing these components in a potential divider, you can produce a voltage that changes with the physical quantity. For instance, with an LDR in the R₂ position, V_out falls when it gets darker. The practical investigation may involve calibrating the sensor by plotting resistance against light intensity using a light meter, or measuring resistance at different known temperatures using a water bath and thermometer.

光敏电阻（LDR）的阻值随光照强度增大而减小。负温度系数（NTC）热敏电阻的阻值随温度升高而减小。将这些元件接入分压器，即可产生一个随物理量变化的电压。例如，将 LDR 置于 R₂ 位置时，V_out 在变暗时下降。实际探究可能涉及用光度计描绘阻值-光照曲线，或利用水浴和温度计在不同已知温度下测量阻值，从而对传感器进行标定。

9. Accuracy, Precision and Systematic vs Random Errors | 准确度、精密度以及系统误差与随机误差

It is vital in any experimental report to distinguish between accuracy (how close a measured value is to the true value) and precision (the spread of repeated measurements). Systematic errors, such as a zero offset on a voltmeter or the internal resistance of a meter altering the circuit, affect all readings in a consistent way and cannot be reduced by averaging. Random errors, such as fluctuations in the power supply or human reaction time, cause scatter but can be reduced by taking many readings and averaging. In electricity experiments, always consider whether the voltmeter is drawing a small current or the ammeter is introducing a small voltage drop.

在任何实验报告中，区分准确度（测量值接近真值的程度）和精密度（多次测量结果的离散程度）都至关重要。系统误差，如电压表零位偏移或表计内阻改变电路，会以一致的方式影响所有读数，且无法通过取平均值来减小。随机误差，如电源波动或人体反应时间，引起数据分散，但可通过多次测量取平均值来减小。在电学实验中，要始终考虑电压表是否分流了一小部分电流，或电流表是否引入了微小的电压降。

10. Recording Data and Plotting Graphs | 记录数据与描绘图像

Good experimental practice requires recording raw data in clear tables with headings and units. When plotting graphs, choose scales that make the plotted points occupy at least half the graph paper in each direction. Label axes with the quantity and unit, and add error bars if uncertainties have been estimated. Draw the best‑fit straight line or smooth curve, ensuring it passes through as many error bars as possible. The gradient and intercepts should be determined using the largest possible triangle on the line, and their units must be derived correctly. In electricity investigations, transforming a non‑linear relation into a linear form (e.g. plotting V against I for internal resistance) is a powerful analysis technique.

良好的实验习惯要求将原始数据记录在清晰的表格中，标明表头和单位。描绘图像时，所选标度应使数据点在两个方向上至少占据方格纸的一半。坐标轴注明物理量和单位，如已估算不确定度则应添加误差棒。画出最佳拟合直线或平滑曲线，确保其经过尽可能多的误差棒。斜率和截距应使用线上尽可能大的三角形来确定，并正确推导其单位。在电学探究中，将非线性关系转化为线性形式（例如绘制 V-I 图像求内阻）是一种强有力的分析手段。

11. Uncertainty Calculations for Electrical Quantities | 电学量的不确定度计算

In an electrical experiment, you may need to combine uncertainties when calculating resistance from V and I. If R = V / I, the percentage uncertainty in R is the sum of the percentage uncertainties in V and I. For a quantity measured as a mean of several readings, the uncertainty can be expressed as ± half the range. When using a digital meter, the manufacturer’s specification often gives an uncertainty of ±(a percentage of reading + a number of least significant digits). You should be able to propagate errors through more complex formulas, such as ρ = (gradient × π d²)/4, by combining the percentage uncertainty in the gradient and that in the diameter (multiplied by 2 because d is squared).

在电学实验中，由 V 和 I 计算电阻时需要合成不确定度。若 R = V / I，则 R 的百分不确定度等于 V 和 I 百分不确定度之和。对于取多次读数平均值的量，不确定度可表示为 ± 极差的一半。使用数字表时，制造商通常给出 ±(读数的百分之几 + 几位最低有效数字) 的准确度指标。你应能通过更复杂的公式传播误差，例如 ρ = (斜率 × πd²)/4，需将斜率的百分不确定度与直径的百分不确定度（因 d 为平方关系，需乘以 2）进行合成。

12. Safety and Practical Precautions in Electricity Labs | 电学实验室的安全与实际注意事项

Even at the low voltages typically used in AS-level electricity experiments (often below 12 V), safety remains important. Avoid short circuits that can cause wires to overheat or damage components. Always check that the power supply is set to zero before switching on, and increase the voltage slowly while monitoring the ammeter. When investigating filament lamps or thermistors, be cautious of hot surfaces. Use insulated connecting leads with shrouded plugs and keep the workspace tidy. For measurements of resistivity, the wire under test can become warm, so take readings quickly and allow cooling time between measurements to maintain constant temperature conditions.

尽管 AS 电学实验通常使用低电压（常低于 12 V），安全依然重要。避免短路，因为短路可能导致导线过热或损坏元件。通电前务必检查电源电压是否归零，并在监测电流表的同时缓慢调高电压。探究灯丝灯泡或热敏电阻时，要小心高温表面。使用带护套插头的绝缘连接导线，并保持工作台整洁。在测量电阻率时，被测导线可能变热，因此应快速读数并在两次测量之间留出冷却时间，以维持恒温条件。

Published by TutorHao | AS Physics Revision Series | aleveler.com

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