📚 Fair Test in A-Level Physics | A-Level物理中的公平测试
In A-level Physics, an experiment is a fair test when only the independent variable is deliberately changed, while all other variables that could affect the result are kept constant. The idea is central to AQA required practicals and exam questions on practical skills. Without a fair test, any observed change in the dependent variable might be caused by a hidden variable, so conclusions become unreliable.
在A-Level物理中，公平测试是指只刻意改变自变量，同时保持所有其他可能影响结果的变量不变。这一思想是AQA必修实验和实验技能考试题的核心。没有公平测试，因变量的任何变化都可能由隐藏变量引起，结论因此不可靠。
1. What is a Fair Test? | 什么是公平测试？
A fair test is an investigation in which one variable (the independent variable) is changed, one variable (the dependent variable) is measured, and all other relevant variables are controlled. In physics, this allows you to say that a change in the measured quantity is caused by the variable you changed, rather than by chance or poor design.
公平测试是一种探究方法，其中改变一个变量（自变量），测量一个变量（因变量），并控制所有其他相关变量。在物理中，这使你可以判断测量量的变化是由你改变的变量引起的，而不是偶然或设计缺陷导致的。
For example, if you investigate how the length of a wire affects its resistance, length is the independent variable and resistance is the dependent variable. Temperature, wire material and wire diameter must be controlled.
例如，如果你探究导线长度如何影响电阻，长度是自变量，电阻是因变量。温度、导线材料和导线直径必须保持控制。
2. Independent, Dependent and Control Variables | 自变量、因变量与控制变量
The independent variable is the quantity you deliberately change or select. The dependent variable is the quantity you measure for each value of the independent variable. Control variables are quantities that could affect the dependent variable but are kept constant.
自变量是你刻意改变或选取的量。因变量是你针对每个自变量值测量的量。控制变量是可能影响因变量但被保持恒定的量。
| Variable type | 变量类型 | Role | 作用 | A-level example | A-Level示例 |
| Independent | 自变量 | Changed deliberately | 刻意改变 | Wire length | 导线长度 |
| Dependent | 因变量 | Measured | 测量 | Resistance R | 电阻 R |
| Control | 控制变量 | Kept constant | 保持恒定 | Temperature, current, diameter | 温度、电流、直径 |
In a resistor length experiment, control variables include current through the wire, wire material, wire diameter, and room temperature. If current is too high, the wire heats up, changing resistance.
在电阻长度实验中，控制变量包括通过导线的电流、导线材料、导线直径和室温。如果电流过大，导线发热，电阻会改变。
3. Why Fair Testing Matters in Physics | 公平测试为何在物理中重要
Physics conclusions often take the form of a mathematical relationship, such as R ∝ L or T² ∝ L. A fair test is necessary to establish these relationships confidently. If a control variable drifts, the graph may still show a trend, but the gradient or intercept could be distorted.
物理结论通常表现为数学关系，例如 R ∝ L 或 T² ∝ L。公平测试对于可靠地建立这些关系是必要的。如果控制变量漂移，图像可能仍显示趋势，但斜率或截距可能被扭曲。
In required practicals, examiners often ask 'Explain one way the student made the test fair.' A good answer names a relevant control variable and states how it was kept constant.
在必修实验中，考官常问“解释学生使测试公平的一种方法”。好的答案会指出一个相关的控制变量并说明如何使其保持恒定。
4. Designing a Fair Test: Step-by-Step | 公平测试的设计步骤
First, identify the independent variable and decide a sensible range and interval. Second, choose a dependent variable that can be measured accurately. Third, list all variables that might affect the dependent variable and decide how to control each one. Fourth, plan repeats to reduce random error.
首先，确定自变量并决定合理的范围和间隔。第二，选择一个可以准确测量的因变量。第三，列出可能影响因变量的所有变量，并决定如何控制每一个。第四，计划重复实验以减少随机误差。
A risk assessment is also part of practical design, but a fair test specifically focuses on variables, not hazards.
风险评估也是实验设计的一部分，但公平测试专门关注变量，而不是危险。
5. Common Control Variables in Physics Experiments | 物理实验中常见的控制变量
In mechanics, common control variables include the mass of an object, the angle of a slope, the type of surface and the release height. In electricity, temperature, wire length, wire thickness and circuit current are often controlled. In waves, frequency, medium and boundary conditions may need to be controlled.
