📚 Dependent Variables in A-Level Physics | A-Level 物理中的因变量
In AQA A-level Physics, practical work is assessed through required practicals and written questions on experimental design. One of the most fundamental skills is identifying and handling the dependent variable correctly. This article explains what a dependent variable is, how to measure it, how to record it, how to plot it and how to analyse the uncertainty in it.
在 AQA A-level 物理中，实验技能通过必修实验和实验设计书面题进行考查。最基本的一项技能就是正确识别和处理因变量。本文解释什么是因变量、如何测量它、如何记录它、如何绘制它以及如何分析它的不确定度。
1. Definition of a Dependent Variable | 因变量的定义
The dependent variable is the physical quantity that you measure or observe during an experiment. Its value depends on changes made to another quantity, called the independent variable. In an experiment, you deliberately change the independent variable and record the resulting values of the dependent variable.
因变量是你在实验中测量或观察的物理量。它的数值取决于另一个物理量（称为自变量）的变化。在实验中，你有意改变自变量，并记录因变量的相应数值。
For example, when a student investigates how the current through a resistor changes with the potential difference across it, the potential difference is the independent variable and the current is the dependent variable.
例如，当学生研究通过电阻的电流如何随电阻两端的电势差变化时，电势差是自变量，电流是因变量。
2. Dependent vs Independent and Control Variables | 因变量、自变量与控制变量的区别
The independent variable is the quantity you change, the dependent variable is the quantity you measure, and control variables are all the other quantities that could affect the dependent variable if they changed. You must keep control variables constant so that the experiment is a fair test.
自变量是你改变的物理量，因变量是你测量的物理量，而控制变量是所有其他可能影响因变量的物理量。你必须保持控制变量不变，以使实验成为公平测试。
In an experiment to measure the acceleration of a trolley pulled by a falling mass, the force is the independent variable and the acceleration is the dependent variable. The mass of the trolley is a control variable because changing it would also change the acceleration.
在测量由下落重物拉动的小车加速度的实验中，力是自变量，加速度是因变量。小车的质量是控制变量，因为改变它也会改变加速度。
3. Identifying the Dependent Variable in Exam Questions | 在考试题中识别因变量
AQA exam questions often describe an experiment and ask you to state the dependent variable. Look for the quantity that the student measures after changing something else. Phrases such as 'measure', 'record', 'determine' or 'find the value of' usually point to the dependent variable.
AQA 考试题经常描述一个实验并让你说明因变量。寻找学生在改变其他条件后所测量的物理量。诸如 'measure'、'record'、'determine' 或 'find the value of' 等表述通常指向因变量。
For example, if the student changes the length of a wire and measures its resistance, the dependent variable is resistance. If the student changes the mass on a spring and measures the time period, the dependent variable is the time period.
例如，如果学生改变导线的长度并测量其电阻，因变量就是电阻。如果学生改变弹簧上的质量并测量周期，因变量就是周期。
In graphical questions, the dependent variable is conventionally plotted on the vertical y-axis, while the independent variable is plotted on the horizontal x-axis.
在图形题中，因变量通常绘制在竖直的 y 轴上，而自变量绘制在水平的 x 轴上。
4. Choosing How to Measure the Dependent Variable | 选择如何测量因变量
Choosing the correct instrument is essential for measuring the dependent variable with suitable resolution and accuracy. You should match the instrument to the size of the quantity and the precision required by the investigation.
选择合适的仪器对于以合适的分辨率和准确度测量因变量至关重要。你应该使仪器与量值的大小以及实验所需的精密度相匹配。
For example, to measure the extension of a spring in a Hooke's law experiment, a metre ruler with millimetre divisions may be sufficient. However, to measure the diameter of a wire in a resistivity experiment, a micrometer screw gauge is needed because the diameter is small and a small error in it causes a large error in the cross-sectional area.
例如，在胡克定律实验中测量弹簧伸长量时，毫米分度的米尺可能已经足够。但在电阻率实验中测量导线直径时，需要使用千分尺，因为直径很小，直径的微小误差会导致横截面积的较大误差。
Repeating measurements of the dependent variable reduces the effect of random errors and allows you to calculate a mean value. This is particularly important when the dependent variable fluctuates, such as the time for a pendulum to complete ten oscillations.
重复测量因变量可以减小随机误差的影响，并允许你计算平均值。当因变量存在波动时这一点尤其重要，例如单摆完成十次振动所需的时间。
5. Resolution, Precision and Accuracy of the Dependent Variable | 因变量的分辨率、精密度与准确度
Resolution is the smallest change in the quantity that an instrument can detect. For a metre ruler it is usually 1 mm, while for a digital ammeter it is the value of the last digit. The resolution directly limits the smallest change in the dependent variable that you can observe.
分辨率是仪器能够检测到的物理量的最小变化。对于米尺，分辨率通常为 1 mm；对于数字电流表，分辨率是最后一位数字的值。分辨率直接限制了你能够观察到的因变量的最小变化。
Precision describes how close repeated measurements of the dependent variable are to each other. Accuracy describes how close a measurement is to the true value. High precision does not guarantee high accuracy because a systematic error may make all readings repeatable but wrong.
精密度描述因变量的重复测量值彼此之间的接近程度。准确度描述测量值与真实值的接近程度。高精密度并不保证高准确度，因为系统误差可能使所有读数都重复但却是错误的。
6. Recording Dependent Variable Data in Tables | 在表格中记录因变量数据
When recording the dependent variable, use a table with clear headings that include both the quantity and its unit. The heading should be written as quantity/unit, for example current/A or extension/mm. This allows the values in the body of the table to be pure numbers.
记录因变量时，使用标题清晰的表格，标题应同时包含物理量及其单位。标题应写成“物理量/单位”的形式，例如 current/A 或 extension/mm。这样表格主体中的数值就是纯数字。
All raw readings of the dependent variable should be recorded to the same number of decimal places, matching the resolution of the instrument. If you repeat measurements,
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