在力学中，常见的控制变量包括物体质量、斜面角度、表面类型和释放高度。在电学中，温度、导线长度、导线粗细和电路电流通常需要控制。在波动中，频率、介质和边界条件可能需要控制。
| Experiment | 实验 | Independent variable | 自变量 | Dependent variable | 因变量 | Key controls | 关键控制变量 |
| Pendulum | 单摆 | Length L | 摆长 L | Period T | 周期 T | Angle less than 10°, bob mass, air draughts | 角度小于10°、摆球质量、气流 |
| Wire resistance | 导线电阻 | Length L | 长度 L | Resistance R | 电阻 R | Current, temperature, diameter, material | 电流、温度、直径、材料 |
| Newton's second law | 牛顿第二定律 | Force F | 力 F | Acceleration a | 加速度 a | Total mass, friction compensation | 总质量、摩擦补偿 |
| Young modulus | 杨氏模量 | Force F | 力 F | Extension x | 伸长量 x | Original length, cross-sectional area, material | 原始长度、横截面积、材料 |
6. Random and Systematic Errors | 随机误差与系统误差
A fair test reduces systematic error because a systematic error would shift every reading by the same amount or same factor, but it does not guarantee accuracy. Random errors are reduced by repeats and averaging; systematic errors are reduced by good instrument calibration and careful technique.
公平测试可以减少系统误差，因为系统误差会使每个读数偏移相同量或相同比例，但它不能保证准确度。随机误差通过重复和取平均来减小；系统误差通过良好的仪器校准和仔细操作来减小。
For example, a zero error on a newton meter is a systematic error. It affects all force readings. Repeating the experiment does not remove a zero error; the instrument must be adjusted or readings corrected.
例如，牛顿计的零误差是系统误差。它影响所有力的读数。重复实验不能消除零误差；必须调整仪器或修正读数。
Random errors include timing by hand, small changes in release, or fluctuating air currents. Taking the mean of several measurements makes the result more reliable.
随机误差包括手动计时、释放时的微小变化或气流波动。取多次测量的平均值使结果更可靠。
7. Reliability, Precision and Accuracy | 可靠性、精密度与准确度
Reliability refers to consistency. If repeated readings are close together, the data are reliable. Precision refers to the smallest change an instrument can detect; a micrometer is more precise than a ruler. Accuracy refers to how close a measurement is to the true value.
可靠性指一致性。如果重复读数彼此接近，数据就是可靠的。精密度指仪器能检测到的最小变化；千分尺比直尺更精密。准确度指测量值与真实值的接近程度。
A fair test improves the validity of the conclusion, but an experiment can be reliable yet inaccurate if every reading carries the same systematic error.
公平测试提高了结论的有效性，但如果每个读数都带有相同的系统误差，实验可能可靠但不准确。
8. Fair Test Example: Pendulum Period | 公平测试示例：单摆周期
In a pendulum experiment to investigate T = 2π√L/g, the independent variable is pendulum length L and the dependent variable is period T. To make it a fair test, keep the angle of swing small (usually less than 10°) because the formula assumes simple harmonic motion. Keep the bob mass constant and avoid draughts.
在探究 T = 2π√L/g 的单摆实验中，自变量是摆长 L，因变量是周期 T。为了公平测试，保持摆动角度小（通常小于10°），因为公式假设简谐运动。保持摆球质量不变并避免气流。
T = 2π√L/g
Measure the time for 10 complete oscillations and divide by 10. This reduces the random error in the period compared with timing a single swing. Start and stop the stopwatch as the bob passes the lowest point, using a fiducial marker.
测量10次全振动的时间并除以10。与计时单次摆动相比，这减少了周期的随机误差。当摆球经过最低点时开始和停止秒表，并使用参考标记。
T² = (4π²/g)L
A graph of T² against L should be a straight line through the origin. If the amplitude is too large or air resistance is significant, the simple model breaks down and the test is no longer fair for investigating this equation.
T² 对 L 的图像应该是过原点的直线。如果振幅过大或空气阻力显著，简单模型失效，探究该方程的测试就不再公平。
9. Fair Test Example: Ohm's Law and Resistance | 公平测试示例：欧姆定律与电阻
To investigate Ohm' alculated. Temperature must be controlled because resistance of a metal wire increases with temperature.
为了探究欧姆定律，自变量是施加在电阻器两端的电势差 V，因变量是电流 I。计算电阻 R = V/I。温度必须控制，因为金属导线的电阻随温度升高而增大。
R = V / I
Fair test techniques include keeping the current low, switching the circuit off between readings, and using a water bath or allowing the wire to cool. Repeating each V-I pair and taking a mean
Published by TutorHao | A-Level Physics Revision Series | aleveler.com
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